m81256 Divide Whole Numbers By the end of this section, you will be able to: Use division notation Model division of whole numbers Divide whole numbers Translate word phrases to math notation Divide whole numbers in applications f7446efa-8302-4ef6-9e5a-bdc05acb3613 Before you get started, take this readiness quiz. Multiply: 27·3. If you missed this problem, review . 81 Subtract: 43−26. If you missed this problem, review 17 Multiply: 62(87). If you missed this problem, review . 5,394

So far we have explored addition, subtraction, and multiplication. Now let’s consider division. Suppose you have the 12 cookies in and want to package them in bags with 4 cookies in each bag. How many bags would we need?

You might put 4 cookies in first bag, 4 in the second bag, and so on until you run out of cookies. Doing it this way, you would fill 3 bags. In other words, starting with the 12 cookies, you would take away, or subtract, 4 cookies at a time. Division is a way to represent repeated subtraction just as multiplication represents repeated addition. Instead of subtracting 4 repeatedly, we can write 12÷4 We read this as twelve divided by four and the result is the quotient of 12 and 4. The quotient is 3 because we can subtract 4 from 12 exactly 3 times. We call the number being divided the dividend and the number dividing it the divisor. In this case, the dividend is 12 and the divisor is 4. In the past you may have used the notation 412, but this division also can be written as 12÷4,12/4,124. In each case the 12 is the dividend and the 4 is the divisor.To represent and describe division, we can use symbols and words. Operation Notation Expression Read as Result Division ÷ ab baa/b 12÷4 124 41212/4 Twelve divided by four the quotient of 12 and 4 Division is performed on two numbers at a time. When translating from math notation to English words, or English words to math notation, look for the words of and and to identify the numbers. Translate from math notation to words. ⓐ 64÷8 ⓑ 427 ⓒ 428 ⓐ We read this as sixty-four divided by eight and the result is the quotient of sixty-four and eight. ⓑ We read this as forty-two divided by seven and the result is the quotient of forty-two and seven. ⓒ We read this as twenty-eight divided by four and the result is the quotient of twenty-eight and four. Translate from math notation to words: ⓐ 84÷7 ⓑ 186 ⓒ 824 ⓐ eighty-four divided by seven; the quotient of eighty-four and sevenⓑ eighteen divided by six; the quotient of eighteen and six.ⓒ twenty-four divided by eight; the quotient of twenty-four and eight Translate from math notation to words: ⓐ 72÷9 ⓑ 213 ⓒ 654 ⓐ seventy-two divided by nine; the quotient of seventy-two and nine ⓑ twenty-one divided by three; the quotient of twenty-one and threeⓒ fifty-four divided by six; the quotient of fifty-four and six

As we did with multiplication, we will model division using counters. The operation of division helps us organize items into equal groups as we start with the number of items in the dividend and subtract the number in the divisor repeatedly. Doing the Manipulative Math Worksheets activity "Model Division of Whole Numbers" will help you develop a better understanding of dividing whole numbers. Model the division: 24÷8. To find the quotient 24÷8, we want to know how many groups of 8 are in 24. Model the dividend. Start with 24 counters. The divisor tell us the number of counters we want in each group. Form groups of 8 counters. Count the number of groups. There are 3 groups. 24÷8=3 Model: 24÷6. Model: 42÷7.

