MATH 4

This is the zero property of multiplication. When we multiply a number byzero, the product is zero (0), or we can say n x 0 = 0Now, look at box B closely.By what common factor are the numbers 3, 5, 7, and 9 multiplied? They are multiplied by one (1). What can you say with their products? The product is the same with theother factor, like 3 when multiplied by 1 gets a product of 3, 5 by 1 is 5. This is known as the identity property of multiplication. When wemultiply a number by one, the product is the same number, in short n x 1 = n.TRY THESEGive the product. 82 x 1 = ______ 79 x 0 = ______ 10 x 0 = ______ 0 x 45 = ______ 12 x 1 = ______ 1 x 47 = ______ 4 482 5 402 6 472 x1 x0 x1 192 756 x0 x1WRAP UP The zero property of multiplication states that anynumber multiplied by zero is equal to zero. The identity property of multiplication states that anynumber multiplied by 1 is equal to the number. 2

ON YOUR OWNA. Multiply. 2. 16 x 0 = 3. 1 x 181 =1. 48 x 0 =4. 4 264 5. 2 641 6. 17 246 x1 x0 x1B. Fill in with the missing number to complete the multiplication sentence.1. 64 x = 0  2. x 1 = 174 3. 75 x = 754. 2 473 5. 17 481 6. x x x1 12 143 0 17 481 3

GRADE IVMULTIPLICATION OF 5 OR MORE DIGIT FACTORS HAVING 1 TO 3 ZEROS IN BOTH FACTORS WITHOUT REGROUPING Objectives: Multiply 5 or more digit factors having 1 to 3 zeros in both factors without regrouping.REVIEWA. Review your multiplication facts. Do you still remember the principle that any number multiplied by zeros the product is zero? Well, try these as fast as you can.1) 45 2) 678 3) 454 x0 x0 x0 4) 5 431 5) 61 587 x0 x0B. Answer the following in your notebook.1) 213 2) 842 3) 524 x3 x2 x3 1

STUDY AND LEARNA. Read the problem. A gasoline attendant sold an average of 1 200 litres of gasoline a day. How many liters of gasoline were sold in 24 days? What is asked? The number of litres of gasoline sold in 24 days. What are the given facts? 1 200 - the average number of litres of gasoline sold each day 24 - the number of days What process should you use to solve the problem? Multiplication What is the number sentence? 1 200 x 24 = n The number sentence can also be written this way. 1 200 x 24 4800 - multiplied by 4 2400__ - multiplied by 2 28800 2

TRY THESEDo the following exercises on your notebook.A. Multiply1. 42 000 b. 60 031 c. 52 002 d. 30 052 e. 40 024 x 30 x 200 x 100 x 100 x 200B. Answer the following 1. Multiply 8 400 by 200. What is the product? 2. If the factors are 2 100 and 42, what is the product? 3. What is 4 200 times 400? 4. What is the correct product of 13 030 multiplied by 300? 5. An agricultural supply dealer has an average sales of 9 200 a day. How much will he earn in 120 days?WRAP UP Any number multiplied by zero equals zero. If the zero on bothfactors are found at the end, multiply the given number then count thenumber of zeros found at the end of the factors and affix them to theanswer. 3

ON YOUR OWNA. Find the products. Use your notebook.1. 30 002 2. 42 102 3. 60 002 4. 32 102 5. 52 303 x 300 x 40 x 50 x 400 x 300B. Do what is asked.1. What is 64 002 multiplied by 400?2. If the factors are 5 200 and 40, what is the product?3. Multiply 9 300 and 200, what is the product?4. What is 30 002 repeated 30 times?5. If you multiply 6 200 by 400, what is the product? 4

GRADE IVMULTIPLICATION OF 5 OR MORE DIGIT FACTORS HAVING 1TO 3 ZEROS IN BOTH FACTORS WITH REGROUPING IN ALL PLACES Objective: Multiply 5 or more digit factors having 1 to 3 zeros in both factors with regrouping in all places.REVIEWSolve the following exercises in your notebook. Perform the indicated operations.1. 8 010 2. 9 300 3. 7 200 4. 8 010 5. 6 100 x 50 x 30 x 30 x 40 x 506. 8 201 7. 8 101 8. 7 320 9. 6 200 x 50 x 60 x 30 x 20 STUDY AND LEARNHave you been to a shoe factory?Have you tried working in a shoe factory?Do you think you can be working in a shoe factory?Have you tried receiving an amount as payment for what you have done?What do you feel when you receive some amount as compensation for what you havedone? 1

