Refer to our Texas Go Math Grade 5 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 5 Lesson 6.4 Answer Key Divide Fractions and Whole Numbers.

## Texas Go Math Grade 5 Lesson 6.4 Answer Key Divide Fractions and Whole Numbers

**Investigate**

Materials; fraction strips

A. Mia walks a 2-mile fitness trail. She stops to exercise every \(\frac{1}{5}\) mile. How many times does Mia stop to exercise?

Draw a number line from 0 to 2. Divide the number line into fifths. Label each fifth on your number line.

Skip count by fifths from 0 to 2 to find 2 ÷ \(\frac{1}{5}\).

There are ________ one-fifths in 2 wholes.

You can use the relationship between multiplication and division to explain and check your solution.

Record and check the quotient.

2 ÷ \(\frac{1}{5}\) = ________ because ________ × \(\frac{1}{5}\) = 2.

So, Mia stops to exercise ________ times.

Answer:

We have to draw a number line from 0 to 2. Divide the number line into fifths. We have to label each fifth on our number line.

Skip count by fifths from 0 to 2 to find 2 ÷ (1/5).

There are **10** one-fifths in 2 wholes.

We can use the relationship between multiplication and division to explain and check our solution.

Record and check the quotient.

2 ÷ (1/5) =**10** because **10** × \(\frac{1}{5}\) = 2.

So, Mia stops to exercise** 10** times.

B. Roger has 2 yards of string. He cuts the string into pieces that are \(\frac{1}{3}\) yard long. How many pieces of string does Roger have?

Model 2 using 2 whole fraction strips.

Then place enough \(\frac{1}{3}\) strips to fit exactly under the 2 wholes. There are _________ one-third-size pieces in 2 wholes.

Record and check the quotient.

2 ÷ \(\frac{1}{3}\) = _________ because _________ × \(\frac{1}{3}\) = 2.

So, Roger has ________ pieces of string.

Answer:

Roger has 2 yards of string. He cuts the string into pieces that are 1/3 yard long.

Model 2 using 2 whole fraction strips.

Then place enough 1/3 strips to fit exactly under the 2 wholes. There are **6** one-third-size pieces in 2 wholes.

Record and check the quotient.

2 ÷(1/3) = **6** because **6** × 1/3 = 2.

So, Roger has **6** pieces of string.

**Make Connections**

You can use fraction strips to divide a fraction by a whole number.

Calla shares half of a package of clay equally among herself and each of 2 friends. What fraction of the whole package of clay will each friend get?

STEP 1: Place a strip under a \(\frac{1}{2}\)-whole strip to show the \(\frac{1}{2}\) package of clay.

STEP 2: Find 3 fraction strips, all with the same denominator, that fit exactly under the \(\frac{1}{2}\) strip.

Each piece is __________ of the whole.

STEP 3: Record and check the quotient.

\(\frac{1}{2}\) ÷ 3 = __________ because _________ × 3 = \(\frac{1}{2}\).

So, each friend will get __________ of the whole package of clay.

Answer:

STEP 1:

Place a strip under a 1/2 whole strip to show the 1/2 package of clay.

STEP 2:

We have to find 3 fraction strips, all with the same denominator, that fit exactly under the 1/2 strip.

Each piece is **1/6** of the whole.

STEP 3:

Record and check the quotient.

1/2 ÷ 3 = **1/6** because **1/6** × 3 = \(\frac{1}{2}\).

So, each friend will get **1/6** of the whole package of clay.

**Math Talk**

**Mathematical Processes**

When you divide a fraction by a whole number how does the quotient compare to the dividend? Explain.

Answer:

**Share and Show**

**Divide and check the quotient.**

Question 1.

Answer:

Explanation:

In the above image we can observe 3 units with 3 fraction strips in each unit. Divide the whole number by fraction. If we divide 3 by 1/3 then the result is 9 because when we multiply 9 with 1/3 the result is 3.

Question 2.

Think: What label should I write for each tick mark?

3 ÷ \(\frac{1}{6}\) = ____________ because ________ × \(\frac{1}{6}\) = 3.

Answer:

3 ÷ 1/6 = **18** because **18** × 1/6 = 3.