We said that addition and subtraction are inverse operations because one undoes the other. Similarly, division is the inverse operation of multiplication. We know 12÷4=3 because 3·4=12. Knowing all the multiplication number facts is very important when doing division. We check our answer to division by multiplying the quotient by the divisor to determine if it equals the dividend. In , we know 24÷8=3 is correct because 3·8=24. Divide. Then check by multiplying. ⓐ 42÷6 ⓑ 729 ⓒ 763 ⓐ 42÷6 Divide 42 by 6. 7 Check by multiplying. 7·6 42✓ ⓑ 729 Divide 72 by 9. 8 Check by multiplying.8·9 72✓ ⓒ 763 Divide 63 by 7. 9 Check by multiplying. 9·7 63✓ Divide. Then check by multiplying: ⓐ 54÷6 ⓑ 279 ⓐ 9 ⓑ 3 Divide. Then check by multiplying: ⓐ 369 ⓑ 840 ⓐ 4 ⓑ 5 What is the quotient when you divide a number by itself? 1515=1because1·15=15Dividing any number (except 0) by itself produces a quotient of 1. Also, any number divided by 1 produces a quotient of the number. These two ideas are stated in the Division Properties of One. Any number (except 0) divided by itself is one. a÷a=1 Any number divided by one is the same number. a÷1=a Divide. Then check by multiplying: ⓐ 11÷11 ⓑ 191 ⓒ 17 ⓐ 11÷11 A number divided by itself is 1. 1 Check by multiplying.1·11 11✓ ⓑ 191 A number divided by 1 equals itself. 19 Check by multiplying.19·1 19✓ ⓒ 17 A number divided by 1 equals itself. 7 Check by multiplying.7·1 7✓ Divide. Then check by multiplying: ⓐ 14÷14 ⓑ 271 ⓐ 1ⓑ 27 Divide. Then check by multiplying: ⓐ 161 ⓑ 14 ⓐ 16ⓑ 4 Suppose we have $0, and want to divide it among 3 people. How much would each person get? Each person would get $0. Zero divided by any number is 0. Now suppose that we want to divide $10 by 0. That means we would want to find a number that we multiply by 0 to get 10. This cannot happen because 0 times any number is 0. Division by zero is said to be undefined. These two ideas make up the Division Properties of Zero. Zero divided by any number is 0. 0÷a=0 Dividing a number by zero is undefined. a÷0 undefined Another way to explain why division by zero is undefined is to remember that division is really repeated subtraction. How many times can we take away 0 from 10? Because subtracting 0 will never change the total, we will never get an answer. So we cannot divide a number by 0. Divide. Check by multiplying: ⓐ 0÷3 ⓑ 10/0. ⓐ 0÷3 Zero divided by any number is zero. 0 Check by multiplying.0·3 0✓ ⓑ 10/0 Division by zero is undefined. undefined Divide. Then check by multiplying: ⓐ 0÷2 ⓑ 17/0 ⓐ 0 ⓑ undefined Divide. Then check by multiplying: ⓐ 0÷6 ⓑ 13/0 ⓐ 0 ⓑ undefined When the divisor or the dividend has more than one digit, it is usually easier to use the 412 notation. This process is called long division. Let’s work through the process by dividing 78 by 3. Divide the first digit of the dividend, 7, by the divisor, 3. The divisor 3 can go into 7 two times since 2×3=6. Write the 2 above the 7 in the quotient. Multiply the 2 in the quotient by 3 and write the product, 6, under the 7. Subtract that product from the first digit in the dividend. Subtract 7−6. Write the difference, 1, under the first digit in the dividend. Bring down the next digit of the dividend. Bring down the 8. Divide 18 by the divisor, 3. The divisor 3 goes into 18 six times. Write 6 in the quotient above the 8. Multiply the 6 in the quotient by the divisor and write the product, 18, under the dividend. Subtract 18 from 18. We would repeat the process until there are no more digits in the dividend to bring down. In this problem, there are no more digits to bring down, so the division is finished. So78÷3=26. Check by multiplying the quotient times the divisor to get the dividend. Multiply 26×3 to make sure that product equals the dividend, 78. 216×3___78✓It does, so our answer is correct. Divide the first digit of the dividend by the divisor. If the divisor is larger than the first digit of the dividend, divide the first two digits of the dividend by the divisor, and so on. Write the quotient above the dividend. Multiply the quotient by the divisor and write the product under the dividend. Subtract that product from the dividend. Bring down the next digit of the dividend. Repeat from Step 1 until there are no more digits in the dividend to bring down. Check by multiplying the quotient times the divisor. Divide 2,596÷4. Check by multiplying: Let's rewrite the problem to set it up for long division. Divide the first digit of the dividend, 2, by the divisor, 4. Since 4 does not go into 2, we use the first two digits of the dividend and divide 25 by 4. The divisor 4 goes into 25 six times. We write the 6 in the quotient above the 5. Multiply the 6 in the quotient by the divisor 4 and write the product, 24, under the first two digits in the dividend. Subtract that product from the first two digits in the dividend. Subtract 25−24. Write the difference, 1, under the second digit in the dividend. Now bring down the 9 and repeat these steps. There are 4 fours in 19. Write the 4 over the 9. Multiply the 4 by 4 and subtract this product from 19. Bring down the 6 and repeat these steps. There are 9 fours in 36. Write the 9 over the 6. Multiply the 9 by 4 and subtract this product from 36. So 2,596÷4=649. Check by multiplying. It equals the dividend, so our answer is correct. Divide. Then check by multiplying: 2,636÷4 659 Divide. Then check by multiplying: 2,716÷4 679 Divide 4,506÷6. Check by multiplying: Let's rewrite the problem to set it up for long division. First we try to divide 6 into 4. Since that won't work, we try 6 into 45.There are 7 sixes in 45. We write the 7 over the 5. Multiply the 7 by 6 and subtract this product from 45. Now bring down the 0 and repeat these steps. There are 5 sixes in 30.Write the 5 over the 0. Multiply the 5 by 6 and subtract this product from 30. Now bring down the 6 and repeat these steps. There is 1 six in 6. Write the 1 over the 6. Multiply 1 by 6 and subtract this product from 6. Check by multiplying. It equals the dividend, so our answer is correct. Divide. Then check by multiplying: 4,305÷5. 861 Divide. Then check by multiplying: 3,906÷6. 651 Divide 7,263÷9. Check by multiplying. Let's rewrite the problem to set it up for long division. First we try to divide 9 into 7. Since that won't work, we try 9 into 72. There are 8 nines in 72. We write the 8 over the 2. Multiply the 8 by 9 and subtract this product from 72. Now bring down the 6 and repeat these steps. There are 0 nines in 6. Write the 0 over the 6. Multiply the 0 by 9 and subtract this product from 6. Now bring down the 3 and repeat these steps. There are 7 nines in 63. Write the 7 over the 3. Multiply the 7 by 9 and subtract this product from 63. Check by multiplying. It equals the dividend, so our answer is correct. Divide. Then check by multiplying: 4,928÷7. 704 Divide. Then check by multiplying: 5,663÷7. 809 So far all the division problems have worked out evenly. For example, if we had 24 cookies and wanted to make bags of 8 cookies, we would have 3 bags. But what if there were 28 cookies and we wanted to make bags of 8? Start with the 28 cookies as shown in .