A. You have something to read. A shoe factory pays each laborer 17 060 annually. How much does the owner pay for its 50 laborers? Analyze the problem, then study the steps on how it is solved.- How many laborers are there in the shoe factory? There are 50 laborers.- What is the salary per year of each laborer? The shoe factory pays each laborer 72 000 annually.- What is asked in the problem? How much does the owner pay for its 50 laborers.- What is the operation to be used? We use multiplication.- How will the problem be solved?- What is the mathematical sentence? 12 060 x 50 = 603 000 or 12 060 x 50 603 000 2

B. Complete the table. Do it in your notebook. The first column is done for you. X 40 50 60 70 80 76 000 304 000 ________ ________ 36 004 1 440 160 ________ 480 320 70 505 2 820 200 4 935 350 80 080 3 200 200 TRY THESEAnswer the following exercises.Do it in your notebook.A.1. 54 000 2. 70 700 3. 390 140 4. 146 006 5. 624 000 x 30 x 40 x 302 x 203 x 100B. Solve the following problems in your notebook. Henry is a salesman of electrical appliances. His average sales for a month is 23 005. What is the sales for 105 months? WRAP UP Step 1. Use the same steps in multiplying. Step 2. Regroup whenever necessary. Step 3. Write zero in the product when multiplied by any number or bring down in the terminal zeros of the factors and proceed with multiplying Step 4. Add the partial products to get the final product. 3

ON YOUR OWNWould you like to test yourself? How far have you learned lessons in multiplication?Answer the exercises below.A.1. 30 108 2. 91 003 3. 362 005 4. 841 000 5. 470 602 x 50 x 400 x 60 x 800 x 405B. Solve the following problems in your paper.1) If the factors are 46 710 and 40 what is the product?2) Multiply 600 by 63 000. What is the product?3) What is 240 056 times 40?4) What is 823 204 times 252?5) Multiply 128 402 by 200 What is the product? 4

GRADE IV MULTIPLICATION OF 5 OR MORE DIGIT FACTORS BY MULTIPLES OF 10, 100 AND 1 000Objectives: Multiply 5 or more digit factors by multiples of 10, 100 and 1 000.REVIEWDo you remember how to multiply a number by 10, 100 and 1 000?Try the following:1. 4 x 10 = 6. 4 x 100 = 11. 25 x 1 0002. 6 x 10 = 7. 5 x 100 = 12. 30 x 1 0003. 7 x 10 = 8. 6 x 100 = 13. 11 x 1 0004. 8 x 10 = 9. 7 x 100 = 14. 45 x 1 0005. 9 x 10 = 10. 8 x 100 = 15. 40 x 1 000 STUDY AND LEARN1. Do you know what a typhoon is?2. What do you think will typhoon bring us?3. Can you go to school if the typhoon is signal number 2?4. Is it safe for you to go out and play when there is a typhoon?5. What do you feel when there is a typhoon?6. Have you tried giving something to people who are victims of typhoons?7. What do you feel if you have given something to people who are victims of typhoons? 1

Read the problem. Some parts of Pangasinan were badly hit by a typhoon last October. The president promised to give each municipality that was damaged by the typhoon an amount of 340 252. If there were 10 municipalities that were damaged by the typhoon, how much amount will be given to Pangasinan?Analyze the problem. 1. What hit Pangasinan last June? Typhoon 2. What did the president promise each municipality hit by the typhoon? The president promised to give each municipality the amount of 340 252. 3. How many municipalities were hit by the typhoon? There were 10 municipalities. 4. What is asked for? How much amount will be given to Pangasinan. 5. What are given in the problem? 340 252 - amount to be given to each municipality 10 - number of municipalities hit by the typhoon 6. What operations will help you solve the problem? Multiplication 7. What is the number sentence? 340 252 x 10 = n or 340 252 x 10 2

