MATH 1

Mathematics I

Module 1 Be Precise and Accurate! What this module is all about This module about measurement has multiple purposes. First, it orients you to twosystems of measurement, namely, the English system and the metric system. Second, itshows you how to convert one unit of measurement to another unit. Lastly, it helps youdetermine the appropriate measuring unit to use. You will study the following lessons in this module: Lesson 1 Measurement by estimation Lesson 2 Metric unit of length conversion Lesson 3 Short cut method of conversion Lesson 4 Metric unit of mass (weight) Lesson 5 Metric conversion of mass (weight) Lesson 6 Measurement of time What you are expected to learn After going through this module, you are expected to: • estimate the length of a given object; • use the appropriate instrument to measure the length, weight, volume, temperature, time and angle; • find an equal measure for a given metric measure; and, • change one unit to another unit of measurement. 1

How to learn from this moduleThis is your guide for the proper use of the module: 1. Read the items in the module carefully. 2. Follow the directions as you read the materials. 3. Answer all the questions that you encounter. As you go through the module, you will find help to answer these questions. Sometimes, the answers are found at the end of the module for immediate feedback. 4. To be successful in undertaking this module, you must be patient and industrious in doing the suggested tasks. 5. Take your time to study and learn. Happy learning! The following flowchart serves as your quick guide in using this module. Start Take the Pretest Check your paper and count your correct answers. Is your score Yes Scan the items you 80% or above? missed. No Proceed to the nextStudy this module module/STOP.Take the Posttest2

What to do before (Pretest)Before you use this module, take the following Pretest.Direction: Encircle the letter of your answer.1. Millimeter, liter and kilogram belong to this system of measurement.a. Metric c. Both a and bb. English d. Traditional2. Which of these measuring devices will you use to measure a book?a. ruler c. meter stickb. caliper d. tape measure3. How many decimeters are there in a dekameter?a. 10 c. 1 000b. 100 d. 10 0004. What is the approximate weight of a chicken egg?a. 17 mg c. 17 dagb. 17 g d. 17 kg5. What is the approximate length of an ordinary pencil?a. 20 hm c. 20 cmb. 20 dam d. 20 mm6. What is the basic unit of length in the metric system of measurement?a. kilometer c. literb. kilogram d. meter7. The net weight of a box of powdered milk is 985 grams. What is the equivalentweight in kilogram?a. 9.85 kg c. 0.985 kgb. 98.5 kg d. 0.0985 kg8. During a rebellion, the President gave the rebel soldiers 2 hours to go back totheir barracks. What is the equivalent of 2 hours in seconds?a. 360 seconds c. 720 secondsb. 600 seconds d. 7200 seconds9. What is the approximate length of one arm length?a. 50 mm c. 50 dm 3

b. 50 cm d. 50 m10. Which of the following weighs about 200 grams?a. apple c. watermelonc. jackfruit d. strawberry11. The distance between two cities is 5 000 meters. What is the distance betweenthe two cities in kilometer?a. 0.5 km c. 50 kmb. 5 km d. 500 km12. The length of an index finger is 2 inches. What is its length in centimeter?a. 2.5 cm c. 5.08 cmb. 4.8 cm d. 5.58 cm13. How many hours are there in one week?a. 120 hours c. 200 hoursb. 168 hours d. 218 hours14. A mother was advised by her doctor to take 100 mg of vitamin B supplementeveryday for three weeks. How much vitamin B does the mother need in all?a. 2.1 g c. 210 mgb. 21 g d. 21,000 mg15. How many books each 1.25 cm thick can be placed in a bookshelf that is 3meters long?a. 240 c. 270b. 250 d. 300 Answer Key on page 28 What you will do Read carefully the lessons that follow, answer the questions asked and then do theactivities patiently to enhance your understanding of measurement. 4

Lesson 1 Measurement by estimation There are different approaches you can employ in estimating the measurement of agiven object and one such technique is to compare the measurement of one object to themeasurement of another object. In this lesson you will employ different techniques ofestimating the measurement of a given object. You will also learn the disadvantage of notusing a standard unit of measurement. Did you know? The early Egyptians make use of body parts like the elbow for measuring length andarea. The distance from the elbow to the tip of the middle finger is called “cubit”. Theearliest known unit for weight was used by early Babylonians. It was known as “mina”. Otherbasic units used by early Greeks were finger for length, “Olympic cubit” for 24 fingers,“talent” for weight and “metrites” for volume (liquid measure). ExplorationActivity 1. Measuring Using Nonstandard Units • Using “Dangkal” (from the thumb to the point finger stretched) as the unit of measures find the following: a. length of your table b. width of your door c. height of your window • Use your elbow to measure the same objects. • Ask somebody to measure the same table using his/her finger and his/her elbow. • Using a ruler measure the same objects. • Tabulate the results you obtained in (1) and the measure obtained by your friend in (2). Summarize the results as follows: 5

Object measured Dangkal Elbow (From Ruler (Thumb and elbow toLength of table point finger finger tip)Width of the book stretched)Height of the window 1) 2) 1) 2) 1) 2)• Which type of measurement in the table shows different answers?______• Which measurement shows the same answer?_____________________• Which unit of measure would you choose to use? ___________________• Why?______________________________________________________Activity 2. Estimating I• Estimate the volume of rice your family consumes every meal.• Compare the amount of rice you cook every meal by using different containers like a small can of sardines, a small can of evaporated milk or a small bottle of soft drink.• Tabulate the result using the given table. Kind of container Number of scoopsCan of sardinesCan of evaporated milkBottle of soft drink• Approximately how many cans of sardines of rice does your family consume every meal? ____________________________• How many cans of evaporated milk of rice does your family consume every meal? _______________• What is the equivalent of your rice consumption using a bottle of soft drink? __________________• Which of the containers you used has the largest volume? _______• Which has the least volume? ___________• What kind of container does your family prefer for measuring rice? ______ 6

