All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 10 Lesson 2 Estimate Products of Fractions** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 10 Lesson 2 Estimate Products of Fractions

**Math in My World**

Example 1

About \(\frac{1}{3}\) of the containers of yogurt in a box are strawberry. If the box contains 17 containers. about how many containers are strawberry?

Estimate \(\frac{1}{3}\) × 17.

Use compatible numbers.

\(\frac{1}{3}\) × 17 ≈ \(\frac{1}{3}\) × ____ ← What number is close to 17 and also compatible with 3?

Complete the bar diagram to find the product of \(\frac{1}{3}\) × ____.

How many yoghurt containers are represented in each section of the bar diagram? ____

So, \(\frac{1}{3}\) × 18 = ____

About ____ yoghurt containers are strawberry.

Answer:

The above-given:

1/3 x 17

The number is close to 17 and compatible with 3.

The number is 18.

1/3 x 18 = 6

Therefore, 6 yoghurt containers are strawberry.

**Helpful Hint**

\(\frac{1}{3}\) × 18 is the same as 18 ÷ 3.

Example 2

Estimate \(\frac{2}{5}\) × \(\frac{6}{7}\).

Use a number line to round each fraction to 0, \(\frac{1}{2}\) or 1.

So, \(\frac{2}{5}\) × \(\frac{6}{7}\) is about

Answer:

The above-given:

2/5 is about 1.

6/7 is about to 1.

Now substituted the values.

Therefore, 2/5 x 6/7 is about 1/2.

Example 3

Estimate 7\(\frac{2}{7}\) × 3\(\frac{7}{8}\).

Round each mixed number to the nearest whole number.

Round 7\(\frac{2}{7}\) down to ____ and round 3\(\frac{7}{8}\) up to ____

7\(\frac{2}{7}\) × 3\(\frac{7}{8}\) ≈ ____ × ____

≈ ____

So, 7\(\frac{2}{7}\) × 3\(\frac{7}{8}\) is about ____

Answer:

The above-given:

7 2/7 x 3 7/8

The given fractions are mixed fractions.

7 2/7 = 7 x 7/7 + 2/7 = 49/7 + 2/7 = 51/7 = 7.28 (the closest number is 7)

3 7/8 = 8 x 3/8 + 7/8 = 24/8 + 7/8 = 31/8 = 3.875 (the closest number is 4)

So, we can write,

7 2/7 + 3 7/8 = 7 x 4 = 28

Therefore, 7\(\frac{2}{7}\) × 3\(\frac{7}{8}\) is about 28.

**Talk Math**

Explain how you would estimate the product of \(\frac{4}{5}\) × \(\frac{5}{6}\).

Answer:

The above-given product:

4/5 x 5/6

The estimated value of 4/5 is 1

The estimated value of 5/6 is 1

Multiply the products.

The product = 1 x 1 = 1.

Therefore, the estimated product of \(\frac{4}{5}\) × \(\frac{5}{6}\) is 1.

**Guided Practice**

Question 1.

Estimate the product of \(\frac{1}{2}\) × 25. Use compatible numbers.

\(\frac{1}{2}\) × 25 ≈ \(\frac{1}{2}\) × ____ Think: What is half of 24?

So, \(\frac{1}{2}\) × 25 is about ____

Answer:

The above-given:

1/2 x 25 ≈ 1/2 x 24

Now calculate for 1/2 of 24

1/2 x 24 = 12

Therefore, \(\frac{1}{2}\) × 25 is about 12.

**Independent Practice**

**Estimate each product. Draw a bar diagram if necessary.**

Question 2.

\(\frac{1}{2}\) × 13

Answer:

The above-given

1/2 x 13

The estimated value would be 12

1/2 x 12 = 6

Therefore, the answer is 6.

Question 3.

\(\frac{1}{3}\) × 20

Answer:

The above-given:

1/3 x 20

Now round up the product 20 to 21.

Now the product is

1/3 x 21 = 7

Now draw the bar diagram:

Therefore, the answer is 7.

Question 4.

\(\frac{1}{2}\) × 33

Answer:

The above-given:

1/2 x 33

Now we can round down the value from 33 to 32.