Try to put the cookies in groups of eight as in .

There are 3 groups of eight cookies, and 4 cookies left over. We call the 4 cookies that are left over the remainder and show it by writing R4 next to the 3. (The R stands for remainder.) To check this division we multiply 3 times 8 to get 24, and then add the remainder of 4. 3×8___24+4___28 Divide 1,439÷4. Check by multiplying. Let's rewrite the problem to set it up for long division. First we try to divide 4 into 1. Since that won't work, we try 4 into 14. There are 3 fours in 14. We write the 3 over the 4. Multiply the 3 by 4 and subtract this product from 14. Now bring down the 3 and repeat these steps. There are 5 fours in 23. Write the 5 over the 3. Multiply the 5 by 4 and subtract this product from 23. Now bring down the 9 and repeat these steps. There are 9 fours in 39. Write the 9 over the 9. Multiply the 9 by 4 and subtract this product from 39. There are no more numbers to bring down, so we are done. The remainder is 3. Check by multiplying. So 1,439÷4 is 359 with a remainder of 3. Our answer is correct. Divide. Then check by multiplying: 3,812÷8. 476 with a remainder of 4 Divide. Then check by multiplying: 4,319÷8. 539 with a remainder of 7 Divide and then check by multiplying: 1,461÷13. Let's rewrite the problem to set it up for long division. 131,461 First we try to divide 13 into 1. Since that won't work, we try 13 into 14. There is 1 thirteen in 14. We write the 1 over the 4. Multiply the 1 by 13 and subtract this product from 14. Now bring down the 6 and repeat these steps. There is 1 thirteen in 16. Write the 1 over the 6. Multiply the 1 by 13 and subtract this product from 16. Now bring down the 1 and repeat these steps. There are 2 thirteens in 31. Write the 2 over the 1. Multiply the 2 by 13 and subtract this product from 31. There are no more numbers to bring down, so we are done. The remainder is 5. 1,462÷13 is 112 with a remainder of 5. Check by multiplying. Our answer is correct. Divide. Then check by multiplying: 1,493÷13. 114 R11 Divide. Then check by multiplying: 1,461÷12. 121 R9 Divide and check by multiplying: 74,521÷241. Let's rewrite the problem to set it up for long division. 24174,521 First we try to divide 241 into 7. Since that won’t work, we try 241 into 74. That still won’t work, so we try 241 into 745. Since 2 divides into 7 three times, we try 3. Since 3×241=723, we write the 3 over the 5 in 745. Note that 4 would be too large because 4×241=964, which is greater than 745. Multiply the 3 by 241 and subtract this product from 745. Now bring down the 2 and repeat these steps. 241 does not divide into 222. We write a 0 over the 2 as a placeholder and then continue. Now bring down the 1 and repeat these steps. Try 9. Since 9×241=2,169, we write the 9 over the 1. Multiply the 9 by 241 and subtract this product from 2,221. There are no more numbers to bring down, so we are finished. The remainder is 52. So 74,521÷241is 309 with a remainder of 52. Check by multiplying. Sometimes it might not be obvious how many times the divisor goes into digits of the dividend. We will have to guess and check numbers to find the greatest number that goes into the digits without exceeding them. Divide. Then check by multiplying: 78,641÷256. 307 R49 Divide. Then check by multiplying: 76,461÷248. 308 R77