Activity 3 Estimating II• Estimate your capacity in drinking water for one meal.• Compare the amount of water you drink by using different containers of water like cup, glass of water or a bottle of 350 ml soft drink.• Tabulate the result using the table below. Kind of container Number of servingsCupGlass of waterBottle of 350 ml soft drink• Approximately how many cups of water do you drink every meal? ______• How many glasses of water do you drink every meal? ______________• What is the equivalent of the water you consumed using the 350 ml bottle of soft drink? ________________________• Which of the container has the smallest capacity? __________________• Which has the largest capacity? ________________• What is your preferred container for drinking water?Activity 4 • Based from the three activities, is there a need to standardize measurement? ______________ • Give your reason. _____________________________________________________Self-check 1A. Identify the measuring instrument you can use to measure the following:________1. Amount of water in a glass ________6. Length of time________2. The body temperature ________7. Fever temperature________3. weight of 12 pieces of mangoes ________8. weight of a bag of guavas________4. length of a pencil ________9. height of a boy________5. width of a cloth ________10. weight of a babyB. Solve the following problems. Encircle the letter corresponding to the best answer. 7

1. What is the approximate height of the one liter (1 L) bottle of coke?a. 5 cm b. 25 cm c. 50 cm d. 100 cm2. What is the approximate height of the door of your school?a. 2 m b. 4 m c. 8 m d. 10 m3. What is the approximate number of days a woman conceives a child?a. 9 days b. 90 days c. 200 days d. 270 days4. If a kilo of rice costs P22.00, how many grams of rice can be bought for P10.00?a. 300 g b. 500 g c. 700 g d. 900 g5. How many bottles of regular soft drink containing 235 ml can be poured into a familysize soft drink whose capacity is 1 L?a. 2 b. 4 c. 6 d. 8 Answer Key on page 28Lesson 2 Metric unit of length conversionDid you know? Nowadays the use of the metric system of measurement is recommended becausecomputations are easier in this system since it uses the power of 10. There are prefixesthat describe each power of 10. The table below shows some of the prefixes used in themetric system of measurement.Prefixes Symbol Value Power of 10 Milli m 0.001 or 1/1000 10-3 Centi 0.01 or 1/100 10-2 Deci C 0.1 or 1/10 10-1Basic unit d 1 100 Deka 10 101 Hecto m 100 102 Kilo da 1000 103 h k 8

The millimeter (mm), centimeter (cm) and decimeter (dm) are metric units used tomeasure short lengths. The meter (m) and kilometer (km) are metric units used to measure long length anddistances.ExplorationActivity 1 Comparison of units • The table above shows the values of various units in the metric system. What is the basic unit in the metric system?_______________________________ • Which is longer: a meter or kilometer?_____________________________ • Which is longer: a decimeter or hectometer?________________________ • Which is longer: a meter or centimeter?____________________________ • What is the equivalent of 3 meters in centimeter?____________________ Solution: Since there are 100 centimeters in a meter, then there are 300 centimeters in 3 meters.Activity 2 Conversion of units Steps in Conversion: 1. Identify the unit you are starting with. 2. Identify the unit you want to end with. 3. Find the conversion factor/s that will convert the starting unit to the ending unit. 4. Set up the mathematical expression so that all units except the unit you want to end with will be cancelled.Example 1.Convert 3 m to cm.Solution: 3 m x 100 cm = 300 cm 1m 9

Example 2.Convert 34 km to m.Solution: 34 km x 1000 m_ = 34 000 m 1 kmExample 3. Convert 850 mm to m. Solution: 850 mm x ___1 m____ = 0.85 m 1 000 mmExample 4 Convert 6800 cm to m. Solution: 6800 cm x _1m__ = 68 m. 100 cmDo you find it interesting?Example 5.Let’s try converting the following: 1. 4 500 cm = ______________dam 2. 85 200 m = ______________hm 3. 92 k = ______________dm 4. 6 000 mm = ______________km 5. 0.38 da = _______________m 10

Self-check 2A. Find the value of x that will make the equation correct.1. 8dm • 1 dam = .08 dam x2. 420 cm •__x __ = 4.2 m 100 cm3. 55 km • 10 hm = x 1 km4. 450 dm • ___x___ = 4,500 cm 1 dm5. 34 hm • ___x___ = 340,000 cm 1 hm6. 2.5 km • __100 dam_ = x 1km7. 86 dm • __x___ = 8,600 mm 1dm8. 3, 500 cm • __1 m__ = 35 m x9. 7,600 dam • __1km__ = 76 km x10. 34 km • ___x___ = 340,000 dm 1 kmB. Solve the following problems. Encircle the letter corresponding to the best answer.1. A peso bill is about 6.5 cm wide. What is the width of the bill in millimeter?a. 0.65 mm b. 6.5 mm c. 65 mm d. 650 mm2. The most common ceiling height of Filipino houses is 2.5 m. What is equivalent ofthis height in centimeters?a. 0.25 cm b. 25 cm c. 250 cm d. 2 500 cm 11

3. The distance between two street lamp posts is 25 m. What is the total distancebetween 5 lamp posts in dekameter?a. 1.25 dam b. 12.5 dam c. 125 dam d. 1 250 dam4. A transmitting power line is 35 m tall. What is the height of a cable which is placed4/5 of its height?a. 25m b. 28 m c. 30 m d. 25 m5. A carpenter wants to make a rectangular fence whose length is 5 m and whose widthis 2 m. How many meters of fencing wire will he need to enclose the whole area?a. 10 m b. 14 m c. 20 m d. 28 m Answer Key on page 28Lesson 3 Short cut method of conversion In Lesson 2, you have learned how to convert one metric unit to another metric unit. In this lesson, let’s take an easier way of converting one metric unit to another metric unit. Did you know? The metric system is the most widely used and accepted system ofmeasurement. The meter is the basic unit of length. The meter used to be defined as oneten-millionth of the distance from North Pole to the equator. Now, it is defined as thedistance traveled by light in a vacuum during a time interval of 1 of a second. 299792458 12

Activity 1 Use the following to convert the metric units. Milli Centi Deci Basi Unit Deka Hecto Kilo Did you know? Rules for Conversion From smaller unit to larger unit. Move the decimal point of the given number to be converted k places to the left, where the value of k is the number of arrows from the smaller unit to the larger unit in the diagram. From larger unit to smaller unit Move the decimal point of the given number to be converted k places to the right, where the value of k is the number of arrows from the larger unit to the smaller unit in the diagram. 13