Explanation:

In the above image we can observe that whole number is divided by a fraction. If we divide 3 by 1/6 then the result is 18. Because when we multiply 18 with 1/6 the product is 3. So, the quotient is correct.

Question 3.

\(\frac{1}{4}\) ÷ 2= ____________ because ________ × 2 = \(\frac{1}{4}\).

Answer:

1/4 ÷ 2= **1/8** because** 1/8** × 2 =1/4.

Explanation:

In the above image we can observe that 1/4 is divided into 2 equal fraction strips. If we divide 1/4 by 2 then the result is 1/8. Because when we multiply 1/8 with 2 the product is 1/4. So, the quotient is correct.

**Problem Solving**

**H.O.T. Sense or Nonsense?**

Question 4.

Emilio and Julia used different ways to find \(\frac{1}{2}\) ÷ 4. Emilio used a model to find the quotient. Julia used a related multiplication equation to find the quotient. Whose answer makes sense? Whose answer is nonsense? Explain your reasoning.

Emilio’s Work

Julia’s Work

If \(\frac{1}{2}\) ÷ 4 = ☐, then ☐ × \(\frac{1}{2}\)

I know that \(\frac{1}{8}\) × 4 = \(\frac{1}{2}\)

So, \(\frac{1}{2}\) ÷ 4 = \(\frac{1}{8}\) because \(\frac{1}{8}\) × 4 = \(\frac{1}{2}\)

Answer:

Emilio’s Work

Emilio’s answer is nonsense.

Julia’s Work

If 1/2 ÷ 4 = **1/8**, then **1/8** × 4 = 1/2.

I know that 1/8 × 4 = 1/2

So,1/2 ÷ 4 = 1/8 because 1/8 × 4 =1/2.

Julia’s answer have sense.

Explanation:

Emilio and Julia used different ways to find 1/2 ÷ 4. Emilio used a model to find the quotient. Emilio answer is nonsense because when we divide 1/2 by 4 the result is 1/8. But Emilio’s answer is 1/4. Julia used a related multiplication equation to find the quotient. If we divided 1/2 by 4 the result is 1/8 then multiply 1/8 with 4 the result is 1/2. So, Julia’s answer have sense.

Question 5.

For the answer that is nonsense, describe how to find the correct answer.

Answer:

**1/2 ÷ 4 = 1/2 x 1/4 = 1/8**

Explanation:

The answer that is nonsense we can find the correct answer by using a related multiplication equation. Divide 1/2 by 4 then the result is 1/8.

Question 6.

**Multi-Step** If you were going to find \(\frac{1}{2}\) ÷ 5, explain how you would find the quotient using fraction strips. Write an equation to show the quotient.

Answer:**
**Place a strip under a 1/2. We have to find 5 fraction strips, all with the same denominator, that fit exactly under the 1/2 strip.

Each piece is

**1/10**of the whole.

Record and check the quotient.

1/2 ÷ 5 =

**1/10**because

**1/10**× 5 = 1/2.

Explanation:

We can find the quotient using fraction strips. Divide 1/2 by 5 the result is 1/10. The equation is 1/2 ÷ 5 = 1/10.

**Daily Assessment Task**

**Fill in the bubble completely to show your answer.**

Question 7.

Ants are lined up along the edges of your sandwich at a picnic. If the sandwich is 9 inches around and each ant is \(\frac{1}{6}\) of an inch, how many ants are lined up around the sandwich?

(A) 15 ants

(B) 16 ants

(C) 27 ants

(D) 54 ants

Answer:

9 ÷ 1/6 = 9 x 6/1 = **54**

54 ants are lined up around the sandwich.

So, option D is correct.

Explanation:

Ants are lined up along the edges of our sandwich at a picnic. If the sandwich is 9 inches around and each ant is 1/6 of an inch. Divide 9 by 1/6 the result is 54. The ants that are lined up around the sandwich are 54. So, draw a circle to option D.

Question 8.

