All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 10 Lesson 4 Multiply Whole Numbers and Fractions** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 10 Lesson 4 Multiply Whole Numbers and Fractions

**Math in My World**

Example 1

Wild parrots spend \(\frac{1}{6}\) of the day looking for food. How many hours a day does a parrot spend looking for food?

Find \(\frac{1}{6}\) × 24. ← There are 24 hours in a

\(\frac{1}{6}\) × 24 = \(\frac{1}{6}\) × \(\frac{24}{1}\) Write 24 as a fraction.

\(\frac{1 \times 24}{6 \times 1}\) ← Multiply the numerators

← Multiply the denominators

= \(\frac{24}{6}\) or _____ Simplify

So, a wild parrot spends _____ hours a day looking for food.

Check \(\frac{1}{6}\) × 24 = 1 × 24 ÷ 6, or _____

Answer:

The day a wild parrot can spend looking for food = 1/6.

The number of hours in a day = 24.

We need to find out the time. Let it be H.

H = 1/6 x 24

Now write 24 as a fraction.

Therefore, a wild parrot spends 4 hours looking for food.

**Key Concept Multiply Fractions**

To multiply a whole number by a fraction, write the whole number as a fraction. Then multiply the numerators and multiply the denominators.

Example 2

Find the unknown in 2 × \(\frac{4}{5}\) = .

Estimate 2 × 1 = ___2_

**Helpful Hint**

Multiplication is commutative.

2 × \(\frac{4}{5}\) = \(\frac{4}{5}\) × 2

2 × \(\frac{4}{5}\) = \(\frac{2}{1}\) × \(\frac{4}{5}\) write 2 as a fraction

= \(\frac{2 \times 4}{1 \times 5}\) ← Multiply the numerators

← Multiply the denominators

Answer:

The above-given equation:

2 x 4/5

Now we have to write 2 as a fraction.

2/1 x 4/5 =

**Talk Math**

Explain how you could find the product of 50 and \(\frac{2}{5}\) mentally.

Answer:

The above-given:

50 x 2/5

write 50 as a fraction

50/1 x 2/5

**Guided Practice**

Question 1.

Find \(\frac{1}{2}\) × 4. Write in simplest form.

\(\frac{1}{2}\) × 4 = \(\frac{1}{2}\) × \(\frac{4}{1}\) write 4 as \(\frac{4}{1}\)

= \(\frac{1 \times 4}{2 \times 1}\) Multiply

= or _____ simplify

So, \(\frac{1}{2}\) × 4 = ______.

Answer:

The above-given:

1/2 x 4

write 4 as a fraction.

Therefore, \(\frac{1}{2}\) × 4 = 2.

**Independent Practice**

**Multiply. Write in simplest form.**

Question 2.

\(\frac{1}{3}\) × 12 = ____

Answer:

The above-given:

1/3 x 12

write 12 in fractions.

Therefore, \(\frac{1}{3}\) × 12 = 4.

Question 3.

\(\frac{1}{4}\) × 20 = ____

Answer:

The above-given equation:

1/4 x 20

write 20 as a fraction

= 1/4 x 20/1

= 1 x 20/ 4 x 1

= 20 / 4

= 5

Therefore, \(\frac{1}{4}\) × 20 = 5

Question 4.

\(\frac{5}{6}\) × 18 = ____

Answer:

The above-given equation:

5/6 x 18

write 18 as a fraction

= 5/6 x 18/1

Therefore, \(\frac{5}{6}\) × 18 = 15

Question 5.

\(\frac{1}{5}\) × 7 = ____

Answer:

The above-given equation:

1/5 x 7

write 7 as a fraction

Therefore, \(\frac{1}{5}\) × 7 = 1 2/5.

Question 6.

\(\frac{2}{3}\) × 14 = ____

Answer:

The above-given equation:

2/3 x 14

write 14 as a fraction,

Therefore, \(\frac{2}{3}\) × 14 = 9 1/3.