You can use a short cut to multiply any number by 10 or a multiple of 10 340 252 x 103402520 - write 0 in the ones place Then multiply by the tens digitTry to multiply multiples of 100 622 437 Write 0 in ones place and tens places. x 100 Then multiply by the hundred digits62 243 700How about in multiplying any number by a multiple of 1 000?Try this: 5 622 437 Write 0s in the ones tens and hundreds places. 1 000 Then multiply by the thousand digit5622437000Try to find the pattern for the following exercises.A. B.52 163 x 4 = 208 652 421 846 x 3 = 65 53852 163 x 40 = 421 846 x 30 =52 163 x 400 = 421 846 x 300 =52 163 x 4 000 = 421 846 x 3 000 =What pattern did you observe?How do you multiply numbers by multiples of 10? 100? 1 000? 3

TRY THESEAre you now ready to have exercises?Do it in your notebook.A. Answer the following. Bring down the zeros before multiplying.1. 31 772 2. 24 634 3. 753 321 4. 821 245 5. 9 638 452 x 10 x 30 x 1 000 x 200 x 500B. Solve for n.1. 31 142 x 500 = n2. 72 413 x 900 = n3. 62 214 x 2 000 = n4. 822 134 x 1 000 = n5. 7 518 321 x 4 000 = n6. 40 056 times 40 = n, find n7. What is n in 8 402 x 200 = n?8. What is 23 204 times 252 equals n?C. Complete the table. Write them in your notebook. X 400 2 0001. 34 3452. 123 6323. 925 8674. 532 3245. 1 134 262 4

WRAP UPHow do we multiply numbers by multiples of 10? 100? 1 000? Multiply the non-zero digits first, then annex to the product as many zeros as there are in the factors.On Your OwnAre you now ready to test how for you have learned the lessons?A. Answer the following. Do it in your notebook.1) 32 186 2) 23 272 3) 521 832 4) 1 833 143 5) 4 718 321 x 10 x 100 x 1 000 x 500 x 7 000B. Solve for n. 4) 622 235 x 1 000 = n 5) 1 734 423 x 400 = n 1) 42 133 x 400 = n 2) 42 314 x 900 = n 3) 364 213 x 2 000 = n 5

GRADE IV ESTIMATING PRODUCTSObjective: Estimate the product of two factors with 5 or more digits by 2 to 3 digit numbers.REVIEWRound the number to the highest place value. Write your answers on your paper.1. 67 6. 1 4212. 485 7. 56 6783. 476 8. 30 5784. 321 9. 215 6785. 1 578 10. 434 261 STUDY AND LEARNRead the problem carefully. The headline of the newspaper read, “ABOUT 2 000 000 PEOPLE ATTENDED THE CLOSING OF A RELIGIOUS ACTIVITY.” How many people really attended the closing ceremony? You need to learn how to make good estimates because there are manyinstances in our daily life when an estimate and not an exact answer is theappropriate answer to give. 1

Read the problem below and do your best to follow through thediscussion. If a poultry farm can produce 15 785 eggs per week, about how many eggscan it produce in 29 weeks?The phrase “about how many” tells us to get the estimated product.S Round off each factor to Multiply the rounded Find the exact product.T its greatest place value factors.E position. 15 785P 15 785 ---- 20 000 20 000 X 29S X 29 ---- X 30 X 30 142 065 600 000 315 70 457 765 The farm can produce about 600 000 eggs in 29 weeks. Is the estimate good? No,because it is far from the actual product.Let’s try 15 790 15 785 rounded to the nearest tens X 30 x 29 rounded to the nearest tens 473 700 Now which estimate is closer? The factors, which are rounded off to the nearesttens have the closer estimated product. What are the two ways that we use to estimate the product? First, we rounded thefactors to the highest place value. Second, we rounded them to the nearest tens which isthe highest place value of the multiplier. 2

TRY THESEA. Round each factor to the greatest place value, then multiply.1. 53 254 rounds to ___________ x 158 rounds to ___________2. 153 254 rounds to ___________ x 26 rounds to ___________3. 86 541 rounds to ___________ x 38 rounds to ___________4. 247 254 rounds to ___________ x 69 rounds to ___________5. 5 133 234 rounds to ___________ x 218 rounds to ___________B. Read and solve. Nineteen big cities around the world pledged to support the reforestation program. If all of them were able to plant 18 465 seedlings each, about how many seedlings were planted in all? (Round first the factors to the nearest tens then multiply.) 3

