MATH 5

ON YOUR OWNMultiply. Express the answers in their lowest terms. Write your solutions andanswers in your notebook.1) 4 3 x 2 2) 7 1 x 4 73 453) 5 1 x 3 4) 5 x 2 2 27 955) 2 x 3 1 56 4

ONE-STEP WORDGPRRAODBE LVEMS INVOLVINGONE-STEP WOMRUDLTPRIPOLBICLEAMTISOINNOVOF LFVRIANCGTMIOUNLSTIPLICATION OF FRACTIONS Objective: Solve one-step word problems involving multiplication of fractions REVIEW Complete the train. Reduce each product to lowest terms if possible. Write your answers in your paper.1) 1x2 = x 4 = x7 = 5 23 13 =  x 11 =  x 3 = x 3 2 42) 45 22  x 4 =  x 1 = 1x 1 2 = 7 53 23) 1

STUDY AND LEARN 1 Everyday, Alvin spends 3 hours reading books. How 2many hours does he spend in a week reading books?Let’s follow the steps below.1. Read and understand the problem. Know what is asked for.The number of hours he spends reading in a week . Know what the given facts are. 1 hours  time spent in reading a day3 27 days  number of days in a week2. Plan  Make a plan that will help you solve the problem. 1 We need to multiply 3 hours by 7, since there are 7 days in a week. 2 1 Therefore, our number sentence is 3 x 7 = N. 23. Solve. 1 3 x7=N 2 1 7 7 49 1 32 x7= 2 x = or 24 1 2 2 1 Express 7 as Reduce toChange 3 fraction. lowest terms. 2to improperfraction. 2

4. Look back. Let’s check if our answer is correct. 1Since there are 7 days a week, one day is of a week. 7 11 1We can check our answer by solving of 24 . If the product is 3 , then our answer 72 2to the problem is correct.Let’s solve.1 1 1 49 49 7 1 x 24 = x = = 3 or 37 2 7 2 14 14 2We got the correct answer! 11So, 3 x 7 = 24 . 22 1Alvin reads 24 hours a week. 2Here’s another example. 11 If Alvin reads 24 hours a week, how many hours will he spend reading in 2 22weeks? Let’s solve together.1. Read and understand the problem.  What is asked? 1 The number of hours Alvin will spend in reading in 2 weeks. 2  What are the given facts? 1124 hours - time spent in reading in a week, 2 weeks 22 3

2. Plan  What process is needed to solve the problem? Multiplication  What is the number sentence? 11 24 x 2 = N 223. Solve. Since the factors are in mixed forms, change 11 them to improper24 x 2 = N fractions. 2249 5 245 1 x = or 6122 4 4 4. Look back. 1 Look at our answer. Does 61 make sense? 4 11In 2 weeks, Alvin will spend 61 hours reading. 24 TRY THESEA. Read the story problems then answer the questions that follow. 6 Anselmo spent of his time in the morning studying Math and Science. He spent 8 1 of this time studying Science. What fraction of the total time did he spend studying 4 Science? 1) What is asked in the problem? 4

2) What are the given facts? 3) What is the process involved? 4) What is the number sentence? 5) What is the answer?B. Read and solve each problem. 52 1) Rusell plays the piano hour a day. Her friend Ronell, plays as long. How long 93 does Ronell play each day? 3 2) Joanne signed up for 24 dancing lessons. She took of them in April. How many 4 dancing lessons did she take in April? WRAP UP In solving word problems, follow these steps: Step 1: Read and understand the problem. Step 2: Plan how you will solve the problem. Step 3: Solve. Step 4: Look back. 5

ON YOUR OWNRead and solve each problem. Write your solutions and answers in your notebook. 821) What is the area of a rectangle whose length is m and width is m? 10 3 332) Gigi bought 1 kg of sugar. She used of it to bake a cake. How much sugar did she 44 use? 43) Aling Aning planted vegetables on of her vacant lot. Two thirds of it was planted with 7 pechay. What fraction of the vacant lot had pechay? 134) Lorna had 2 liters of beef broth. She used of it to make soup. How much beef 25 broth did she use to make soup? 15) A recipe calls for 1 liters of milk. How many liters of milk do you need to make 2 3 recipes? 6