Question 7.

\(\frac{2}{5}\) × 11 = ____

Answer:

The above-given equation:

2/5 x 11

write 11 as a fraction

Therefore, \(\frac{2}{5}\) × 11 = 4 2/5

Question 8.

12 × \(\frac{1}{6}\) = ____

Answer:

The above-given equation:

12 x 1/6

write 12 as a fraction

Therefore, 12 × \(\frac{1}{6}\) = 2

Question 9.

13 × \(\frac{2}{13}\) = ____

Answer:

The above-given equation:

13 x 2/13

write 13 as a fraction

Therefore, 13 × \(\frac{2}{13}\) = 2

Question 10.

24 × \(\frac{3}{4}\) = ____

Answer:

The above-given equation:

24 x 3/4

write 24 as a fraction.

Therefore, 24 × \(\frac{3}{4}\) = 18

**Mathematical Practice 2 Use Algebra Find the unknown in each equation. Write in simplest form.**

Question 11.

5 × \(\frac{1}{4}\) =

= ____

Answer:

The above-given equation:

5 x 1/4

write 5 as a fraction.

Therefore, 5 × \(\frac{1}{4}\) = 1 1/4.

Question 12.

15 × \(\frac{7}{10}\) =

= ____

Answer:

The above-given:

15 x 7/10

write 15 as a fraction.

Therefore, 15 × \(\frac{7}{10}\) = 10 1/2

Question 13.

32 × \(\frac{5}{6}\) =

= ____

Answer:

The above-given:

32 x 5/6

write 32 as a fraction.

Therefore, 32 × \(\frac{5}{6}\) = 26 2/3

**Problem Solving**

Question 14.

Arleta is making nacho cheese dip for a party. She needs to make 5 batches. How much salsa will she need?

Answer:

The number of batches she needs to make = 5

The salsa she need = S

S = 5 x 1/2

S = 5/2

In mixed fraction, we can write 2 1/2

Therefore, she needs 2 1/2 cups of salsa.

Question 15.

Maria ate \(\frac{1}{4}\) of a pizza. If there were 20 slices of pizza, how many slices did Maria eat?

Answer:

The above-given:

The amount of pizza Maria ate = 1/4

The number of slices of pizza she has = 20

The number of slices she ate = P

P = 1/4 x 20

P = 5

Therefore, she ate 5 slices of pizza.

Question 16.

**Mathematical PRACTICE 4 Model Math** Write and solve a real-world problem that involves multiplying 8 × \(\frac{5}{8}\).

Answer:

Maria ate \(\frac{5}{8}\) of a pizza. If there were 8 slices of pizza, how many slices did Maria eat?

The equation is given:

8 x 5/8 = 5

8 and 8 get cancelled and the remaining number is 5

Therefore, she ate 5 slices of pizza.

**HOT Problems**

Question 17.

**Mathematical PRACTICE 3 Which One Doesn’t Belong?** Circle the expression that does not belong with the other three Explain.

\(\frac{1}{2}\) × 12 9 × \(\frac{2}{3}\) \(\frac{1}{4}\) × 20 \(\frac{1}{6}\) × 36

Answer:

The above-given equations:

1/2 x 12 = 6

2/3 x 9 = 6

1/4 x 20 = 5

1/6 x 36 = 6

\(\frac{1}{4}\) × 20 does not belong with the other three.

If I could change the 20 to 24 then the product would be 6.

Question 18.

**? Building on the Essential Question** Can all whole numbers be written as fractions? Explain.

Answer:

Yes, any whole number can be written as a fraction by placing the whole number over a denominator of 1.

Suppose we have a whole number 6 and we want to represent it as a fraction.

It needs to be of the form p/q.

So the numerator p will be 6 and the denominator q will be 1 to give 6/1.

Thus, we divide the whole number by 1 to represent it as a fraction.