Earlier in this section, we translated math notation for division into words. Now we’ll translate word phrases into math notation. Some of the words that indicate division are given in . Operation Word Phrase Example Expression Division divided byquotient ofdivided into 12 divided by 4the quotient of 12 and 44 divided into 12 12÷412412/4412 Translate and simplify: the quotient of 51 and 17. The word quotient tells us to divide. the quotient of 51 and 17Translate.51÷17Divide.3We could just as correctly have translated the quotient of 51 and 17 using the notation 1751or5117. Translate and simplify: the quotient of 91 and 13. 91 ÷ 13; 7 Translate and simplify: the quotient of 52 and 13. 52 ÷ 13; 4

We will use the same strategy we used in previous sections to solve applications. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We then translate the phrase into math notation and simplify it to get the answer. Finally, we write a sentence to answer the question. Cecelia bought a 160-ounce box of oatmeal at the big box store. She wants to divide the 160 ounces of oatmeal into 8-ounce servings. She will put each serving into a plastic bag so she can take one bag to work each day. How many servings will she get from the big box? We are asked to find the how many servings she will get from the big box. Write a phrase. 160 ounces divided by 8 ounces Translate to math notation. 160÷8 Simplify by dividing. 20 Write a sentence to answer the question.Cecelia will get 20 servings from the big box. Marcus is setting out animal crackers for snacks at the preschool. He wants to put 9 crackers in each cup. One box of animal crackers contains 135 crackers. How many cups can he fill from one box of crackers? Marcus can fill 15 cups. Andrea is making bows for the girls in her dance class to wear at the recital. Each bow takes 4 feet of ribbon, and 36 feet of ribbon are on one spool. How many bows can Andrea make from one spool of ribbon? Andrea can make 9 bows. Dividing Whole Numbers Dividing Whole Numbers No Remainder Dividing Whole Numbers With Remainder

Operation Notation Expression Read as Result Division ÷ ab baa/b 12÷4 124 41212/4 Twelve divided by four the quotient of 12 and 4 Division Properties of One Any number (except 0) divided by itself is one. a÷a=1 Any number divided by one is the same number. a÷1=a Division Properties of Zero Zero divided by any number is 0. 0÷a=0 Dividing a number by zero is undefined. a÷0 undefined Divide whole numbers. Divide the first digit of the dividend by the divisor. If the divisor is larger than the first digit of the dividend, divide the first two digits of the dividend by the divisor, and so on. Write the quotient above the dividend. Multiply the quotient by the divisor and write the product under the dividend. Subtract that product from the dividend. Bring down the next digit of the dividend. Repeat from Step 1 until there are no more digits in the dividend to bring down. Check by multiplying the quotient times the divisor.