TWO-STEP WORD PROBLEMGRSAIDNEVVOLVING MULTIPLICATIONTWO-STEP WOARNDDPRAODBDLITEIMOSNIONFVOFRLAVCINTGIOMNUSLTIPLICATION AND ADDITION OF FRACTIONS Objective: Solve two-step word problems involving multiplication and addition or subtraction of fractions REVIEW A. Read the story problem. Answer the questions that follow. Romy drives at an average of 47 kilometres per hour. How far can he 4 travel in 1 hours? 5 1) What is asked in the problem? 2) What are the given facts? 3) What process is involved? 4) What is the number sentence? 5) What is the answer? B. Read and solve. 1) A worker receives 300 a day. How much will he receive for working in 2 2 days? 3 11 2) Manel bought 2 meters of cloth. She used of it to make a blouse. What 42 fraction of the cloth did she use? 1

STUDY AND LEARNMrs. Vale bought 2 chickens. One weighed 311 kg and the other one 2 kg. These were 45cut up and combined in one bag. She cooked2 of the chickens for lunch. What fraction of3all the chickens did she cook?Let’s follow the steps below to solve this problem.1) Understand  What are the given facts? 31 1 kg and 2 kg of chicken - the weight of each chicken Mrs. Vale bought. 45 2 of chickens - the fractional part of the chicken that she cooked. 3  What is asked? The fractional part of all the chicken that she cooked  What must be known first before we can solve for the final answer? The total weight of the two chickens2) Plan  What processes are involved in the problem? (addition and multiplication)  What should we do to solve the problem? 2 We should find first the total weight of the 2 chickens, and get of it. 3  What would be our number sentence? 231 3 x (1 4 + 2 5 ) = n 2

3) Solve and look back. 2 31 x (1 + 2 ) = n 3 45 311 and 2 are dissimilar fractions. Change them to similar fractions first before 45adding.2 15 4 x (1 + 2 ) = n3 20 202 19 Change the mixed forms to improper fractions. x3 Use cancellation whenever possible. Simplify the answer.3 2012 79 79 x=3 20 30 1079 19 =230 30 19Mrs. Vale cooked 2 kg of chickens. 30 19Look at our answer. Is 2 kg reasonable? 30TRY THESEA. Read the story problem. Answer the questions that follow. 4In a class of 45, are boys. How many are girls? 91. What processes are involved in the problem?a. addition and subtraction b. addition and multiplicationc. subtraction and multiplication d. multiplication and division2. What is the appropriate number sentence? 54 94a. ( 9 + 9 ) x 45 = n c. ( - ) x 45 = n 99 3

54 d. 9 x 4 ) – 45 = nb. ( - ) x 45 = n ( 99 99B. Solve the following word problems. Choose the letter of the correct answer. 511. Myrna has of a pizza. She ate of it. What part of the pizza was left? 63 45 a. b. 99 32 c. d. 99 522. The juice pitcher was full. Freddie drank of it. What part of the juice was 85 left? 53 a. b. 88 13 c. d. 44 323. Kimo planted vegetables in of his garden. of it is planted with eggplants. 53 What part of the vegetable garden is not planted with eggplants? 12 a. b. 55 34 c. d. 55WRAP UPIn solving a two-step word problem, remember these steps: Step 1: Read and understand the problem. Step 2: Know the given facts, what is asked and the hidden question. Step 3: Plan what you should do to solve the problem. Step 4: Solve and look back. 4

ON YOUR OWNRead and solve the word problems below. Write your solutions and answers in yournotebook. 31) Aika is taking a 50-item test in Math. of the test is about fractions and the rest is 5 about decimals. How many items are about decimals? 32) A jar contains 35 assorted cookies. If of the contents are chocolate cookies, how 7 many cookies are not chocolate? 53) A basket is full of santol and guavas. If of the fruits are santol and there are 81 9 fruits in all, how many of each kind are there? 334) Mang Daniel had 4 hectares of land. He used of it for planting mango trees and 45 the rest with santol trees. How much land was planted with santol trees? 915) Misty had m of yellow ribbon and m of green ribbon. If she used all the green 10 2 1 ribbon and of the yellow ribbon for her project, how many meters of ribbon was 3 used? 5