Example 1. Convert 900 cm to dekameter. Solution: Since there are 3 arrows from centimeter to dekameter and the movement of decimal is from right to left because the conversion of unit is from smaller to larger unit, then move the decimal point 3 places to the left. Therefore, 900 cm = 0.9 dam.Example 2. Convert 3 450 dm to kilometer. Solution: There are 4 arrows from decimeter to kilometer and the movement is also from right to left since the conversion is from smaller unit to larger unit. Therefore, move the decimal point 4 places to the left. Thus, 3 450 dm = 0.345 km.Example 3. Convert 265 hm to centimeter. Solution: Since there are 4 arrows from cm to hm and the movement, this time, is from left to right because the unit being converted is from bigger unit to smaller unit, then move the decimal point 4 places to the right. Thus, 265 hm = 2 650 000 cm.Example 4 Convert 28 km to centimeter. Solution: Since there are 5 arrows from centimeter to kilometer and the movement is from left to right, therefore, 28 km = 2 800 000 cm. 14

Activity 2. • How many meters are there in 22 km?___________________________ • How many millimeters are there in 942 dm?_______________________ • How many dekameters are there in 5 890 km?_____________________ • How many hectometers are there in 3 200 cm?____________________ • How many meters are there in 840 cm?__________________________Self-check 3Using the shortcut method of conversion, convert the following:1. 8 256 m =__________km 6. 120 hm = _________ dm2. 25 000 mm = _______hm 7. 42 km = __________m3. 864 dm = __________dam 8. 8.16 m = ___________cm4. 3 450 000 cm = _____km 9. 0.012 dm = _________mm5. 317 000 cm = ______hm 10. 0.59 dam = __________dm Answer Key on page 28 15

Lesson 4 Metric conversion mass(weight) Mass and weight are very much related, but the two are not the same. The mass ofan object is the amount of matter it contains. The weight, on the other hand , is the pull ofgravity on the object. The mass of an object does not change but the weight of an objectchanges. The weight of an astronaut on Earth differs from his/her weight on the moon. In this lesson you will become familiar with the conversion of the unit of mass. Theshort cut method you have learned in lesson 3 can be used in converting one unit of massto another unit. Did you know? The gram is the unit of mass in the metric system. It is used to weigh light objects.The weight of an ordinary paper clip is about one gram. A kilogram is the weight of 1 liter of water in its densest state. The standard metric unit of mass is a cylinder made of a hard metal called platinum –iridium. It weighs one kilogram and is kept in France.Activity 1 • What things do you usually weigh?_____________________________________ • What do you use to measure your weight?_______________________________ • What units of weight are often used for weighing fruits and vegetables? _________________________________________________________________ • The following table shows the conversion of the different weight measure: 16

Table of weight measurement Unit of weight Equivalent weight 10 milligrams mg 1 centigram 10 centigrams cg 1 decigram 10 decigrams dg 1 gram 10 grams g 1 dekagram 10 dekagrams dag 1 hectogram 10 hectograms hg 1 kilogram (kg) • From the table, since 10 mg is equivalent to 1 cg and 10 cg is equivalent to 1 dg, therefore, 100 mg is equivalent to 1 dg. What is the equivalent of 1 g to mg?_____________________ • What is the equivalent of 1 kilogram in gram?_______________________ • What is the equivalent of 1 kilogram in milligram?____________________Activity 2 • Fill up the table below by converting one unit to the other. Metric unit 1 gram 1 dekagram 1 hectogram 1 kilogram milligram 1 000 mg 1 000 cg centigram 1g decigram 1 000 dg gram 1 000 g • The table shows that 1 000 mg equals 1 gram. What is the equivalent of 1 dag in centigram? __________________________ • What is the equivalent of 1 hectogram in decigram?____________ • What is the equivalent of 1 kg in gram?______________________ 17

Activity 3 • Construct another conversion table by filling up the table below:Metric unit 1 milligram 1 centigram 1 decigram 1 gramGram 1/1 000 gDekagram 1/1 000 dagHectogram 1/1 000 hgKilogram 1/1000 kg• The table shows that 1 mg equals 1/1 000 gram. What is the equivalent of 1 centigram in dekagram?_____________________• What is the equivalent of 1 dekagram in hectogram?____________• What is the equivalent of 1 gram in kilogram?_________________Activity 4 Let us convert any unit of metric weight to another unit of metric weightExample 1. Convert 350 g to kilogram. Solution: 350 g x __1 Kg__ = 0.35 kg 1 000 gExample 2. Convert 48 hg to centigram. Solution: 48 hg x 10 000 cg = 480 000 cg 1 hg 18

Self-check 4A. Convert the following to the indicated unit:1. 3 kg = _________ dg 6. 24 cg = ___________g2. 0.5 g = __________ mg 7. 18 mg = ___________hg3. 28.6 dag = ________g 8. 240 dg = ___________kg4. 400 hg = _________dag 9. 540 g = ___________dag5. 5 100 dg = ________mg 10. 28 000 cg = ________kgB. Solve the following problems. Encircle the letter corresponding to the best answer.1. If a meat costs P130.00 a kilo, how much will 500 grams of meat cost?a. P65.00 b. P100.00 c. P130.00 d. P2602. A box contains 12 cans of sardines. If each can weighs about 250 gram, what is thetotal weight of the box in kilogram?a. 2 kg b. 3 kg c. 4 kg d. 5 kg3. A bottle contains 90 vitamin C tablets. If each tablet contains 500 mg of vitamins,how many grams of vitamins are there in all?a. 4.5 g b. 45 g c. 450 g d. 4 500 g4. If a boat can accommodate 50 000 kg of goods in its storage, how many boxes of goods can be stored in the boat if each box weighs 20 kg? a. 25 boxes b. 250 boxes c. 2 500 boxes d. 25 000 boxes5. Luna sold fifty (50) kilograms of pork at P130 a kilo. How much did the pork cost inall?a. P1 300 b. P6 500 c. P13 000 d. P65 000 Answer Key on page 28 19

Lesson 5 Metric conversion of mass(weight) Capacity and volume are synonymous terms although they have different meanings.Volume is defined as the amount of space a region takes up while capacity is defined ashow much a certain container will hold. It follows that anything that can be poured ismeasured in capacity units. The lesson focuses only on the unit of capacity and itsconversion. Did you know? An average person must drink 8 to 10 glasses of water a day! A cubic centimeter (cm3) or one millimeter (ml) of water weighs one gram. A thousand cubic centimeters or one liter of water weighs one kilogram at 4 0C.Activity 1 Connecting to health • Do you know the capacity of your drinking glass or cup?_______________ • Get a clean empty bottle of 350 ml soft drink. Fill the 350 ml soft drink bottle with water from your drinking glass or cup. Which has a greater capacity, the 350 ml of soft drink bottle or your drinking glass?__________ • Approximately what is the capacity of your drinking glass or cup?_______ • Fill a liter of soft drink with water from your drinking glass. Approximately how many drinking cups of water did you pour into the liter of soft drink?__________________________________________________ • A glass contains 210 ml of water. How many glassfuls of water can be contained in a liter bottle? ____________________________ • Based from the above activities, how many liters of water must you drink every day?__________________________ 20