Use Division Notation In the following exercises, translate from math notation to words. 54÷9 fifty-four divided by nine; the quotient of fifty-four and nine 567 328 thirty-two divided by eight; the quotient of thirty-two and eight 642 48÷6 forty-eight divided by six; the quotient of forty-eight and six 639 763 sixty-three divided by seven; the quotient of sixty-three and seven 72÷8 Model Division of Whole Numbers In the following exercises, model the division. 15÷5 10÷5 147 186 420 315 24÷6 16÷4 Divide Whole Numbers In the following exercises, divide. Then check by multiplying. 18÷2 9 14÷2 273 9 303 428 7 436 455 9 355 72/8 9 864 357 5 42÷7 1515 1 1212 43÷43 1 37÷37 231 23 291 19÷1 19 17÷1 0÷4 0 0÷8 50 undefined 90 260 undefined 320 120 0 160 72÷3 24 57÷3 968 12 786 5465 93 4528 924÷7 132 861÷7 5,2266 871 3,7768 431,324 7,831 546,855 7,209÷3 2,403 4,806÷3 5,406÷6 901 3,208÷4 42,816 704 63,624 91,8819 10,209 83,2568 2,470÷7 352 R6 3,741÷7 855,305 6,913 R1 951,492 431,1745 86,234 R4 297,2774 130,016÷3 43,338 R2 105,609÷2 155,735 382 R5 4,93321 56,883÷67 849 43,725/75 30,144314 96 26,145÷415 273542,195 1,986 R17 816,243÷462 Mixed Practice In the following exercises, simplify. 15(204) 3,060 74·391 256−184 72 305−262 719+341 1,060 647+528 25875 35 1104÷23 Translate Word Phrases to Algebraic Expressions In the following exercises, translate and simplify. the quotient of 45 and 15 45 ÷ 15; 3 the quotient of 64 and 16 the quotient of 288 and 24 288 ÷ 24; 12 the quotient of 256 and 32 Divide Whole Numbers in Applications In the following exercises, solve. Trail mix Ric bought 64 ounces of trail mix. He wants to divide it into small bags, with 2 ounces of trail mix in each bag. How many bags can Ric fill? Ric can fill 32 bags. Crackers Evie bought a 42 ounce box of crackers. She wants to divide it into bags with 3 ounces of crackers in each bag. How many bags can Evie fill? Astronomy class There are 125 students in an astronomy class. The professor assigns them into groups of 5. How many groups of students are there? There are 25 groups. Flower shop Melissa’s flower shop got a shipment of 152 roses. She wants to make bouquets of 8 roses each. How many bouquets can Melissa make? Baking One roll of plastic wrap is 48 feet long. Marta uses 3 feet of plastic wrap to wrap each cake she bakes. How many cakes can she wrap from one roll? Marta can wrap 16 cakes from 1 roll. Dental floss One package of dental floss is 54 feet long. Brian uses 2 feet of dental floss every day. How many days will one package of dental floss last Brian? Mixed Practice In the following exercises, solve. Miles per gallon Susana’s hybrid car gets 45 miles per gallon. Her son’s truck gets 17 miles per gallon. What is the difference in miles per gallon between Susana’s car and her son’s truck? The difference is 28 miles per gallon. Distance Mayra lives 53 miles from her mother’s house and 71 miles from her mother-in-law’s house. How much farther is Mayra from her mother-in-law’s house than from her mother’s house? Field trip The 45 students in a Geology class will go on a field trip, using the college’s vans. Each van can hold 9 students. How many vans will they need for the field trip? They will need 5 vans for the field trip Potting soil Aki bought a 128 ounce bag of potting soil. How many 4 ounce pots can he fill from the bag? Hiking Bill hiked 8 miles on the first day of his backpacking trip, 14 miles the second day, 11 miles the third day, and 17 miles the fourth day. What is the total number of miles Bill hiked? Bill hiked 50 miles Reading Last night Emily read 6 pages in her Business textbook, 26 pages in her History text, 15 pages in her Psychology text, and 9 pages in her math text. What is the total number of pages Emily read? Patients LaVonne treats 12 patients each day in her dental office. Last week she worked 4 days. How many patients did she treat last week? LaVonne treated 48 patients last week. Scouts There are 14 boys in Dave’s scout troop. At summer camp, each boy earned 5 merit badges. What was the total number of merit badges earned by Dave’s scout troop at summer camp?

Contact lenses Jenna puts in a new pair of contact lenses every 14 days. How many pairs of contact lenses does she need for 365 days? Jenna uses 26 pairs of contact lenses, but there is 1 day left over, so she needs 27 pairs for 365 days. Cat food One bag of cat food feeds Lara’s cat for 25 days. How many bags of cat food does Lara need for 365 days?

Explain how you use the multiplication facts to help with division. Answers may vary. Using multiplication facts can help you check your answers once you’ve finished division. Oswaldo divided 300 by 8 and said his answer was 37 with a remainder of 4. How can you check to make sure he is correct?

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?