VISUALIZAGRTAIODENVOF RATIO VISUALIZATION OF RATIO Objective: Visualize the ratio of two given sets of objects REVIEWAnswer the following problems. 11. Tony needs 3 cans of paint for each room in his house. How many cans of paint 2 will be needed for 3 rooms? 312. Richard plays the piano of an hour a day. Belen, his sister, plays as long. How 42 long does Belen play each day? 23. Marielle signed up for 48 piano lessons. She took of them by September. How 3 many piano lessons did she take by September? 94. In water, sound travels approximately of a mile per second. How far will sound 10 1 travel in second? 2 1

STUDY AND LEARNLook at the picture below.We will write ratio. To do that, we will compare two quantities.We can see from the illustration that there are ___ rectangles and ___ circles. There are___ figures altogether.The ratio of rectangles to circles to 3 to 4The ratio of circles to triangles to4 to 3The ratio of rectangles to the total number of figuresto3 to 7 2

Let’s have another example.Example: There are ____ mangoes and ____ apples. Together, there are ____ fruits.What is the ratio of the following:a. apples to mangoesb. mangoes to applesc. apples to total number of fruitsd. mangoes to total number of fruitsThere are 6 apples to 10 mangoes or 6 to 10.There are 10 mangoes to 6 apples or 10 to 6.There are 6 apples to 16 fruits or 6 to 16.There are 10 mangoes to 16 fruits or 10 to 16. 3

TRY THESEWrite the ratios. 1. cats to birds 2. dogs to Guinea pigs 3. guinea pigs to total number of pets 4. dogs and cats to Guinea pigs WRAP UP What is ratio?  Ratio is a comparison of two quantities. 4

ON YOUR OWNWrite the following ratios. Write your answer in your notebook.1. a. blouses to skirts b. skirts to blouses c. blouses to total number of clothes d. skirts to total number of clothes2. a. baseball bats to balls b. balls to baseball bats c. baseball bats to total number of bats and balls d. balls to total number of bats and balls3.flowers to leaves = ___ to ___ 5

4. a. spatial figures to plane figures _______ _______ = _______ to _______ b. plane figures to spatial figures _______ _______ = _______ to _______ c. spatial figures to total number of geometric figures _______ _______ = _______ to _______ d. plane figures to total number of geometric figures _______ _______ = _______ to _______ 6

EXPREGSRSAINDEGVRATIO EXPRESSING RATIO Objective: Express the ratio of two numbers using the appropriate notation REVIEWWrite the ratio of the following:1. a. pencils to notebooks b. notebooks to pencils c. pencils to total numbers of things d. notebooks to total number of things2. a. eggs to baskets b. baskets to eggs c. eggs to total number of things d. baskets to total things 1

STUDY AND LEARN There are 7 boys and 8 girls playing volleyball. Questions: 1. What is the ratio of boys to girls? 2. What is the ratio of girls to players? 3. What is the ratio of boys to players? 4. How do we express ratio of 2 numbers?The ratio of boys to girls is 7 to 8.The ratio of girls to boys is 8 to 7.The ratio of girls to players is 8 to 15.The ratio of boys to players is 7 to 15.What are other ways of expressing the ratio of 2 numbers?Look at this: 7 7 to 8 can be expressed as 7:8 or 8 7 7 to 15 can be expressed as 7:15 or 15We can express ratio of 2 numbers using a fraction or the colon symbol __:__. 2