Activity 2 • Fill up the conversion table below: Metric unit 1 liter 1 dekaliter 1 Hectoliter 1 kiloliter Milliliter 1 000 ml Centiliter 100 cl Deciliter 10 dl 1l Liter• From the above table, the conversion of 1 000 milliliter equals 1 liter. What is the equivalent of 1 kilo in milliliter?________________• What is the equivalent of 1 hectoliter in centiliter?______________• What is the equivalent of 1 dekaliter in liter?___________________Activity 3 • Construct another conversion table by filling up the table below: Metric unit 1 milliliter 1 centiliter 1 deciliter 1 liter Liter 1/1 000 l Dekaliter 1/10 000 dal Hectoliter 1/100 000hl Kiloliter 1/1 000 000 kl • One milliliter equals 1/1 000 liter. What is the equivalent of 1 centiliter in liter? _______________________ • What is the equivalent of 1 centiliter in dekaliter? ______________ • What is the equivalent of 1 liter in kiloliter? ___________________ 21

Activity 4 Using the above conversion tables , you can convert any unit of capacity to anotherunit.Example 1 Convert 414 600 milliliter to dekaliter. Solution: 414 600 ml x __1 dal__ = 41.4 dal 10 000 mlExample 2. Convert 26 liter to centiliter? Solution: 26 l x 100 cl = 2 600 cl 1l Self-check 5 6. 4.3 dl = ___________hl 7. 35 dl = ___________lConvert the following: 8. 12 000 l = ___________kl1. 43 kl = __________ cl 9. 180 cl = ___________dal2. 3.9 dal = __________ dl 10. 35 000 ml = _________dl3. 34.08 hl = __________l4. 240 dl = ___________ml5. 5 600 l = ___________cl Answer Key on page 29 22

Lesson 6 Measurement of time This lesson will increase your awareness about the importance of time and willencourage you to spend your time properly.Did you know? Time is measured by the rotation of the earth on its axis which is equivalent to awhole day and the revolution of the earth around the sun which is equivalent to one year (365 ¼ days). Every four years, a day is added to account for the ¼ day in excess eachyear. Such year with 29 days in February is called a leap year.• Here is how Kenneth spends his time for the whole day.Schedule of Kenneth5:00 – 6:00 preparing for school6:00 – 3:00 attending class3:00 – 5:00 siesta5:00 – 7:00 doing his homework7:00 – 8:00 supper time8:00 – 5:00 bed time• How many hours does he attend his class? _____________________• Express the time he spends in school in minutes. ___________________• Express the time he spends in school in seconds.___________________ The table that follows shows the units used to measure time and their equivalences.Use this table to convert measurement of time to another. 23

60 seconds 1 minute60 minutes 1 hour24 hours 1 day12 months 1 year365 days 1 year366 days 1 leap year10 years 1 decade20 years 1 score100 years 1 century1 000 years 1 millennium• How many seconds are there in 1 day?Solution: 1day x 24 hours x 60 minutes x 60 seconds 1 day 1 hour 1 minute = 86 400 seconds.• How many hours are there in a year?Solution: 1 year x 365 days x 24 hours = 8 760 hours 1 year 1 day• How many decades are there in 3 centuries?___________________• How many decades are there in 2 millennium? __________________• How many days are there in a score? _________________________Self-check 6Convert the following:1. 420 days = ________h 6. 18 min. = __________hour2. 8 decades = _______ year 7. 60 hours= __________days3. 5 centuries= ______ decade 8. 12 years = __________hour4. 240 min. = _______ second 9. 180 seconds = _______min.5. 48 hours = _______second 10.4 800 hours = _______ day Answer Key on page 29 24

Let’s summarize• Measurement is the method of determining the length, quantity, weight, or amount of something by comparing an unknown quantity to a standard known quantity.• There are two standard system of measurements that we are using, the English system and the metric system• Prefixes used in metric systemPrefixes Symbol Value Power of 10 10-3milli m 0.001 or 1/1000 10-2 10-1centi c 0.01 or 1/100 100 101deci d 0.1 or 1/10 102 103meter m 1deka da 10hector h 100kilo k 1000Rules for short cut method of conversion.  From smaller unit to larger unit: Move the decimal point of the given number to be converted k places tothe left, where the value of k is the number of arrows from the smaller unit to thelarger unit in the diagram.  From larger unit to smaller unit: Move the decimal point of the given number to be converted k places tothe right, where the value of k is the number of arrows from the larger unit to thesmaller unit in the diagram. 25

What to do after ((Posttest)Direction: Encircle the letter of the best answer. 1. A bag of sugar weighs 35 kilograms. What is its weight in gram? a. 3.5 g b. 350 g c. 350 g d. 35,000 g 2. Which of the following devices will you use to measure a fabric? a. ruler b. measuring cup c. tape measure d. graduated cylinder 3. Which of the following is the longest time? a. 2 days b. 50 hours c. 3600minutes d. 180 000 seconds 4. A dress needs 2 meters of cloth. What is its equivalent in centimeter? a. 20 cm b. 200 cm c. 2 000 cm d. 20 000 cm 5. The normal room temperature is 270C. What is its equivalent in 0F? a. 480F b. 80.60F c. 800.60F d. 8060F 6. What is the basic unit of length in the metric system of measurement? a. liter b. meter c. centimeter d. kilogram 26