Identify Counting Numbers and Whole Numbers In the following exercises, determine which of the following are (a) counting numbers (b) whole numbers. 0,2,99 ⓐ 2, 99ⓑ 0, 2, 99 0,3,25 0,4,90 ⓐ 4, 90ⓑ 0, 4, 90 0,1,75 Model Whole Numbers In the following exercises, model each number using base-10 blocks and then show its value using place value notation. 258 104 Identify the Place Value of a Digit In the following exercises, find the place value of the given digits. 472,981 ⓐ 8ⓑ 4ⓒ 1ⓓ 7ⓔ 2 ⓐ tensⓑ hundred thousandsⓒ onesⓓ ten thousandsⓔ thousands 12,403,295 ⓐ 4ⓑ 0ⓒ 1ⓓ 9ⓔ 3 Use Place Value to Name Whole Numbers In the following exercises, name each number in words. 5,280 Five thousand, two hundred eighty 204,614 5,012,582 Five million, twelve thousand, five hundred eighty-two 31,640,976 Use Place Value to Write Whole Numbers In the following exercises, write as a whole number using digits. six hundred two fifteen thousand, two hundred fifty-three 15,253 three hundred forty million, nine hundred twelve thousand, sixty-one 340,912,061 two billion, four hundred ninety-two million, seven hundred eleven thousand, two Round Whole Numbers In the following exercises, round to the nearest ten. 412 410 648 3,556 3,560 2,734 In the following exercises, round to the nearest hundred. 38,975 39,000 26,849 81,486 81,500 75,992

Use Addition Notation In the following exercises, translate the following from math notation to words. 4+3 four plus three; the sum of four and three 25+18 571+629 five hundred seventy-one plus six hundred twenty-nine; the sum of five hundred seventy-one and six hundred twenty-nine 10,085+3,492 Model Addition of Whole Numbers In the following exercises, model the addition. 6+7 38+14 Add Whole Numbers In the following exercises, fill in the missing values in each chart. In the following exercises, add. ⓐ 0+19 ⓑ 19+0 ⓐ 19ⓑ 19 ⓐ 0+480 ⓑ 480+0 ⓐ 7+6 ⓑ 6+7 ⓐ 13ⓑ 13 ⓐ 23+18 ⓑ 18+23 44+35 79 63+29 96+58 154 375+591 7,281+12,546 19,827 5,280+16,324+9,731 Translate Word Phrases to Math Notation In the following exercises, translate each phrase into math notation and then simplify. the sum of 30 and 12 30 + 12; 42 11 increased by 8 25 more than 39 39 + 25; 64 total of 15 and 50 Add Whole Numbers in Applications In the following exercises, solve. Shopping for an interview Nathan bought a new shirt, tie, and slacks to wear to a job interview. The shirt cost $24, the tie cost $14, and the slacks cost $38. What was Nathan’s total cost? $76 Running Jackson ran 4 miles on Monday, 12 miles on Tuesday, 1 mile on Wednesday, 8 miles on Thursday, and 5 miles on Friday. What was the total number of miles Jackson ran? In the following exercises, find the perimeter of each figure. 46 feet

Use Subtraction Notation In the following exercises, translate the following from math notation to words. 14−5 fourteen minus five; the difference of fourteen and five 40−15 351−249 three hundred fifty-one minus two hundred forty-nine; the difference between three hundred fifty-one and two hundred forty-nine 5,724−2,918 Model Subtraction of Whole Numbers In the following exercises, model the subtraction. 18−4 41−29 Subtract Whole Numbers In the following exercises, subtract and then check by adding. 8−5 3 12−7 23−9 14 46−21 82−59 23 110−87 539−217 322 415−296 1,020−640 380 8,355−3,947 10,000−15 9,985 54,925−35,647 Translate Word Phrases to Math Notation In the following exercises, translate and simplify. the difference of nineteen and thirteen 19 − 13; 6 subtract sixty-five from one hundred seventy-four decreased by eight 74 − 8; 66 twenty-three less than forty-one Subtract Whole Numbers in Applications In the following exercises, solve. Temperature The high temperature in Peoria one day was 86 degrees Fahrenheit and the low temperature was 28 degrees Fahrenheit. What was the difference between the high and low temperatures? 58 degrees Fahrenheit Savings Lynn wants to go on a cruise that costs $2,485. She has $948 in her vacation savings account. How much more does she need to save in order to pay for the cruise?