TRY THESEExpress the ratio of the following in two ways. Colon Fraction1. Noemi has 18 tiger’s small triangles and Gali has 15 big triangles. What is the ratio of Noemi’s triangles to Gali’s?2. Laura ran 2 kilometers in 25 minutes. What is the ratio of time to distance?3. On Monday, player A won 2 times in 4 chess games. On Tuesday, he won once in 3 tries. What is the ratio of total winnings to total chess games?4. Candies cost 2 for 3 pieces. What is the ratio of 3 pieces of candies to the total cost?5. Jumbo, my dog, had 9 puppies. Four were black and 5 were white. What is the ratio of white to black puppies? WRAP UPWe can express the ratio of two numbers as a fraction or using thenotation ___:___. 3

ON YOUR OWNWrite the ratio of the following. a.) using a colon b.) as a fraction. Write your answers inyour notebook. Colon Fraction1. In my mother’s flower garden, she has 15 varieties of roses and 16 varieties of orchids. What is the ratio of orchids to roses?2. In problem #1, what is the ratio of the variety of roses to all plants?3. Devini’s hobby is collecting stamps. She had collected 189 US stamps and 217 Philippine stamps. What is the ratio of US stamps to the total of stamps collected?4. There are 85 Math books and 65 Science books in the library. What is the ratio of Math books to Science books?5. In problem #5, what is the ratio of Science books to Math books? 4

RATIO IN ITGSRSAIDMEPVLEST FORM RATIO IN ITS SIMPLEST FORM Objective: Reduce a ratio to its simplest formREVIEWExpress the ration required a.) using a colon b.) using a fraction. Write the answers inyour notebook. COLON FRACTION1. Ellen has 2 chicken eggs and 3 quail eggs _______ _______ in a tray. What is the ratio of quail eggs to chicken eggs?2. There are 5 baskets of mangoes. Each _______ _______ basket contains 75 mangoes. What is the ratio of 5 baskets to the total number of mangoes?3. Kris bought 2 pairs of shoes and 5 pairs of _______ _______ socks. What is the ratio of shoes to socks?4. Rina planted 15 tomato seedlings and 20 _______ _______ pechay seedlings. What is the ratio of pechay seedlings to tomatoes seedlings?5. In problem number 4, what is the ratio of _______ _______ pechay seedlings to the total number of seedlings? 1

STUDY AND LEARN1. How many animals are there in the race? 11  How many are snails?  How many are turtles?  How many are lions?  How many are hens?2. What is the ratio of snails to turtles? 6:33. What is the ratio of turtles to other animals? 3:84. What is the ratio of turtles to snails? 3:6We can reduce ratios to lowest terms.Which item can be reduced to lowest terms? Think of reducing fractions to lowestterms when reducing ratios to lowest terms.  The ratio of the number of turtles to snails - 6:3 or 2:1  The ratio of the number of snails to turtles - 3:6 or 1:2How can we reduce ratios to lowest terms? 2

Think: In reducing a ratio to its lowest terms think of the greatest common divisor. Consider the ratio 6:3. The greatest common divisor for 6 and 3 is 3. 63=2 33=1 So, 6:3 = 2:1 If the ratio has no common divisor except 1, the given ratio is in its lowest term already. TRY THESEWrite the ratio in lowest terms. 1) 18 boys to 9 girls 2) 35 apples to 7 oranges 3) 3 monkeys to 21 bananas 4) 100 pupils to 10 teachers 5) 15 games to 5 lossesWRAP UP  In reducing a ratio to its lowest term, divide each of the numbers by greatest common divisor.  If the ratio has no common divisor except 1, there is no need to reduce the ratio to its lowest term. It is already in its simplest form. 3

ON YOUR OWNWrite the ratio in lowest terms. Write your answer in your notebook. 721) 32) 36:123) A shelf in a library has only Math and Science books. If there are 22 Math books and 31 Science books, write a ratio to compare the a. number of Math books to the number of Science books. b. number of Science books to the number of Math books.4) The ratio of boys to girls in an athletic team is 28 to 14. The lowest terms of 28 to 14 is _____.5) There are 9 mangoes and 5 chicos in a fruit basket. a. ratio of mangoes to chicos b. ratio of chicos to mangoes c. ratio of mangoes to fruits 4