**Use Tools** Which is the division problem modeled by the picture?

(A) 4 ÷ \(\frac{1}{12}\)

(B) 3 ÷ \(\frac{1}{4}\)

(C) 3 ÷ \(\frac{1}{3}\)

(D) 12 ÷ \(\frac{1}{3}\)

Answer:

**3 ÷ 1/3 = 9**

So, option C is correct.

Explanation:

The division problem that model by the above picture is 3 ÷ 1/3. Divide 3 by 1/3 the result is 9. So, draw a circle for option C.

Question 9.

**Multi-Step** Maddie divided 6 by \(\frac{1}{2}\), and then divided that answer by \(\frac{1}{3}\). What was her final answer?

(A) 9

(B) 1

(C) 12

(D) 36

Answer:

6 ÷ 1/2 = 12

12 ÷ 1/3 = **36**

The final answer is 36.

So, option D is correct.

Explanation:

Maddie divided 6 by 1/2, and then divided that answer by 1/3. First divide 6 by 1/2 the result is 12. Divide 12 by 1/3 the result is 36. The final answer is 36. So, draw a circle for option D.

**Texas Test Prep**

Question 10.

Reid has 4 bags of soil. He uses \(\frac{1}{3}\) of a bag to fill each planter. How many planters can Reid fill with the bags of soil?

(A) 1\(\frac{1}{3}\)

(B) 12

(C) 3\(\frac{2}{3}\)

(D) 4\(\frac{1}{3}\)

Answer:

Reid can fill 13/3 planters with the bag of soil.

So, option D is correct.

Explanation:

Reid has 4 bags of soil. He uses 1/3 of a bag to fill each planter. 4(1/3) planters can Reid fill with the bag of soil.

So, draw a circle for option D.

### Texas Go Math Grade 5 Lesson 6.4 Homework and Practice Answer Key

**Divide and check the quotient.**

Question 1.

Answer:

Explanation:

In the above image we can observe 4 units with 4 fraction strips in each unit. Divide the whole number by fraction. If we divide 4 by 1/4 then the result is 16 because when we multiply 16 with 1/4 the result is 4.

Question 2.

Answer:

Explanation:

In the above image we can observe that whole number is divided by a fraction. If we divide 2 by 1/6 then the result is 12. Because when we multiply 12 with 1/6 the product is 2. So, the quotient is correct.

Question 3.

Answer:

Explanation:

In the above image we can observe that 1/3 is divided into 2 equal fraction strips. If we divide 1/3 by 2 then the result is 1/6. Because when we multiply 1/6 with 2 the product is 1/3. So, the quotient is correct.

Question 4.

Answer:

Explanation:

In the above image we can observe that whole number is divided by a fraction. If we divide 3 by 1/5 then the result is 15. Because when we multiply 15 with 1/5 the product is 3. So, the quotient is correct.

Question 5.

Answer:

Explanation:

In the above image we can observe that 1/5 is divided into 2 equal fraction strips. If we divide 1/5 by 2 then the result is 1/10. Because when we multiply 1/10 with 2 the product is 1/5. So, the quotient is correct.

**Problem Solving**

Question 6.

Julie buys a board that is 6 feet long. She wants to cut it into pieces that are \(\frac{1}{2}\) foot each. How many pieces will Julie have after she cuts the board?

Answer:

6 ÷ 1/2 = 6 x 2/1 = 12

Julie have 12 pieces after she cuts the board.

Explanation:

Julie buys a board that is 6 feet long. She wants to cut it into pieces that are 1/2 foot each. Divide 6 by 1/2 the product is 12. Julie have 12 pieces after she cuts the board.

Question 7.

Mr. Morales makes four batches of cookies for family math night. He divides half of a pound of butter equally into 4 mixing bowls. How much butter is in each bowl?

Answer:

1/4 x 1/2 = 1/8

In each bowl 1/8 butter.

Explanation:

Mr. Morales makes four batches of cookies for family math night. He divides half of a pound of butter equally into 4 mixing bowls. Divide 1/2 pound of butter into four equal parts. Each part contains 1/4 of butter. Multiply 1/4 with 1/2 the product is 1/8. In each bowl 1/8 butter.

**Lesson Check**

**Fill in the bubble completely to show your answer.**

Question 8.

Which is the division problem modeled by the picture?