WRAP UP To estimate products, round the factors to its greatest placevalue or to a specified place value, then multiply.ON YOUR OWNA. Estimate the product to the nearest hundreds.1. 59 561 2. 321 578 3. 1 267 434 x 234x 58 x 147 4. 621 541 5. 254 324 x 678 x 729B. Round each number to the highest place value then multiply.1. 32 578 2. 89 564 3. 187 464 x 26 x 58 x 246 4. 1 898 464 5. 12 578 464 x 31 x 329 4

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GRADE IVTWO-STEP WORD PROBLEMS INVOLVING MULTIPLICATION AND ADDITION OR SUBTRACTION Objective: Solve two-step word problems involving multiplication and addition or subtraction following the steps in solving two step problems. REVIEW A. Read and understand the problem below. Then fill in each blank with the correct answer. 1. Mariam has 18 toys. Lisa has 8 toys. How many toys do they have altogether? I must add _____ and _____ together. _____ + _____ = _____ They have _____ toys altogether. 2. Hesed and Leo together have 24 marbles. Hesed has 5 marbles. How many marbles has Leo? I must subtract _____ from _____. _____ - _____ = _____ Leo has _____ marbles. 1

3. How many feet do 10 carabaos have altogether? I must multiply _____ by _____. _____ x _____ = _____ Ten carabaos have _____ feet altogether.B. Solve for n. Do first the operation inside the parenthesis. a. (4 x 2) - 5 = n b. (3 x 4) + 6 = n c. (3 + 4) x 3 = n STUDY AND LEARN Read and study. 1. Marlon drew 10 circles in each of the 5 boxes. He shaded 12 circles. How many circles were not shaded? Let us draw a picture. 2

By counting you will know that 38 circles are not shaded. Drawing a picture is one of the best ways to solve problems. However, you shouldalso learn solving problems through mathematical operations. What is asked? Circles that are not shaded What are given? 10 circles, 5 boxes What is the hidden question? Total number of circles What operations are to be used? Multiplication and subtraction What is the number sentence? (5 x 10) - 12 = n Let us solve the problem. (5 x 10) - 12 = n 50 - 12 = 38 So 38 circles are not shaded. Do we have the same answer?2. The school principal hired 5 buses. Each bus contained 60 passengers. If 250 of the passengers were boys, how many were girls?Make a diagram.60 60 60 60 60bus 1 bus 2 bus 3 bus 4 bus 5What will you do first to find out how many were girls?Correct!You are going to add 60 + 60 + 60 + 60 + 60 = 300What do you call 300? total number of passengersWhat will you do next?Correct again! Subtract 250 from 300.So 300 - 250 = 50There were 50 girls.Going back to our repeated addition:60 + 60 + 60 + 60 + 60 = 300. 3

Can you still recall the fastest way to arrive at the total without usingrepeated addition? We do it this way: ( 5 x 60 ) - 250 = nbuses passengers per bus boys ( 5 x 60 ) - 250 = n 300 - 250 = 50 So there were 50 girls. The examples given involved multiplication and subtraction. How about wordproblems that use multiplication and addition?Here is one example. Aling Maring bought 3 kilos of mangoes at 45.00 per kilo and 2 kilosof bananas at 27.00 per kilo. How much did she pay in all?What are you asked to find? The total amount Aling Maring paid in all What are the given facts? 3 kilos of mangoes at 45.00 per kilo and 2 kilos ofbananas at 27.00 per kilo What is the hidden question? The amount paid for the mangoes and the amountpaid for the bananasWhat is/are the operation/s to be used? Multiplication and additionWhat is the number sentence? (3 x 45.00) + (2 x 27.00) = _____Let’s solve: 45.00 27.00 135.00 X3 x2 + 54.00 54.00 189.00 135.00Aling Maring paid 189.00 for all the mangoes and the bananas. 4