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GRADE V PROPORTIONObjective: Form proportion from 2 ratios REVIEW 3) 9Reduce the following fractions to lowest terms. 18 8 15 5 16 18 1047 8910 21 14 27 STUDY AND LEARN Crissy uses 3 tablespoonfuls of baking powder to make 24 putos. What is theratio of the number of putos to the amount of baking powder used?The ratio of putos to baking powder is 24 to 3 or 24:3. 1

We can form another ratio from 24:3 by reducing this to its lowest terms.24:3 = 8:1How did we do this?We get the lowest term of the given ratio using the greatest common divisor todivide each the two numbers in the given ratio.24 ÷ 3 = 83 ÷ 3 124:3 = 8:1How do we check if the second ratio is proportional to the given ratio?There are two parts in a proportion: the means and the extremes.24 : 3=8: 1 means extremes“Means” refer to the inner terms in a proportion.“Extremes” refer to outer terms in a proportion.The two ratios are proportional if the product of the extremes is equal to theproduct of the means.Example 1: 24 : 3 = 8 : 1 24 3x8 24 24 x 1If the ratios are written in fractional form, we can also check if they areproportional. 2

24 8 =31To find if they are proportional, we can use cross multiplication.24 8 =31 24 x 1 = 24 3 x 8 = 24Let’s have another example.Example 2: There are 18 boys and 21 girls in a Grade V class. What is the ratio of boys togirls? Ratio Colon Form Fractional Form 18 to 21 18:21 18 21Lowest term of 18:2118 3 6 Therefore, 18:21 = 6:7 ÷= .21 3 7Checking:Ex.: 18 : 21 = 6 : 7 126 21 x 6 126 18 x 7 3

In fractional form: 18 6 = 21 7 Cross-multiply: 18 6 = 21 7 18 x 7 = 126 21 x 6 = 126 Another method to find proportional ratios is to produce ratio in higher terms: Let us find higher terms of 3:2. Simply multiply the two quantities by the same non-zero digit except one. Let us multiply 3:2 by 2:2 you’ll get 6:4. So 3:2 = 6:4. To check if they are proportional, let us apply the method of checking discussedearlier. Ex.: 3 : 2 = 6 : 4 12 2x6 12 4x3 Let’s study more! Example 3 : 7 x 3 : 3 = 9 : 21 so 3 : 7 = 9 : 21 Example 4 : 5 x 5 : 5 = 20 : 25 so 4 : 5 = 20 : 25 4

Let us check. 3 : 7 = 9 : 21 63 7x9 63 21 x 3Can you check the last one?TRY THESEForm a proportion by reducing the given ratio to its lowest term then check.1) 4:10 8) 24:302) 2:30 9) 6:213) 4:14 10) 8:124) 10:40 11) 5:155) 6:4 12) 9:306) 15:57) 3:24 5

WRAP UP A proportion can be formed a given ratio in two ways:  by finding its lowest terms  by finding its higher terms  check by multiplication The correctness can be checked as follows: If the product of the means is equal to the product of the extremes, the two ratios are proportional. ON YOUR OWNMultiply the given ratios by 3 to form a proportion. Check your work. Write youranswers in your notebook. 1) 8:10 2) 6:8 3) 15:5 4) 3:15 5) 3:4 6) 2:5 7) 7:9 6

RENAMING FRACTGIROANDSE IVN DECIMAL FORM RENAMING FRACTIONS IN DECIMAL FORMObjective: Rename in decimal form fractions whose denominators are powers of 10. REVIEW Write the following in standard form. 1) four and two tenths = ______ 2) seventy hundredths = ______ 3) five tenths = _____ 4) nine and two hundredths = _____ 5) three hundred eighty-one thousandths = _____ STUDY AND LEARN Dolor took a 100-item test in Math. She got 70 correct answers. Look at the illustration below. The big rectangle is divided into 100 equal parts. These represent the 100-item test taken by Dolor. The shaded parts represent the correct answers. 70 7The shaded parts are represented by the fraction: or in lowest terms. 100 10Notice that the denominators of the two fractions are both powers of ten.1