7. Two decades is equal to _____ years. a. 20 b. 200 c. 2,000 d. none of the above8. The basic unit of capacity is: a. liter b. meter c. gram d. Celsius9. The equivalent of 348 gram to centigram is:a. 3.48 cg c. 348 cgb. 34.8 cg d. 34 800 cg10. Rosario bought 1.3 kg of bangus fish while Katherine bought 1 200 grams ofgalunggong fish. Who of the two bought more?a. Rosario c. Both are equalb. Katherine d. none of them11. Kamille took one hour and 25 minutes to finish her test. How many minutes in all didshe spend for the quiz?a. 25 minutes c. 90 minutesb. 85 minutes d. 125 minutes12. Mayet prepared a chocolate mixture of about 2 000 g. If a chocolate bar she ispreparing contains about 50 cg, how many bars of chocolate can she prepare?a. 40 bars c. 4 000 barsb. 400 bars d. 40 000 bars13. Grace started to study at 6:00 in the evening. If she studied for 100 minutes, whendid she stop studying?a. 8:00 PM c. 10:00 PMb. 7:40 PM d. 11:00 PM14. The height of the flagpole is 5.25 m. What is the length of the flagpole in centimeter?a. 0.525 cm c. 525 cmb. 52.5 cm d. 5 250 cm15. It takes about 1 hour and 30 minutes to drive from Manila to Tagaytay. What is theapproximate time of arrival in Tagaytay if the driver leaves Manila at 7:30 AM?a. 8:00 am c. 9:00 AMb. 8:30 AM d. 9:30 AM Answer Key on page 29 27

Answer KeyPretest page 3 6. d 11 a1a 7d 12 b2a 8d 13 b3b 9b 14 b4a 10 a 15 a5cLesson 1 Self Check 1 page 7A 6. Clock B1 Graduated cylinnder 7 Thermometer 1B2 Thermometer 8 Weighing scale 2B3 Weighing scale 9 Meter stick 3D4 Ruler 10 Weighing scale 4B5 Tape measure 5BLesson 2 Self Check 2 page 10 BA 1C 2C1 x = 100 dm 6. x = 250 dam 3B 4B2 x=1m 7 x = 100 mm 5B3 x = 550 hm 8 x = 100 cm B4 x = 10 cm 9 x = 100 dam 1A 2B5 x = 10,000 cm 10 x = 10,000 dm 3A 4CLesson 3 Self Check 3 page 15 5B1 8.256 km 6. 120,000 dm2 0.25 hm 7 42 000 m3 8.64 dam 8 816 cm4 34.5 km 9 1.2 mm5 31.7 hm 10 59 dm Lesson 4 Self Check 4 page 19 6. 0.24 g 7 0.00018 hgA 8 0.02 kg 9 54 dag1 30,000 kg 10 0.28 kg2 500 mg3 286 g4 4,000 dag5 510,000 mg 28

Lesson 5 Self Check 5 page 221 4,300,000 cl 6. 0.0043 hl2 390 dl 7 3.5 l3 3 408 l 8 12 kl4 24 000 ml 9 0.18 dal5 560 000 cl 10 350 dlLesson 6 Self Check 6 page 241 10,080 hrs 6. 3/10 hr2 80 yrs 7 5/2 days3 50 decades 8 105 120 hrs4 14,400 sec 9 3 min5 172 800 sec 10 200 daysPost test page 26 6. b 11 b 7a 12 c1d 8a 13 b2c 9d 14 c3c 10 a 15 c4b5b 29

BIBLIOGRAPHYGrosnickle, F. E., Brueckner, L.. and Reckzeh, J. (1968). Discovering meanings in elementary school mathematics. (5th ed.) USA: Holt, Rinehart and Winston Inc.Mckeague, C. P. (1992). Basic mathematics. (3rd ed.) USA:Wadsworth Publishing Co.Thorton, C.A., Tucker, B. A., Dossey, J. A. and Bazik, E. F. (1983). Teaching mathematics to children with special needs. USA:Addison-Wesley Publishing Co. 30

Module 2 The Shorter the Better What this module is all about You have learned in Module1 the different systems of measurement and the variousinstruments used to measure length, weight, temperature, volume, time, and angle.Moreover, you have developed skills on how to convert one unit to another unit. This module discusses the concept of ratio and its application to measurement. It willdevelop your skills in rounding big numbers. Most importantly this module will provide youwith the techniques and the confidence to solve problems not only in measurement but in allareas of mathematics. This module has 3 lessons: Lesson 1 Ratio Lesson 2 Rounding off numbers Lesson 3 Solving problems involving measurements What you are expected to learn After going through this module, your are expected to: • Express relationships between two quantities using ratio. • Round off measurements to a given place value (e.g. nearest ten, nearest tenth, nearest hundred, etc.) • Solve problems involving measurements. 1

How to learn from this moduleThis is your guide for the proper use of the module: 1. Read the items in the module carefully. 2. Follow the directions as you read the materials. 3. Answer all the questions that you encounter. As you go through the module, you will find help to answer these questions. Sometimes, the answers are found at the end of the module for immediate feedback. 4. To be successful in undertaking this module, you must be patient and industrious in doing the suggested tasks. 5. Take your time to study and learn. Happy learning! The following flowchart serves as your quick guide in using this module. Start Take the Pretest Check your paper and count your correct answers. Is your score Yes Scan the items you 80% or above? missed. No Go to the nextStudy this module module/STOP.Take the Posttest 2

What to do beforeBefore you use this module, take the following Pretest.Multiple Choice. Choose the letter of the correct answer.. 1. The altitude of a right triangle is 30 centimeters and its shorter leg is 18 centimeters, What is the ratio of the altitude to its shorter leg? a. 6 : 7 c. 5 : 3 b. 3 : 5 d. 4 : 3 2. Jose took 18 days to finish his class project while Rony took 3 weeks to do the same task. What is the ratio of the length of time spent by Jose to the length of time spent by Rony to finish their respective project? a. 2 : 1 c. 6 : 7 b. 5 : 6 d. 7 : 8 3. The ratio of the sides of two squares is 4 : 5. If the sum of their areas is 180 cm2, what is the length of the side of the bigger square? a. 8 cm c. 10 cm b. 9 cm d. 12 cm 4. What is the ratio of 60 centimeters to 1 meter? a. 2 : 5 c. 5 : 2 b. 3 : 5 d. 5 : 3 5. What is 3 728 when rounded to the nearest thousand? a. 3 700 c. 4 000 b. 3 000 d. 3 720 6. What is 38.2752 rounded off to the nearest hundredths? a. 38.28 c. 37.27 b. 38.00 d. 37.28 7. Aling Nita went to the market and bought the following: 1 1 kilograms of meat for P165.00, 2 kilograms of onion for P65.00, 1 1 22 kilograms of dried fish for P25.00 and P1.50 for a glove of garlic. How much did Aling Nita spend? Round off your answer to the nearest centavo. a. P256.50 c. P250.70 b. P25.70 d. P25.00 3