TRY THESE Try solving the following problems.1. Ms. Santos had 15 trays of eggs with 30 eggs in each tray. She sold 215 eggs. How many eggs were left unsold?2. Miguel has 2 five hundred peso-bill, in his wallet. If he buys a polo shirt worth 679.95, how much money will be left?3. There are four sections in Maybago Elementary School. Three sections have 48 students each and the fourth has 52 students. How many grade IV students are there in all? WRAP UP When we solve two-step word problems we seek answers to the following guide questions.  What is asked?  What are given?  What is the hidden question?  What operations are we going to use?  What is the number sentence? You can draw a picture or diagram to visualize the problem. 5

ON YOUR OWNRead the following problems carefully. Then solve them.1. Ruel bought 10 pads of colored papers and Jessie bought 6 pads of colored papers. If each pad has 90 pieces of papers, how many colored papers are there in all?2. Mrs. Aguilar’s Grade IV class would like to join the field trip to Calabarzon Area. The tour would cost 250 per child. If Mrs. Aguilar was able to collect 2,500 initially, how much does she still need to collect if she has 40 pupils?3. Father harvested 5 cavans of palay in his ricefield. Each cavan of palay costs 750. If his total expenses is 1,175, how much was his profit? 6

GRADE IV DIVISION OF 5 OR MORE DIGIT NUMBER BY 3 DIGIT NUMBERS WITHOUT REMAINDERObjective: Divide 5 or more digit numbers by 3 digit number without remainder. REVIEWRecall simple division exercises. Do them as fast as you can1) 20 ÷ 5 = n 6) 10 ÷ 2 = n2) 42 ÷ 6 = n 7) 8 ÷ 1 = n3) 24 ÷ 4 = n 8) 12 ÷ 4 = n4) 18 ÷ 3 = n 9) 21 ÷ 3 = n5) 35 ÷ 7 = n 10) 32 ÷ 8 = nSTUDY AND LEARNStudy the problem below. Ruben helps his father in gathering eggs in their poultry farm. On the average, they are able to gather about 245 eggs in one day. If they had gathered 13 720 eggs, how many days did they spend in gathering the eggs? Answer the following questions.  What did Ruben do?  What kind of a child is Ruben? Why?  Do you like Ruben? Why? 1

Now let’s go to the solution to the problem.How many eggs did they gather in one day? 245How many eggs did they gather in all? 13 720To get the quotient, you need to divide 13 720 by 245.Here are the steps. Divide 1372 by 245, 1372 ÷ 245 = 5. 5 Write 5 above 2. Multiply: 5 x 245 = 245 1-3 720  1 1225. Write 1225 below 1372. Get the difference: 1372 - 1225 = 147. 12 25 Then bring down 0. 1 470  Divide 1470 ÷ 245 = 6. 56 Write 6 above 0. Then, multiply 6 by 245 13 720  1 245 which is equal to 1470. Write 1470 below 1470. Get the difference 1-2 25 1470 - 1470 = 0. 1 470So, 13 720  245 = 56 -1470 0 To check if your answer is correct, multiply the divisor by the quotient. If theproduct is equal to the dividend your answer is correct. 245 x 56 1470+ 1225 13720 2

Let’s have another example.346 680  214 = n 1 620 1. Divide: 346  214 = 1214 346 6 8 0 Multiply: 1 x 214 = 214 - 214 Subtract: 346 – 214 = 132 132 6 Bring down: 6 - 128 4 2. Divide: 1326  214 = 6 4 28 - 4 28 Multiply: 6 x 214 = 1284 Subtract: 1326 – 1284 = 42 00 -0 Bring down: 8 0 3. Divide: 428  214 = 2 Multiply: 2 x 214 = 428 Subtract: 428 – 428 = 0 Bring down: 0 4. Divide: 0  214 = 0 Multiply: 0 x 214 = 0 Subtract: 0 – 0 = 0 So the quotient is 1 620. Bring down: 6TRY THESE 4. 167 072 ÷ 368 = 5. 266 299 ÷ 473 = 1. 52 216 ÷ 122 = 2. 57 024 ÷ 132 = 3. 45 150 ÷ 175 = 3