 Fractions with 10, 100, 1000 or other powers of 10 as denominators can be written as decimals. 7 = 0.7 10 7 = 0.07 100 115 = 0.115 1000 In changing fractions with denominators like 10,100 and 1000 or powers of ten, we consider the number of zeros in the denominators. The number of zeros in the denominator represents the number of decimal places. The number of decimal places and the number of zeros in the denominator must be equal. The decimal place is the number of digits right after the decimal point. For example in the decimal 0.7, there is one decimal place because there is only one digit after the decimal point. In 0.07, there are two digits after the decimal point or two decimal places. There are three decimal places in the decimal, 0.115. You’ll notice that to change fractions with powers of ten as denominator, we write the numerator, then count the zeros in the denominator or the decimal places. We affix zeros to complete the decimal places. Mixed numbers in which the fraction part has a power of 10 as denominator can be written as a mixed decimal. 2 Examples: 5 = 5.2 10 15 25100 = 25.25 312 9 = 9.312 1000 The digits at the left of the decimal point constitute the whole number. While the digits at the right of the decimal point constitute the decimal number. 2

 Each decimal is read in the same way as the fraction it represents. 3 Examples: = 0.3 is read as three tenths 10 15 = 0.15 is read as fifteen hundredths 100 125 = 0.125 is read as one hundred twenty-five thousandths 1000 35 12 = 12.35 is read as twelve and thirty-five hundredths 100Take note of the following:  To read decimals: 1. The digits to the left of the decimal point are read as a whole number. 2. The decimal point is read as “and”. 3. The digits to the right of the decimal point are read as a whole number followed by the place value of the rightmost digit.  Adding one or more zeroes to the right of a decimal does not change the value of the decimal. Example: 0.30 = 0.3 = 0.300TRY THESERename the following fractions in decimal form. 181 81) = ____ 7) = ____ 1000 100 7 122) 3 = ____ 8) 7 = ____ 10 1000 35 93) 2 = ____ 9) 13 = ____ 100 100 5 24) = ____ 10) 100 = ____ 1000 10 216 95) 4 = ____ 11) = ____ 1000 40 10 596) 10 = ____ 12) = ____ 1000 100 3

WRAP UP To rename fractions whose denominators are powers of 10 to decimals, remember that the number of zeros in the denominator of the fraction is the same as the number of digits to the right of the decimal point. We can use zero (0) as a placeholder.ON YOUR OWNMatch Column A with the correct answer in Column B. Write your answers in yournotebook.Column A Column B 9 a. 0.045 b. 22.31. c. 2.11 1000 d. 0.6 11 e. 0.0092. 2 100 33. 22 10 454. 1000 65. 10 4

ROUNDINGGROAFDFE VDECIMALS ROUNDING OFF DECIMALSObjective: Round off decimals to the nearest tenths/hundredths/thousandthsREVIEWA. Give the place value of digit 7 in each given number. Write your answer in your notebook. 1) 967009 2) 476281 3) 798139 4) 909376 5) 405786B. Write in notebook the place value of 5 in each given number.1) 7.3259 6) 3.522) 136.252 7) 5.1233) 37.533 8) 0.3054) 9.3225 9) 13.1585) 0.568 10) 51.312 1

STUDY AND LEARNRead and understand the story problem below. The Philippine Monkey-Eating Eagle is the second largest eagle in the world. Itweighs 7.85 kilos. It’s one of the endangered species, that need protection andpreservation.How do we round off 7.85?Do you remember how to round off decimal numbers?Let’s see. To round off a decimal number, encircle the digit in the place value you need to round it off to.Example: 7.85 1.3523 Look at the digit to the right of the encircled numbers.a. If the digit is 5 or greater, add one to the encircled digit and drop all digits that come after it.5.293 5.3 9 is > 50.1569 0.157 9 is > 5b. If the digit is less than 5, keep the encircled digit and drop all digits that come after it.3.523 3.5 2 is < 50.894 0.89 4 is 5c. If the digit to be rounded is 9 and it is followed by a digit more than 5, add 1 to the digit to be rounded.Example: 0.296 0.30 1.983 2.0 2