(A) \(\frac{1}{2}\) ÷ 6

(B) \(\frac{1}{6}\) ÷ 12

(C) \(\frac{1}{6}\) ÷ 2

(D) \(\frac{1}{12}\) ÷ 2

Answer:

Option C is correct.

Explanation:

In the above image we can observe that 1/6 is divided into 2 equal fraction strips. If we divide 1/6 by 2 then the result is 1/12. Because when we multiply 1/12 with 2 the product is 1/6. The division problem modeled by the above picture is 1/6 ÷ 2. So, draw a circle for option C.

Question 9.

Which is the division problem modeled by the picture?

(A) 3 ÷ \(\frac{1}{8}\)

(B) 24 ÷ \(\frac{1}{4}\)

(C) 3 ÷ \(\frac{1}{24}\)

(D) 8 ÷ \(\frac{1}{3}\)

Answer:

Option A is correct.

Explanation:

In the above image we get the information by observing the number line. The whole number is divided by a fraction. If we divide 3 by 1/8 then the result is 24. Because when we multiply 24 with 1/8 the product is 3. The division problem modeled by the above picture is 3 ÷ 1/8. So, draw a circle for option A.

Question 10.

Evan brings 8 liters of juice to be served at family math night. He pours 1/5 liter into each glass. How many glasses of juice can be served?

(A) 8

(B) 40

(C) 13

(D) 10

Answer:

8 ÷ 1/5 = 8 x 5/1 = 40

40 glasses of juice can be served at family math night.

So, option B is correct.

Explanation:

Evan brings 8 liters of juice to be served at family math night. He pours 1/5 liter into each glass. Divide 8 by 1/5 the result is 40. At family math night 40 glasses of juice can be served. So, draw a circle for option B.

Question 11.

Marissa is painting one of her bedroom walls. She marks off \(\frac{1}{4}\) of the wall. Then she divides the marked section into 3 equal parts and paints one part blue. What fraction of the whole wall is blue?

(A) \(\frac{1}{3}\)

(B) \(\frac{1}{4}\)

(C) \(\frac{1}{7}\)

(D) \(\frac{1}{12}\)

Answer:

1/4 ÷ 3 = 1/4 x 1/3 = **1/12**

1/12 fraction of the whole wall is blue.

So, option D is correct.

Explanation:

Marissa is painting one of her bedroom walls. She marks off 1/4 of the wall. Then she divides the marked section into 3 equal parts and paints one part blue. Divide 1/4 by 3 the result is 1/12. 1/12 fraction of the whole wall is blue. So, option D is correct.

Question 12.

**Multi-Step** Rex combines \(\frac{1}{4}\) cup sugar and 1/4 cup flour Into a small bowl. Then he divides the amount in the small bowl into 4 empty mixing bowls. What amount of dry Ingredients is in each mixing bowl?

(A) \(\frac{1}{16}\) cup

(B) \(\frac{1}{2}\) cup

(C) \(\frac{1}{8}\) cup

(D) 2 cups

Answer:

1/4 + 1/4 = 1/2

1/2 ÷ 4 = 1/8

In each mixing bowl 1/8 amount of dry ingredients.

So, option C is correct.

Explanation:

Rex combines 1/4 cup sugar and 1/4 cup flour Into a small bowl. Add 1/4 with 1/4 the sum is 1/2. Then he divides the amount in the small bowl into 4 empty mixing bowls. Divide 1/2 by 4 the result is 1/8. In each mixing bowl 1/8 amount of dry ingredients. So, draw a circle for option C.

Question 13.

**Multi-Step** Jamie divided 8 by \(\frac{1}{2}\), and then multiplied that answer by \(\frac{1}{4}\). What was her final answer?

(A) 4

(B) 1

(C) 64

(D) 32

Answer:

8 ÷ 1/2 = 16

16 x 1/4 = 4

The final answer is 4.

So, option A is correct.

Explanation:

Jamie divided 8 by 1/2 and then multiplied that answer by 1/4. First divide 8 by 1/2 the result is 16. Multiply 16 with 1/4 the product is 4. The final answer is 4. So, draw a circle for option A.