WRAP UPHere are the steps in division.Step 1. DivideStep 2. MultiplyStep 3. SubtractStep 4. Bring down the next digit then repeat the process from Step 1. ON YOUR OWN You can now test yourself if you were able to comprehend the activity you have undergone. Answer it in your notebook. A. Divide the following 1) 39 751 ÷ 127 2) 240 264 ÷ 422 3) 237 744 ÷ 312 B) You have 375 750 worth of money that you want to share with other people. How much would each person get if you want to divide it among 225 persons?you. 4

GRADE IV DIVISION OF 5 OR MORE DIGIT NUMBER BY 3 DIGIT NUMBERS WITH REMAINDERObjective: Divide 5 or more digit numbers by 3 digit number with remainder.REVIEWA. Fill up with the necessary digits to complete the division process. 5 r. 111) 203 30885 2) 412 14916 . 23 17 105 132 -1015 396 435 - 396 -406 363) 412 148732 - 1236 2513 - 412 - 412 0 1

STUDY AND LEARNObserve closely how we divide big numbers. 1 How many 2 237 will there be in 2237 259515 2 595? You can have 1. Put 1  2237 3581 above 5. Multiply: 1 x 2 237 = 2 237 Subtract: 2 595 – 2 237 = 358 Bring down 1. 11 Divide: 3 581  2 237 = 1 2237 259515 Put 1 above 1. Multiply: 1 x 2 237 = 2 237  2237 Subtract : 3 581  2 237 = 1 344 3581 Bring down 5 - 2237 13345 116 r 23 Divide: 13 445  2 237 = 6 2237 259515 Put 6 above 5. Multiply: 6 x 2 237 = 13 422. = 23  2237 Subtract: 13 445  13 422 = 23 23 is smaller than the divisor so 3581 the final answer will be 116 r. 23  2237 13345  13422 23 2

Can you follow the steps we made in dividing 259 515 by 2 237? TRY THESE1. 256 ) 297135 3. 1679 ) 57492322. 1719 ) 476422 WRAP UP To divide big numbers you have to remember the following: When dividing big numbers look at the digits in the divisor. Use as manydigits in the dividend as there are in the divisor starting from the left. If thedivisor is still not contained in the partial dividend add one digit more in thedividend. Then follow the steps. Divide, multiply and subtract until the onesdigit in the dividend is used. 3

ON YOUR OWNFind the quotient. Write your answers in your notebook.1.) 421) 83358 2) 218) 3868283) 531) 797562 4) 1362) 38167345) 2653) 564372 4

GRADE IVDIVISION OF LARGE NUMBERS WITH ZERO DIFFICULTYObjective: Divide 4 to 5 digit numbers by 2 to 3 digit numbers with zero in the middle or continuous zeros in the dividend.REVIEWComplete the table. ÷ 10 ÷ 100 ÷ 1 000 Numbers 1) 63 000 2) 46 721 3) 396 380 4) 743 215 5) 846 000 STUDY AND LEARNStudy this sample problem. The Girl Scouts of the Philippines collected 13 044 kg of rice to be distributed to the poor families in Mindanao. If each family is given 12 kg, how many families will be given rice? Answer the following questions based on the problem you have just read. You may write your answers in your notebook or in a piece of paper. 1

 What organization distributed rice to poor families? Do you have this organization in your school? Are you a member of this organization? Why? Is it good to help the poor families in your community? Why?Okay, let us now solve the problem. What is asked for in the problem? The number of poor families who will be given rice. What are the given information in the problem? → 13 044 kg of rice → 12 kg to be given per family What will you do to solve the problem? → Divide What will be the number sentence? 13 044 ÷ 12 kg = n 2

Okay, let us solve it together. The process is quite long but you’ll find enjoymentonce you learned a challenging task. Let’s begin! 1087 13 ÷ 12 = 1 Write 1 above 3. 12 x 1 = 12 13 – 12 = 1 Bring down 0. 12 13044 10 ÷ 12 = 0 (since 10 is smaller than 12) -12 10 Write 0 above 0. 0 x 12 = 0 0 10 – 0 = 10 Bring down 4. 104 -96 104 ÷ 12 = 8 Write 8 above 4. 8 x 12 = 96, 104 – 96 = 8 Bring down 4. -8844 0 84 ÷ 12 = 7 Write 7 above 4. 7 x 12 = 84 84 – 84 = 0 To check if your answer is correct, multiply 1 087 by 12TRY THESEDo these in your notebook.1. 21 4305 2. 15 3600 3. 215 25800 WRAP UPWhen we divide numbers, we follow these steps:Step 1. divideStep 2. multiplyStep 3. subtractStep 4. bring down In case the partial dividend is smaller than the divisor, the answershould always be zero. 3