Let’s try another example.Example:This time let us round 7.89 to the nearest whole number.7.89 = 8 (since the digit to the right of 7 is 8 which mean, round up)13.47 = 13 Why?TRY THESEA. Round to the nearest whole number.1) 6.437 3) 94.86 5) 11.7982) 0.98 4) 215.963 6) 9.982B. Round to the nearest tenths. 5) 115.26 6) 59.961) 7.39 3) 26.452) 0.826 4) 39.06 5) 112.999 6) 7.046C. Round to the nearest hundredths. 5) 4.584671) 28.736 3) 37.678 6) 7.9116592) 19.158 4) 9.241D. Round to the nearest thousandths.1) 8.53967 3) 12.983622) 0.76463 4) 3.54545 3

WRAP UPTo round off a decimal:  Look at the digit in the place value which the decimal is to be rounded off.  If the digit to the right is 5 or more, add 1 to the digit in the place you are rounding to. Drop all the digits to its right.  If the digit to the right of the rounding place is less than 5, drop that digit and other digits to its right.ON YOUR OWNComplete the chart. Write your answer in your notebook. Rounded to the Nearest… Whole Tenths Hundredths Thousandths Ten Number Thousandths1) 3.893762) 1.234563) 9.823974) 121.827655) 49.25432 4

ADDITION AND SUBTRACGTRIAODNE OV F DECIMALS UP TO THE ADDITION AND SUHBUTNRDARCETDIOTHNSOPFLDAECCEIMALS UP TO THE HUNDREDTHS PLACEObjective: Add and subtract decimals up to the hundredths place without and with regrouping REVIEW Write the correct decimal number for each of the following. 1) 83 hundredths 2) 47 hundredths 3) 28 hundredths 4) 352 thousandths 5) 65 thousandths STUDY AND LEARNExample 1: Mercedes Anne was asked by her mother to go to the market to buy 0.75 kg of beef and 0.5 kg of fish. How many kilograms of beef and fish did she buy? 1

Let’s solve the problem following the steps below. 1 Write the decimals in column. 0.50  Use zero Align the decimal points. Use zero + 0.75 to fill up as a place holder. empty spaces 2 Add the digits in the hundredths 0.50 place. Regroup if necessary. + 0.75 5 3 Add the digits in the tenths place. 1 Regroup 1 Regroup if necessary whole into 0.50 ones place + 0.75 25 4 Add the ones. Place the decimal 0.50 point in the sum below the decimal + 0.75 points of the addends. 1.25Mercedes Anne bought 1.25 kilograms of beef and fish.Look at the other examples below.Example 2: 0.34 + 0.16 + 0.2 = N 0.34  Place a zero. 0.16 + 0.20 0.70Example 3: 0.39 + 0.28 + 0.64 = N 12  Place a zero. 0.39 0.28 + 0.64 1.31 2

Example 4: How much heavier is the beef than the fish that Melissa bought? What operation shall we use to find the answer? Let’s show the step by step solution to the problem. 1 Write the decimals in column. Align the decimal 0.75 points. Use zero as a place holder when needed. - 0.50  Place a zero.2 Subtract the digits in the hundredths place. 0.75 Regroup if necessary. - 0.50 53 Subtract the digits in the tenths place. Regroup if 0.75 necessary. - 0.50 25Place the decimal point to the difference directly4 below the decimal points of the minuend and 0.75 subtrahend. - 0.50 0.25So, beef is 0.25 kg heavier than the fish.Here are other examples. Study them carefully. 8 12 3 15 2 12 0.92 0.45 0.32- 0.63 - 0.26 - 0.16 0.29 0.19 0.16 3

TRY THESE 2) 0.37 3) 0.45 - 0.22 + 0.83A. Write the missing numbers. 1) 0.25 5) _____ + 0.34 + 0.43 0.92 4) _____ - 0.27 0.62B. Solve for the answer. 1) What must be added to 0.37 to get a sum of 0.92? 2) What is 0.70 less 0.27? 3) What is 0.24 more than 0.79? WRAP UPTo add or subtract decimals, follow these steps:  Arrange the numbers in column with the decimal points aligned. Use zeros as placeholders when needed.  Add or subtract as whole numbers.  Place a decimal point in the answer. It should be aligned with the decimal point of the addends or of the minuend and subtrahend. 4

