Estimating Products and Quotients

Lesson 5.5

• 1. 2• 2. 2• 3. 4• 4. 8• 5. 6• 6. 7• 7. 4• 8. 3• 9. 3• 10. 2 times• 11. a. 2 • b. 2 • c. 4 • d. 6• 12. 2 _ 3• 13. 1 3 _ 7• 14. 4 1 _ 6

• 15. 1 2 _ 3• 16. 2 2 _ 5• 17. 1 3 _ 7• 18. 5 _ 8• 19. 1 1 _ 2• 20. 1 1 _ 3• 21. 5 1 _ 3 sections• 22. 12 servings• 23. 6_8 ÷ 2_8 = 3 or 3_4 ÷ 2_8 = 3

or • 6_8 ÷ 1_4 = 3 or 3_4 ÷ 1_4 = 3 • 24. 2_3 ÷ 1_3 = 2 • 25. 7_8 • 26. 4_9 • 27. 5 11 _ _15• 28. 3 1__12

Warm-Up1. 6 × ? = 72

2. ? × 9 = 63

3. What is of 20?

4. What is of 30?

12

7

15

10

Estimating Products and Quotients

Estimate products and quotients using compatible numbers.

Lesson 5.5

Good to Know!Finding exact answers to problems involving multiplying and dividing fractions takes time and requires the use of paper and pencil.

Compatible numbers are very important when estimating products and quotients. Compatible numbers are numbers that are easy to mentally compute.

Example: and 24 are compatible numbers14

1 1 of 24 = 24 6

4 4

Estimating Using Compatible Numbers

Use COMPATIBLE NUMBERS that are easier to compute with

OR

ROUND to the nearest whole number

Explore! 4-H Club

The Barnyard Critters 4-H Club held a fundraiser for their club. Each member raised money separately. The club leader collected all of the money. The pie chart to the right shows the fraction of the money spent on each type of animal the club members raise.

Step 1 Parrish collected $28 during the fundraiser. He wants to determine the amount of his money that was spent on goats.

a. What calculation could Parrish do to find the exact answer?b. Parrish wants to estimate the answer in his head. He changed the

amount he collected to a number that is compatible with . Which number, 27 or 29, is more compatible with ? Why?

c. Use this number to determine the approximate amount of Parrish’s funds spent on goats.

3

13

1

of the money raised by the 4-H club goes to pigs. Nichole raised $35. She wants to determine the amount of her money that will be spent on pigs.

Explore! 4-H Club

a. What calculation could Nichole do to find the exact answer?

b. Nichole estimated the answer in her head. What whole number close to 35 is compatible with ? Why?

c. Use this number to determine the approximate amount of Nichole’s funds spent on pigs.

6

1

6

1

EX Estimate each of the following calculations using compatible numbers. Explain in words why you chose the numbers you did.

Explore! 4-H Club

a. b. c.203

1 17

5

1

8

138

Example 1Estimate the value of .

The number 20 cannot beequally divided into sixths.

List the multiples of 6.

Example 2Johanna has a inch long piece of tubing for her science project. The project directions suggest cutting the tubinginto inch long pieces. About how many pieces will she be able to cut?

1453

238

Example 3Jack needed about cups of dirt for each pot he was filling. He had pots left to fill. Approximately how much dirt does he still need?

345

144

Communication PromptWhy would you want to estimate to find approximate answers for problems that include fractions or mixed numbers?

Exit Problems

1. Estimate using compatible numbers.

2. Estimate using compatible numbers.

3. Estimate using compatible numbers.

4. Merrick had pounds of dog food. He ran a kennel and fed the dogs about pounds of food each day. About how many days can he use this bag of dog food before he runs out?

433

1

54

41 547

97

81 45

5133

314

14

8

25

about 8 days