ON YOUR OWNYou can test yourself if you have fully understood the lesson by the following exercises.1. 27 54054 2. 38 19000 3. 415 16600 4. 35 70035 5. 242 72600 4

GRADE IV DIVISION OF WHOLE NUMBERS BY 10, 100 AND 1 000Objective: Divide whole numbers by 10, 100 and 1000.REVIEWTry doing this activity. c) 221 3860A. Find the quotient. a) 112 1680 b) 195 4572B. Try multiplying the following numbers and look at the products. This will give you an idea about the lesson you are supposed to study. a) 56 321 x 10 b) 100 x 74 153 c) 1 000 x 492 618 1

STUDY AND LEARNRead and analyze the problem below. The Citizens Drug Watch in a town had 120 members. They were formed into groupsof 10 members each. How many groups were formed?We divide 120 by 10 find the answer: 120 ÷ 10 = nLook at this: 12 ← 1 x 10 ← 2 x 1010 120 - 10  200 - 200 0Look at the quotient and the dividend.What can you say? Okay let us try another example. 6324 r. 15 100 632415 - 600 324 - 300 241 - 200 415 - 400 15 Again, look at the quotient and the dividend. What can you say? If thedividend has a non-zero terminal digits the quotient will have the ones digit asremainder if it is divided by 10, The ones and the tens digits as remainders if we 2

divide by 100, and the ones the tens and hundreds digits as remainders, if wedivide by 1 000. The rest becomes the whole number part of the quotient. Is it clear with you? Okay you can go to practice items.TRY THESEDo this exercise based on what you have learned. ÷10 ÷100 ÷1 00034 156721 532913 287648 941287 635 WRAP UPTo divide whole numbers by 10, 100 and 1 000 do these:Step 1. When there are terminal zeros in the dividend, cancel as manyzeros in the dividend as there are in the divisor and the remaining digitsbecome the quotientStep 2. When there are no terminal zeros, the ones digit in the dividendbecomes the remainder if you divide by 10.Step 3. The ones and the tens digits become the remainders and the restthe quotient if you divide by 100Step 4. And the ones, the tens and the hundreds digits of the dividendbecome the remainder, the rest the quotient, if you divide by 1 000. 3

ON YOUR OWNNow it’s time for you to test yourself.Divide the following a) 10 2587 b) 10 43100 c) 100 58732 d) 100 615400 e) 1000 387642 f) 1000 765400Check your answers with the answer key. If you get….5-6 - Excellent! You may now proceed to the next lesson.3-4 - You need to review the processes you missed.0-2 - You need to repeat the whole process. Ask your teacher or elder to help you. 4

GRADE IV ESTIMATING QUOTIENTSObjective: Estimate the quotient of 4 to 5 digit dividends by 2-digit numbers. This module will guide you on how to estimate the quotient of big numbers using avariety of strategies. This will teach you to estimate by rounding off the dividend and thedivisor and by using compatible numbers.REVIEWA. Round off the following numbers to the highest place value.1) 18 6) 35 4262) 23 7) 72 1243) 25 8) 42 9614) 2 638 9) 52 8165) 3 448 10) 39 562 Check your answers using the key to correction. If your score is 8 - 10, you maynow proceed to this module. If you get 7 correct answers or below, review first the pastlessons. 1