8. At a bargain sale, 3 shirts sell for P250. Estimate the cost of each shirt.a. P83.33 c. P833.00b. P8.33 d. P833.339. Given the figure at the right, what is the ratio of the number of squares that are shaded to the number of unshaded squares?a. I : 4b. 1 : 3c. 2 : 5d. 2 : 710. A town map has a scale of 1 cm = 6500 m. If two streets are 7 cm apart on themap, what is their actual distance in kilometers? Round off your answer to thenearest tens.a. 40 km c. 50 kmb. 45.5 km d. 45 km11. The outside dimensions of a picture frame are 30 1 cm by 25 3 cm . If the wood 24used to make the frame is 11 cm in width, what are the dimensions of the frame? 2a. 33 1 cm by 28 3 cm c. 27 1 cm by 22 3 cm 24 24b. 29 cm by 24 1 cm d. 25 1 cm by 20 3 cm 4 2412. What is the weight of 152 pieces of peso coins in kilograms if a peso coin weighs15 grams?a. 5 kg c. 3 kgb. 4 kg d. 2 kg13. Four framed paintings are to be placed side by side with a 2.5 cm space betweenthem. If each frame has a width of 29.2 cm and a height of 58.5 cm, what is theapproximate area needed for display by the paintings in square meters?a. .78m2 c. .73m2b. .75m2 d. .67m214. A professor in a certain university earns P396 per hour of extra load. If the professor works 12 hours in a week for an extra load and 25% withholding tax is deducted from the gross pay, how much net monthly income does the professor expect for the extra load? (Assume that there are 4 weeks in a month and no recorded absences by the professor.) 4

a. PHP 18 640 c. PHP 12 948b. PHP 14 256 d. PHP 10 27815. The area of a rainforest in Burma is 120 446 square miles and that of Venezuelais 123 060 square miles. Approximately, how many square kilometers is theVenezuela rainforest larger than that of Burma?a. 6 767.3 sq km c. 8 167.3 sq kmb. 7 067.3 sq km d. 9 078.3 sq km Answer Key on page 20 What you will do Lesson 1 Ratio How do you compare two quantities? For example, let’s compare the sales of twonewspaper boys, Tom and Jerry. Tom sold 300 newspapers while Jerry sold 200newspapers. What is the ratio of the sales of the two boys? Did you know? Ratio, that is usually expressed as a fraction, expresses a relationship between twoquantities. There are two ways of using ratio:  Ratio is used as a comparison if the two quantities are of the same kind and with the same unit. The result of the comparison is a number without any unit.  Ratio is used as a rate if the two quantities are of different kinds. 5

To compare the sales of Tom and Jerry in the situation above, we divide the numberof newspapers Tom sold by the number of newspapers Jerry sold. Since 300 ÷ 200 = 3 or 21 1 , we say Tom sold 1 1 times as many newspapers as Jerry. We can also say that every 223 newspapers Tom sold, Jerry sold 2.Example 1Consider the following table about the lengths of the different parts of the body oftwo persons. Height Arm span Neck WaistMarie 1.5 m 68 cm 34 cm 30 inPeter 1.7 m 70 cm 40 cm 34 in The ratio of Marie’s arm span to Peter’s arm span is 68 cm : 70 cm or 34 : 35 insimplest form. This can be written as 34 in fraction. 35 How will you compare Peter’s waistline to Marie’s waistline? (a) __________ Whatis the ratio of the circumference of Marie’s neck to Peter’s arm span? (b) __________ Whatis the ratio of Peter’s waistline to his arm span? ( c ) _________ Suppose you are asked to find the ratio of Peter’s height to that of Marie’s, how willyou form the ratio? To form the ratio of 1.5 m to 1.7 m, write the ratio in the form of fractionwithout decimal point. Thus, 1.7m = 1.7 x 10 = 17 or 17 : 15. 1.5m 1.5 10 15 How about if you are asked to find the ratio of Marie’s arm span to her height, howwill you go about this? The length of Marie’s arm span is 68 cm while her height is 1.5 m.The units used are different. First change 1.5 m to cm thus, 1.5 m x 100cm = 150cm . 1mTherefore, the ratio of Marie’s arm span to her height is 68 cm to 150 cm or 68cm = 34 or34 : 75 What is the ratio of Peter’s arm span to his height? (d) _____________150cm 75 Based on the discussion above, how will you form the ratio of two quantities if theseare in decimal form? (e) _____________________________________________________When the two quantities you compare have different units, how will you form their ratio?(f) ______________________________________________________________________What is ratio? (g) _______________________________________________ Answer Key on page 20 6

Example 2 ............................... Look at the pie. Two parts of the pizza pie are shaded, while 6 parts of it arenot. Therefore, the ratio of the dotted parts to the unshaded ones is 2 or 1 . One- 63third means that there is one slice for every 3 slices of the pizza or 1 : 3. What is theratio of the unshaded part to the shaded part? (a) ________________________ Answer Key on page 20Example 3 10 cm 4 cm What is the ratio of the length to the width of this rectangle? The length of therectangle is 10 cm and the width is 4 cm. So, the ratio is 10 or 5 . This means that 42there are 5 units of length for every 2 units of width.Example 4 A 56 cm ribbon is to be cut into two pieces. The ratio of their lengths is 2 : 5.What is the length of each piece? In this case, you must add 2 and 5. What is their sum? (a)__________ 7

To find the length of the shorter piece, form a fraction whose numerator is 2 anddenominator is the sum of the 2 and 5. Thus, 2 or 2 . Multiply 2 by 56. What is 2+5 7 7the product? (b) __________The product obtained is the length of the shorter piece. What is its length?(c )__________What is the length of the longer piece? (d) ____________How will you check the correctness of your answer? (e) ____________ Answer Key on page 20 Self-check 1A. Give the ratio of the pair of quantities in each of the following statements.. 1. A horse runs a distance of 16 kilometers in 2 hours. 2. A car consumed 15 liters of gasoline in 3 hours. 3. An envelope is 8 3 inches long and 4 3 inches wide. 44B. Solve these problems. 1. The ratio of the three angles of a triangle is 1 : 3 : 5. What is the measure of the three angles? 2. The ratio of width of a rectangular lot to its length is 3 : 4. If the perimeter is 84 meters, what is its dimension? Answer Key on page 21 8