### McGraw Hill My Math Grade 5 Chapter 10 Lesson 4 My Homework Answer Key

**Practice**

**Multiply. Write in the simplest form.**

Question 1.

\(\frac{2}{3}\) × 12 = ____

Answer:

The above-given equation:

2/3 x 12

write 12 as a fraction

Therefore, \(\frac{2}{3}\) × 12 = 8

Question 2.

\(\frac{3}{10}\) × 8 = ____

Answer:

The above-given equation:

3/10 x 8

write 8 as a fraction

Therefore, \(\frac{3}{10}\) × 8 = 2 2/5.

Question 3.

8 × \(\frac{1}{5}\) = ____

Answer:

The above-given equation:

8 x 1/5

write 8 as a fraction.

= 8/1 x 1/5

= 8/5

In mixed fractions, we can write as 1 3/5.

Question 4.

13 × \(\frac{1}{2}\) = ____

Answer:

The above-given equation:

13 x 1/2

write 13 as a fraction

13/1 x 1/2

= 13/2

In mixed fractions, we can write 6 1/2.

Question 5.

20 × \(\frac{3}{5}\) = ____

Answer:

The above-given equation:

20 x 3/5

write 20 as a fraction

= 20/1 x 3/5

= 60/5

= 12

Therefore, 20 × \(\frac{3}{5}\) = 12

Question 6.

\(\frac{3}{10}\) × 7 = ____

Answer:

The above-given equation:

3/10 x 7

write 7 as a fraction

= 3/10 x 7/1

= 21/10

In mixed fractions, we can write as 2 1/10.

**Problem Solving**

Question 7.

The length of a popcorn machine is \(\frac{3}{4}\) of its height. What is the length of the machine?

Answer:

The above-given:

The length of popcorn = 3/4

The height of the machine = 24

The length of the machine = M

M = 24 x 3/4 [ 4 x 6 = 24]

M = 6 x 3

M = 18

Question 8.

Quinten is making bread and wants to triple the recipe. The recipe calls for \(\frac{2}{3}\) cup of sugar. How much sugar will he need?

Answer:

The above-given:

Quinten wants to triple the recipe means 3 times.

The equation can be written as:

2/3 x 3 = 2/3 + 2/3 + 2/3

If we solve the equation 2/3 x3

write 3 as a fraction.

2/3 x 3/1

= 2 x 3/ 3 x 1

= 6/3

= 2.

Therefore, he needs e cups of sugar.

Question 9.

Joaquin has $24. He used \(\frac{5}{8}\) of his money to buy a pair of jeans. How much money did Joaquin spend on jeans?

Answer:

The above-given:

The amount Joaquin has = 24

The amount of money he used = 5/8

The money he spends on jeans = J

J = 24 x 5/8 [ 8 x 3 = 24]

J = 3 x 5

J = 15

Therefore, he spends $15 on jeans.

Question 10.

**Mathematical PRACTICE 2 Use Number Sense** Write and solve a real-world problem involving the multiplication of a fraction and a whole number whose product is between 10 and 15.

Answer:

Jean is working in a pizza shop. She has 60 kg of flour. She has used one-sixth of it for making pizzas. How much flour does she need?

60 x 1/6 = 10

therefore, the product is 10.

If we replace 1/6 with 1/4

– Jean is working in a pizza shop. She has 60 kg of flour. She has used one-fourth of it for making pizzas. How much flour does she need?

60 x 1/4 = 15

Therefore, the product is 15.

**Test Practice**

Question 11.

Rico is making punch for 18 people. How much punch should Rico make if each person will drink \(\frac{1}{6}\) gallon of punch?

A. 2 gallons

B. 3 gallons

C. 4 gallons

D. 5 gallons

Answer: Option B is correct.

The above-given:

The number of people = 18

The gallon of punch = 1/6

The number of punch = P

P = 1/6 x 18

P = 3

Therefore, he can make 3 punches.