ON YOUR OWNA. Solve. Write your solutions and answers in your notebook.1) 0.24 more than 0.692) 0.82 less 0.293) difference between 0.68 and 0.024) sum of 0.42, 0.10 and 0.585) 0.91 6) 0.47 7) 0.77 8) 0.24 - 0.27 - 0.16- 0.32 - 0.28B. Read the problem then find the answer. Write your solutions and answers in your notebook. 1) Me-anne has 0.9 meter of cloth. She used 0.5 meter for her project. How much cloth was left unused? 2) Freddie consumed 0.55 liter of gasoline in the morning and 0.75 liter in the afternoon. How much gasoline did he consume the whole day? 5

ADDITION AND SUBTRACGTRIAODNE VOF DECIMALS THROUGH ADDITIOTNHOAUNSDASNUDBTTHRSAWCTITIOHNOUOTF RDEEGCIRMOAULPSINTGHROUGH THOUSANDTHS WITHOUT REGROUPINGObjective: Add and subtract decimals through thousandths without regrouping. REVIEWFind the sum or difference.1) 202 + 131 + 34 = 2) 864 – 523 = 3) 132 + 314 + 223 = 4) 1 589 + 345 = 5) 978 – 242 =  STUDY AND LEARNStudy the diagram below.0.745 0.328 0.545Example 1: How far is Pepe’s house from Nelia’s house? 1

To find the distance between Pepe’s house and Nelia’s house, we add 0.545 km and0.322 km. STEP 1 STEP 2 STEP 3Write the numbers in a Add as you would add whole Align the decimal point incolumn, align the decimal numbers. Add from right to the sum in line with thepoints left. decimal point of the addends. 0.545 0.545 0.545+ 0.322 0.322 0.322 0 867 0.867The distance from Pepe’s house to Nelia’s house is 0.867 km.Example 2: Norma learned that her friend Pepe is sick. She wanted to visit him. If she hadwalked 0.243 km from her house, how far would she have to walk to reach Pepe’s house?To solve the problem, we need to subtract 0.352 from 0.745.Let’s subtract. STEP 1 STEP 2 STEP 3Write the numbers in Subtract as you would Place the decimal point in thecolumn, align the decimal subtract whole numbers. difference in line with thepoints Subtract from right to left. decimal point of the minuend and subtrahend. 0.758 0.758 0.758- 0.243 - 0.243 - 0.243 0.515 0.515So, 0.758 – 0.243 = 0.515.Norma still needs to walk 0.515 km more to reach Pepe’s house.Adding and subtracting decimals is easy and simple! 2

Example 3:Let’s have some more examples.A ) Let’s add. Align the decimal points. B ) Let’s subtract. 0.346 + 0.23 = N Use zero as placeholder if 0.346 – 0.23 = N 0.346 needed. + 0.230 0.346 - 0.230 0.346 Add/subtract as you would 0.346 + 0.230 add/subtract whole - 0.230 . numbers. 0 576 0 116 0.346 Place the decimal point in 0.346 + 0.230 the result. Align with the + 0.230 other decimal points. 0.576 0.116 TRY THESEA. Add or subtract. Match with the correct answer. Write your answers in your notebook.B. Column A Column B 1) 0.257 + 0.212 a) 0.525 2) 0.928 – 0.403 b) 0.766 3) 0.754 – 0.22 c) 0.469 4) 0.316 + 0.45 d) 0.987 5) 0.863 + 0.124 e) 0.534 3

B. Find your way out of the woods. Do the process indicated to find your way out. WRAP UP In adding/subtracting decimals follow these steps: Step 1: Arrange the numbers in a column. Align the decimal points. Use 0 as placeholder if needed. Step 2: Add/subtract as you would add/subtract whole numbers. Step 3: Place a decimal point in the sum/difference. Align this with the other decimal points. 4