Use Multiplication Notation In the following exercises, translate from math notation to words. 8×5 eight times five; the product of eight and five 6·14 (10)(95) ten times ninety-five; the product of ten and ninety-five 54(72) Model Multiplication of Whole Numbers In the following exercises, model the multiplication. 2×4 3×8 Multiply Whole Numbers In the following exercises, fill in the missing values in each chart. In the following exercises, multiply. 0·14 0 (256)0 1·99 99 (4,789)1 ⓐ 7·4 ⓑ 4·7 ⓐ 28ⓑ 28 (25)(6) 9,261×3 27,783 48·76 64·10 640 1,000(22) 162×493 79,866 (601)(943) 3,624×517 1,873,608 10,538·22 Translate Word Phrases to Math Notation In the following exercises, translate and simplify. the product of 15 and 28 15(28); 420 ninety-four times thirty-three twice 575 2(575); 1,150 ten times two hundred sixty-four Multiply Whole Numbers in Applications In the following exercises, solve. Gardening Geniece bought 8 packs of marigolds to plant in her yard. Each pack has 6 flowers. How many marigolds did Geniece buy? 48 marigolds Cooking Ratika is making rice for a dinner party. The number of cups of water is twice the number of cups of rice. If Ratika plans to use 4 cups of rice, how many cups of water does she need? Multiplex There are twelve theaters at the multiplex and each theater has 150 seats. What is the total number of seats at the multiplex? 1,800 seats Roofing Lewis needs to put new shingles on his roof. The roof is a rectangle, 30 feet by 24 feet. What is the area of the roof?

Use Division Notation Translate from math notation to words. 54÷9 fifty-four divided by nine; the quotient of fifty-four and nine 42/7 728 seventy-two divided by eight; the quotient of seventy-two and eight 648 Model Division of Whole Numbers In the following exercises, model. 8÷2 312 Divide Whole Numbers In the following exercises, divide. Then check by multiplying. 14÷2 7 328 52÷4 13 2626 971 97 0÷52 100÷0 undefined 3555 3828÷6 638 311,519 750525 300 R5 5,166÷42 Translate Word Phrases to Math Notation In the following exercises, translate and simplify. the quotient of 64 and 16 64 ÷ 16; 4 the quotient of 572 and 52 Divide Whole Numbers in Applications In the following exercises, solve. Ribbon One spool of ribbon is 27 feet. Lizbeth uses 3 feet of ribbon for each gift basket that she wraps. How many gift baskets can Lizbeth wrap from one spool of ribbon? 9 baskets Juice One carton of fruit juice is 128 ounces. How many 4 ounce cups can Shayla fill from one carton of juice?

Determine which of the following numbers are ⓐ counting numbersⓑ whole numbers.0,4,87 ⓐ 4, 87ⓑ 0, 4, 87 Find the place value of the given digits in the number 549,362. ⓐ 9ⓑ 6ⓒ 2ⓓ 5 Write each number as a whole number using digits. ⓐ six hundred thirteenⓑ fifty-five thousand two hundred eight ⓐ 613ⓑ 55,208 Round 25,849 to the nearest hundred. Simplify. 45+23 68 65−42 85÷5 17 1,000×8 90−58 32 73+89 (0)(12,675) 0 634+255 09 0 8128 145−79 66 299+836 7·475 3,325 8,528+704 35(14) 490 260 733−291 442 4,916−1,538 495÷45 11 52×983 Translate each phrase to math notation and then simplify. The sum of 16 and 58 16 + 58; 74 The product of 9 and 15 The difference of 32 and 18 32 − 18; 14 The quotient of 63 and 21 Twice 524 2(524); 1,048 29 more than 32 50 less than 300 300 − 50; 250 In the following exercises, solve. LaVelle buys a jumbo bag of 84 candies to make favor bags for her son’s party. If she wants to make 12 bags, how many candies should she put in each bag? Last month, Stan’s take-home pay was $3,816 and his expenses were $3,472. How much of his take-home pay did Stan have left after he paid his expenses? Stan had $344 left. Each class at Greenville School has 22 children enrolled. The school has 24 classes. How many children are enrolled at Greenville School? Clayton walked 12 blocks to his mother’s house, 6 blocks to the gym, and 9 blocks to the grocery store before walking the last 3 blocks home. What was the total number of blocks that Clayton walked? Clayton walked 30 blocks.

dividend When dividing two numbers, the dividend is the number being divided. divisor When dividing two numbers, the divisor is the number dividing the dividend. quotient The quotient is the result of dividing two numbers.