The estimated product:

1/2 x 32 = 16

The bar diagram is represented as:

Therefore, the answer is 16.

Question 5.

17 × \(\frac{1}{4}\)

Answer:

The above-given:

17 x 1/4

Now we can round down the product from 17 to 16.

16 x 1/4 = 4

Now the bar diagram is represented as:

we have to divide the four sections as the denominator is having 4.

Therefore, the answer is 4.

Question 6.

\(\frac{7}{8}\) × \(\frac{1}{9}\)

Answer:

The above-given:

The estimated value of 7/8 = 0.875 (the closest value is 1)

The estimated value of 1/9 = 0.11 (the closest value is 0)

Now multiply both the estimated products.

The product = 1 x 0 = 0

Therefore, the answer is 0.

Question 7.

\(\frac{3}{5}\) × \(\frac{8}{9}\)

Answer:

The above-given:

3/5 x 8/9

Now we have to find out the estimated products.

The estimated value of 3/5:

3/5 ≈ 2/4 = 1/2

The estimated value of 8/9 = 1

Now multiply both the products.

The product = 1/2 x 1 = 1/2.

Question 6.

\(\frac{1}{6}\) × \(\frac{5}{7}\)

Answer:

The above-given:

1/6 x 5/7

Now we have to find out the estimated products.

The estimated value of 1/6 is 0.

The estimated value of 5/7 is 1

Now multiply the products.

The product: 1 x 0 = 0

Therefore, the estimated product of \(\frac{1}{6}\) × \(\frac{5}{7}\) is 0.

Question 7.

\(\frac{1}{4}\) × \(\frac{8}{9}\)

Answer:

The above-given:

1/4 x 8/9

Now we have to find out the estimated products.

The estimated value of 1/4 is 0

The estimated value of 8/9 is 1

Now multiply both the products

The product = 0 x 1 = 0

Therefore, the estimated product of \(\frac{1}{4}\) × \(\frac{8}{9}\) is 0.

Question 8.

\(\frac{1}{6}\) × \(\frac{5}{7}\)

Answer:

The above-given:

1/6 x 5/7

Now we have to find out the estimated products.

The estimated value of 1/6 is 0.

The estimated value of 5/7 is 1

Now multiply the products.

The product: 1 x 0 = 0

Therefore, the estimated product of \(\frac{1}{6}\) × \(\frac{5}{7}\) is 0.

Question 9.

\(\frac{1}{4}\) × \(\frac{8}{9}\)

Answer:

The above-given:

1/4 x 8/9

Now we have to find out the estimated products.

The estimated value of 1/4 is 0

The estimated value of 8/9 is 1

Now multiply both the products

The product = 0 x 1 = 0

Therefore, the estimated product of \(\frac{1}{4}\) × \(\frac{8}{9}\) is 0.

Question 10.

2\(\frac{2}{3}\) × 3\(\frac{1}{6}\)

Answer:

The above-given:

2 2/3 x 3 1/6

They are in mixed fractions, now convert them into proper fractions.

2 2/3 = 3 x 2/3 + 2/3 = 6/3 + 2/3 = 8/3.

3 1/6 = 6 x 3/6 + 1/6 = 18/6 + 1/6 = 19/6

The estimated value of 8/3 is 3

The estimated value of 19/6 is 3

Now multiply both the estimated values.

The product = 3 x 3 = 9

Therefore, the estimated product of 2\(\frac{2}{3}\) × 3\(\frac{1}{6}\) is about 9.

Question 11.

6\(\frac{4}{5}\) × 5\(\frac{7}{8}\)

Answer:

The above-given:

6 4/5 x 5 7/8

They are in mixed fractions, now convert them into proper fractions.

6 4/5 = 5 x 6/5 + 4/5 = 30/5 + 4/5 = 34/5

5 7/8 = 8 x 5/8 + 7/8 = 40/8 + 7/8 = 47/8

Now we have to find out the estimated products.

The estimated value of 34/5:

34/5 ≈ 35/5 = 7

The estimated value of 47/8

47/8 ≈ 48/8 = 6

Now multiply both the products.

The product = 7 x 6 = 42.