STUDY AND LEARNRead the problem below. Mr. Cruz harvested 3 478 pieces of mangoes from his orchard. Hewants to place them in baskets. If a basket can hold 46 pieces ofmangoes, about how many baskets will he need?Answer the following questions. Write you answers in your notebook and presentthem to your teacher. What do you think is the work of Mr. Cruz? What can a farmer do for our country? Would you like to be a farmer someday? Why? Okay, let us solve the problem together. Are you asked to give an exact answer? - No, you are asked for an estimate because of the phrase “about how many” - An estimate maybe a little bigger or smaller than the exact answer. What will you do if you are to estimate? - Round off both the dividend and the divisor or make them compatible.3 478 → Dividend → 3 000 → rounded 46 → Divisor → 50 → rounded50 3000 We cancelled one zero in the dividend since we cancelled only one zero in the divisor. 2

Now we can divide 60 or 60 Divide 30 by 550 3000 5 300 then affix 0 to the quotient. -30 -30 0 0 -0 0What do you notice with the divisor and dividend? Since they all end with 0, letus apply first the cancellation method.The other method is to make the numbers compatible.50 and 3 500 are compatible numbers.The answer is about 70 basketsNow, let us solve for the exact answer and compare what is the better estimate. 75 r. 28 → 76 baskets needed46 3478 322  258 230 28Ist estimate by rounding → 602nd estimate by compatible numbers → 70Actual answer 75 or 76What is the better estimate → 70 using compatible numbers.Can you now work alone without our guidance? Ok. Do the following with theexact number. 3

TRY THESEFind the estimated and exact quotients using the two processes learned. Compare theestimates with the exact quotients. a) 5 436 ÷ 27 = n b) 1 501 ÷ 26 = n c) 42 561 ÷ 21 = n d) 62 926 ÷ 72 = n e) 31 563 ÷ 43 = n WRAP UP When you are asked to estimate you don’t give the exact answer. Key words or phrases may give you a cue that you are to estimate. Examples are “by how much”, “about how many” a little less than the actual answer. You can either round off the numbers to each highest place value or use compatible numbers, depending on the situation. This reminder should always be followed if you are to find quotient estimates. 4

ON YOUR OWNI think you are now ready to test the skill you have learned from the module. Answer theactivities in your notebook.A. Write the reasonable estimate for each of the problem. a) 9 676 ÷ 48 = n b) 41 872 ÷ 19 = n c) 17 399 ÷ 34 = n d) 19 475 ÷ 23 = n e) 69 673 ÷ 68 = nB. Estimate. Then choose the correct answer.1) 11 4432 a. 400 b. 40 c. 4002) 13 63473) 17 42497 a. 6 b. 60 c. 6004) 21 513475) 47 67389 a. 2 000 b. 200 c. 20 a. 250 b. 2 500 c. 25 a. 14 b. 140 c. 1 400Check your answers with the answer8-10 - Excellent! You may now proceed to the next lesson. 5

7-5 - You need to review the processes you missed.0-4 - You need to repeat the whole process. Ask your teacher or elder to help you. 6

GRADE IV ONE STEP WORD PROBLEMS INVOLVING DIVISIONObjective: Solve one step word problems involving division of 5 or more digit numbers by 3 or more digit number including money.REVIEWLook for the hidden message by solving the indicated operations and matching theanswer to the coded number._____ _____ _____ _____ _____ _____ _____ _____ _____12 34 5 67 891) 63 4095 2) 35 28070 3) 156 60400 a. 802 h. 68 r. 1124) 411 28060 5) 27 54054 6) 24 20160 f. 2348 r. 320 s. 8407) 325 763420 8) 423 836421 9) 123 638200 m. 65What is the hidden message? Have you uncovered it? n. 5188 r. 76 i. 2002 t. 387 r. 28 u. 1977 r. 150 Check your answers using the key to correction. If your score is 7 or 9, you maynow proceed to this module. If you get 6 correct answers or below, review first the pastlessons. 1

STUDY AND LEARNRead the problem below and analyze the solution made for you. Mr. Siñod, a factory owners has 125 workers. The weekly pay of the workers amounts to 212 500.00. How much does each worker earn weekly?Now, let us solve the problem step by step for you to fully understand the solution.  What is asked in the problem? The weekly earning of each worker.  What are the facts given? 125 workers 212 500 – weekly pay of all the workers  What operation are you going to use? division  What is you number sentence? 212 500.00 ÷ 125 = n  The solution: 1700 125 212500 - 125 875 - 875 00 -00 0 1 700 per worker 2