Lesson 2 Rounding Off Numbers Did you know? Writing very big or very small numbers can be difficult and may cause errors incomputation. It is for these reasons that we round off some numbers to make computationssimpler. Rounding numbers is an approximation technique, which replaces complicatednumbers with simpler ones. Numbers can be rounded to the nearest 10, 100, 1000 etc. To help you understand how to round off numbers, let us consider the followingexamples.Example 1 If you divide 9 by 52, what is its quotient? Did you get 0.1730769? (a) ___________ We can make this number simpler by rounding it off to a given place value. Forexample, if we round off this number to the nearest ten thousandths, then the answer is0.1731. We drop 769 and add 1 to zero because the first digit to be dropped in the threedigits is 7 which is greater than 5. How will you round off 0.1730769 to the nearest thousandths? Since the number tobe dropped is 07697 and 0 is the first digit of the five digits to be dropped, you will not add 1to 3 since 0 is less than 5. Thus, the answer is 0.173. How will you round off 0.1730769 to the nearest hundredths? (b) ________To the nearest tenths? (c) ______________ Answer Key on page 21 9

Example 2 Round off 654 to the nearest tens. 654 = 650 since 4 the digit to be dropped is less than 5. Add zero after five in placeof the unit place value. 654 = 700 to the nearest hundreds because the digits to dropped 54 is more thanhalf of 100. How will you round off 2500 to the nearest thousand? (a) ________________ Answer Key on page 21Example 3 A car travels at the rate of 110.25 kilometers per hour. What is its speed in metersper minute. Round off your answer to the nearest whole number. To solve this, convert km/hr to m/min, using the following converting factors. I km = 1000 m 1 hr = 60 minThus, 110.25km x 1000m x 1hr = 1837.5 or 1 837.5 m/min. hr 1km 60 min minRounding off the answer to nearest whole number is equal to 1 838 m/min.Rules in rounding off numbers: 1. Find the place value position being rounded to. 2. Look at the digit to the right of the number to be rounded off. 3. Round up or increase by 1 if the digit to the right is 5 or greater. 4. Retain the number if the digit to the right is less than 5. 10

Note: For whole numbers, replace the dropped digits by zero. For decimals, there is no replacement for the dropped digits.Self-check 21. Round off each measurement to the indicated place.0.5472 cm Nearest tenth Nearest hundredth Nearest thousandth31.2345 m Nearest ten Nearest hundred Nearest thousand2.3262 km 8465 ml 7546 g 8446 oz2. Riding on a bus, the student delegates traveled 385 kilometers in 5 hours and 45 minutes. To the nearest ten, estimate the average speed for the trip in km/hr.3. The thickness of a table is 0.6 m. If its volume is 1.53 m3, what is the length of the table if the width 1.2 m? Round off your answer to nearest tenth. Answer Key on page 21Lesson 3: Solving problems involving measurements Let’s take a look at how problems involving measurements are solved. 11

Did you know? Let us recall Polya’s four–step process in solving a problem. Below is the flow chart of the steps. Understand the problem Make a plan Carry out the plan Look backAside from Polya’s four-step process in solving problems, there are other methods that willhelp you solve many routine and nonroutine problems. They can be solved by makingtables, drawing diagrams and forming equations. ExplorationLet us consider the following examples.Example 1 The average diesel consumption of a jeepney driver for the whole day is 20 liters.How many liters of diesel did he consumed in 4 1 days. 2 You may solve this by making a table. 12

Number. of days 1 1.5 2 2.5 3 3.5 4 4.5Amount of diesel (in liters) 20 30 40 50 60 Analyze the table above. In one day the jeepney driver consumed 20 liters of diesel while in 1 1 days he 2consumed 30 liters. The number of liters consumed can be determined multiplying thenumber of days by the amount of diesel consumed in one day. That is, 1.5 days X 20 liters = 30 liters, consumed in 1 1 days 2 2 days X 20 liters = 40 liters, consumed in 2 days 2.5 days X 20 liters = 50 liters, for 2 1 days 2 3 days X 20 liters = 60 liters, for 3 days Using the same process, how many liters of diesel will the driver consume in 3.5days? ( a ) ___________ 4 days? ( b ) __________and 4.5 days? (c )_________ Based on the pattern, to find the amount of diesel in liters for a given number of daysyou multiply the number of days by the number of liters of diesel in one day. This isexpressed by the following equation: Amount of diesel in liters = number of liters per day X number of daysHence, 90 liters of diesel is consumed by the jeepney driver in 4 1 days. 2 Answer Key on page 21Example 2 It is recommended that a person should drink at least 8 glasses of water each day. Ifa glass contains about 180 ml, how many milliliters of water is consumed by a person in 5days?Consider the following table.Number of days 1 2 3 4 5Number of glasses per day 8 16 24 32 40Amount of water consumed (in ml ) 1 400 2 880 4 320 13

Look at the table and analyze how the values in the table were computed. To find the number of glasses of water each day, multiply the number of days by 8glasses. Thus, 1day X 8 glasses of water = 8 glasses of water, 2 days X 8 glasses of water = 16 glasses of water 3 days X 8 glasses of water = 24 glasses of water.The last two values are left for you to determine. To compute the amount of water consumed, you will multiply the number of glassesconsumed for the day by 180 ml. Thus, 8 glasses of water X 180 ml = 1 400 ml for 1 day, 16 glasses of water x 180 ml = 2 880 ml for 2 days and 24 glasses of water X 180 ml = 4 320 ml for 3 days. How many milliliters of water are consumed in 4 days? ( a ) ___________;In 5 days? ( b ) ____________ Answer Key on page 21Example 3 Peters house is 4 kilometers from Angel’s house, while that of Jimmy is 2.75kilometers from Angel’s house. It Jimmy is 1.25 kilometers away from SM Fairview, what isthe distance of Peter’s house if they are in the same direction? You can visualize this situation by making a diagram like the one below.Peter 4 km Angel 2.75 km Jimmy 1.75 km SM You are computing for the distance of Peter’s house from SM Fairview. That is givenby 4 km + 2.75 km + 1.75 km = 8 km.Therefore, the distance of Peter’s house from SM Fairview is 8 kilometers.Example 4 One sixth of the length of the ribbon was cut off. The length of the remaining ribbonwas 75 centimeters. What was the original length of the ribbon? To do this, first understand the problem by taking note of the facts: 14

Facts: 1 of the length of the ribbon was cut off. 6 75 cm was the length of the remaining ribbon. What is asked is the length of the ribbon before cutting.Working backwards, we do this: 75 cm is 5 of the original length of the ribbon 6 75 is 1 of the original length of the ribbon 56 The original length of the ribbon is: 75 + ( 75 ) = 75 cm + 15 cm 5 = 90 cm Looking back, 90 cm is the original length of the ribbon. The portion of the ribbonthat was cut off was 1 of 90 cm. Thus, the length of the remaining ribbon was 75 cm. 6 or 90 cm original length of ribbon - 15 cm 1 of 90 cm 6 75 cm, which is 5 of the original length 6Example 5 If you remove 8 kilos of mangoes from a basket and place 12 kilos of mangoes in itinstead, the basket contains 21 kilos of mangoes. How many kilos of mangoes are insidethe basket at the start? Enumerate the given data: 21 kilos = total kilos of mangoes in the basket - 12 kilos = additional kilos 9 kilos = kilos left after removing 12 kilos + 8 kilos 17 kilos = the number of kilos inside the basket Therefore, the number of kilos of mangoes inside the basket is 17. 15

Self-check 31. Fill in the blanks to make each sentence true a. 12 m x 7 m = ____________x 12 m = _____________b. 9 cm X _________cm = ___________x 9 cm = 225 cm2c. ( 9 in x 8 in ) x _______ = 9 in x (8 in x _____) = 432 in32. Dyndel sold 3 of her farmland. If she had 6 hectares after the sale, how 4 many hectares did she own originally?3. Fe pays P14 400 for a piece of land whose dimension is 12 m by 60 m. This is four-fifth of the price of the land. What is the price of the land?4. An 11 by 11 square are colored alternately red and white. If the corner unit square is red, how many red and white unit squares are there?5. Jimmy rode his bike 6 km east, 4 km west, and 5 km east. How far is he from his starting point?6. What combination of 1 centavo, 10 centavo, and 25 centavo coins has a total value of 99 centavos?7. Three cubic centimeters of water dropped from a faucet every 2 minutes. How many cubic centimeters of water dropped in 15 minutes? 45 minutes? Complete the table below.Number of minutes Number of cubic meters per minute= 3cm3 X number of minutes 15 2 min 45 90 3cm3 x15 min = ________________________ 120 2 min 16

8. Recall that to find the perimeter of a regular polygon, perimeter = length of sides X number of sides of a regular polygon. Complete the table below.Regular Length of Perimeter Round off topolygon side P = length X nearest number of sidesTtriangle 12.02 cm 3 x 12.02 = _____ tenth =Square 2.168 m Hundredth =Pentagon 8.3 dm Ten =Hexagon 9.001 ft Tenth = Answer Key on page 21Let’s summarize• Ratio is a comparison by division of two quantities of the same kind and with the same unit.• Quantities of different kinds are usually called rate instead of ratio.• Rounding numbers is an approximation technique which replaces complicated numbers with simpler ones.• Rules in rounding off numbers 1. Find the place value position being rounded to. 2. Look at the digit to the right of the number to be rounded off. 3. Round up or increase by 1 if the digit to the right is 5 or greater. 4. Retain the number if the digit to the right is less than 5 17

What to do afterTake the following Posttest.Multiple Choice. Choose the letter of the correct answer.. 1. The circumference of two circles are 8πcm and 14πcm respectively. What is the ratio of the circumference of the smaller circle to the larger circle? a. 4 : 5 c. 4 : 7 b. 4 : 6 d. 4 : 8 2. Glenn took 24 hours to finish his project while Romy took 1 1 days. What is the 2 ratio of the length of time spent by Glenn to the length of time spent by Romy to finish their respective project? a. 1 : 3 c. 2 : 1 b. 1 : 5 d. 2 : 3 3. The ratio of the sides of two squares is 2 : 5. What is the length of the side of the smaller square if their perimeter is 182 cm? a. 12 cm c. 14 cm b. 13 cm d. 15 cm 4. What is the ratio of 90 centimeters to 1.5 meters? a. 2 : 5 c. 4 : 5 b. 3 : 5 d. 5 : 6 5. What is 17 385 rounded to the nearest hundred? a. 17,100 c. 17,400 b. 17,300 d. 17,500 6. Which is equivalent to 24.8455 rounded to the nearest thousandth? a. 24.845 c. 24.855 b. 24.846 d. 24.856 7. Zeny bought 10 kilos of rice for P225.00, 1 kilo of beef for P165.00, 1 1 kilos of 2 bangus for P150.00 and 2 kilos of vegetables for P75.00. How much did Zeny spend? Round your answer to the nearest ten. a. P620 c. P595 b. P610 d. P590 8. At a bargain sale, 6 handkerchiefs sell for P200. Estimate the cost of each handkerchief. 18

a. P3.33 c. P333.33b. P33.33 d. P333.009. Given the figure at the right, what is the ratio of the number of squares that are shaded to the number of squares that are unshaded ?a. 8 : 25 c. 8 : 17b. 8 : 19 d. 8 : 1510. The distance from Manila to Dasmarinas is approximately 32.5 km. What is itsdistance in meters? Round off your answer to the nearest thousand.a. 32 000 m c. 34 000 mb. 33 000 m d. 35 000 m11. The length and width of a rectangle is 25 cm and 18 cm respectively. If the lengthand width are each reduced by 4 cm, what is the perimeter of the new rectangle?a. 60 cm c. 66cmb. 63 cm d. 70 cm12. A collection of one peso coin weighs 4290 grams and each coin weighs 15grams. How many one peso coins are there?a. 300 c. 290b. 296 d. 28613. How many hours did a professor render his service for one month if he earnedPhp 12,600 if his rate per hour is Php 350?a. 40 c. 24b. 36 d. 1814. Five holes are to be drilled along the centerline of a strip of wood so that thecenters are 4.25 cm. apart. The centers of the two end holes must be 5 cm fromthe end of the wood. How long must the wood be?a. 31.25cm c. 20 cmb. 28 cm d. 18 cm15. The land area of Columbia (S>A) is 439,769 square miles and that of Peru (S.A.)’is 496,260 square miles. How many square kilometers larger is Peru (S.A.)’s landarea compared to Columbia (S.A.)?a. 386,345.2 sq. km c. 200,435.2 sq. kmb. 240,424.2 sq. km d. 146,255.2 sq. km Answer Key on page 22 19