Therefore, the estimated product of 6\(\frac{4}{5}\) × 5\(\frac{7}{8}\) is about 42.

Question 12.

10\(\frac{1}{7}\) × 4\(\frac{4}{5}\)

Answer:

The above-given:

10 1/7 x 4 4/5

They are in mixed fractions, now convert them into proper fractions.

10 1/7 = 7 x 10/7 + 1/7 = 70/7 + 1/7 = 71/7

4 4/5 = 5 x 4/5 + 4/5 = 20/5 + 4/5 = 24/5

Now we have to find out the estimated products.

The estimated value of 71/7

71/7 ≈ 70/7 = 10

The estimated value of 24/5

24/5 ≈ 25/5 = 5

Now multiply both the products.

The product = 10 x 5 = 50

Therefore, the estimated product of 10\(\frac{1}{7}\) × 4\(\frac{4}{5}\) is about 50.

Question 13.

2\(\frac{6}{7}\) × 6\(\frac{2}{9}\)

Answer:

The above-given:

2 6/7 x 6 2/9

They are in mixed fractions, now convert them into proper fractions.

2 6/7 = 7 x 2/7 + 6/7 = 14/7 + 6/7 = 20/7

6 2/9 = 9 x 6/9 + 2/9 = 54/9 + 2/9 = 56/9

Now we have to find out the estimated products.

The estimated value of 20/7

20/7 ≈ 18/6 = 3

The estimated value of 56/9

56/9 ≈ 60/10 = 6

Now multiply both the products.

The product = 3 x 6 = 18

Therefore, the estimated product of 2\(\frac{6}{7}\) × 6\(\frac{2}{9}\) is about 18.

**Problem Solving**

Question 14.

A cup of chocolate chips weighs about 9 ounces. A recipe calls for 3\(\frac{3}{4}\) cups of chocolate chips. About how many ounces of chocolate chips are needed?

Answer:

The above-given:

The weight of a cup of chocolate chips = 9

The number of cups of chocolate chips a recipe calls = 3 3/4 = 15/4

The estimated value for 15/4:

15/4 ≈ 16/4 = 4.

Now we need to find out the number of ounces of chocolate chips needed. Let it be C.

C = 9 x 4

C = 36.

Therefore, 36 ounces of chocolate chips are needed.

Question 15.

**Mathematical PRACTICE 5 Use Math Tools** Isabella sent out 22 invitations to her birthday party. If about \(\frac{1}{4}\) of the invitations are for her school friends, how many invitations are for her school friends? Draw a bar diagram to help you solve.

Answer:

The above-given:

The number of invitationsIsabella sent to her birthday party = 22

The number of invitations for school friends = 1/4 (in fractions given)

Now we need to find out in number.

The number of invitations = S

S = 22 x 1/4

Now we can estimate the value of 22.

The estimated value of 22 is 24.

S = 24 x 1/4

S = 6

The bar diagram can be represented as:

Therefore, she sent 6 invitations for her school friends.

**HOT Problems**

Question 16.

**Mathematical PRACTICE 1 Make a Plan** Write a real-world problem involving the multiplication of two mixed numbers whose product is about 14. Then solve the problem.

Answer:

Chelsie has 2 1/2 containers to put her special designer fabric that is 6 1/2 inches long. Chelsie currently has 2 copies. how many inches long is both fabric?

Solving the equation:

The equation: 2 1/2 x 6 1/2 = 14

2 1/2: it is in a mixed fraction, now convert it into a proper fraction.

2 1/2 = 2 x 2/2 + 1/2 = 4/2 + 1/2 = 5/2

6 1/2 = 2 x 6/2 + 1/2 = 12/2 + 1/2 = 13/2.

The estimated value of 5/2:

5/2 ≈ 4/2 = 2

The estimated value of 13/2

13/2 ≈ 14/2 = 7

Now multiply both the products.

The product = 2 x 7 = 14

Therefore, the answer is proved.

Question 17.

**? Building on the Essential Question** Explain when estimation would not be the best method for solving a problem.

Answer:

Even the most seasoned project management professionals can draft estimates that miss the mark. When they occur they’re usually off by just a little, though occasionally they’re off by miles. But because so much of the project management process relies on these estimates, even a minor flaw can have a large impact on the team’s ability to achieve success.

– Finally, in projects, we cannot use estimations that lead to calculation errors and miscommunications about the information received from the external partner.

### McGraw Hill My Math Grade 5 Chapter 10 Lesson 2 My Homework Answer Key

**Practice**

**Estimate each product. Draw a bar diagram if necessary.**

Question 1.

\(\frac{2}{3}\) × 26

Answer:

The above-given:

2/3 x 26

We can estimate 26 as 27.

2/3 x 27 = 2 x 9 = 18

The bar diagram can be represented as:

– we need to divide 3 sections as the value of the denominator is 3.

The fraction is 2/3 so we rounded two 9’s.

The answer is 18.

Therefore, the estimated product of \(\frac{2}{3}\) × 26 is about 18.

Question 2.

\(\frac{7}{8}\) × \(\frac{5}{6}\)

Answer:

The above-given:

7/8 x 5/6

The estimated value of 7/8 is 1

The estimated value of 5/6 is 1

Now multiply both the estimated products.

The product = 1 x 1 = 1

Therefore, the estimated product of \(\frac{7}{8}\) × \(\frac{5}{6}\) is about 1.

Question 3.

5\(\frac{1}{5}\) × 8\(\frac{5}{6}\)

Answer:

The above-given:

5 1/5 x 8 5/6

They are in mixed fractions, now convert them into proper fractions.

5 1/5 = 5 x 5/5 +1/5 = 25/5 + 1/5 = 26/5

8 5/6 = 6 x 8/6 + 5/6 = 48/6 + 5/6 = 53/6

Now we have to find out the estimated product.

The estimated value of 26/5:

26/5 ≈ 25/5 = 5

The estimated value of 53/6:

53/6 ≈ 54/6 = 9

Now multiply both the estimated products

The product = 5 x 9 = 45

Therefore, the estimated product of 5\(\frac{1}{5}\) × 8\(\frac{5}{6}\) is about 45.

**Problem Solving**

**Use the table to answer Exercises 4 and 5.**

Question 4.

**Mathematical PRACTICE 3 Justify Conclusions** The table shows the results of a class survey about pets. Suppose 53 students were surveyed. About how many students have one pet? Justify your answer.

Answer:

The number of students was surveyed = 53

The number of students has one pet = P

P = 1/2 x 53

We can estimate the number 53 as 50.

P = 1/2 x 50

P = 25

Therefore, 25 students have one pet.

Question 5.

If 100 students are surveyed, about how many students own 2 or more pets? Explain.

Answer:

The number of students surveyed = 100

The number of students who own 2 or more pets = P1

P1 = 9/20 x 100

P1 = 9 x 5

P1 = 45

Therefore, 45 student owns 2 or more pets.

Question 6.

A rectangular floor measures 10\(\frac{1}{8}\) feet by 13\(\frac{3}{4}\) feet. If Mary buys 150 square feet of carpet, will she have enough carpet to cover the floor?

Answer:

The number of square feet of carpet Mary buys = 150

The given measurements of the floor:

The given mixed fractions are:

10 1/8 and 13 3/4

Convert them into proper fractions.

10 1/8 = 81/8; 13 3/4 = 55/4

The estimated value of 81/8:

81/8 ≈ 80/8 = 10

The estimated value of 55/4

55/4 ≈ 52/4 = 13

Now multiply both the products:

The product = 10 x 13 = 130.

Yes, she has enough carpet to cover the floor.

**Test Practice**

Question 7.

A cup of water holds about 8 ounces. If a recipe calls for \(\frac{1}{3}\) cup of water, which is the best estimate of the number of ounces that are needed? Draw a bar diagram if necessary.

A. 1 ounce

B. 3 ounces

C. 6 ounces

D. 8 ounces

Answer: Option B is correct.

Explanation:

The above-given:

The number of ounces of water a cup can hold = 8

The cup of water a recipe calls = 1/3

The best estimation. Let it be O.

O = 8 x 1/3

We can estimate 8 as 9.

O = 9 x 1/3

O = 3

Therefore, 3 ounces are needed.

The bar diagram can be represented as: