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

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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.
Texas Go Math Grade 5 Lesson 6.4 Answer Key 1
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.
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-1

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?
Texas Go Math Grade 5 Lesson 6.4 Answer Key 2
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?
Texas Go Math Grade 5 Lesson 6.4 Answer Key 13
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.
Texas Go Math Grade 5 Lesson 6.4 Answer Key 14
Answer:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-14
Explanation:
In the above image, we can observe 3 units with 3 fraction strips in each unit. Divide the whole number by a 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.

Go Math 5th Grade Lesson 6.4 Answer Key Question 2.
Texas Go Math Grade 5 Lesson 6.4 Answer Key 15
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 the 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.
Texas Go Math Grade 5 Lesson 6.4 Answer Key 16
\(\frac{1}{4}\) ÷ 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.
Texas Go Math Grade 5 Lesson 6.4 Answer Key 3
Emilio’s Work
Texas Go Math Grade 5 Lesson 6.4 Answer Key 4

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
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-4
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.

Lesson 6.4 Answer Key Go Math Grade 5 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:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-4(1)
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?
Texas Go Math Grade 5 Lesson 6.4 Answer Key 5
(A) 4 ÷ \(\frac{1}{12}\)
(B) 3 ÷ \(\frac{1}{4}\)
(C) 3 ÷ \(\frac{1}{3}\)
(D) 12 ÷ \(\frac{1}{3}\)
Answer:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-5(1)
3 ÷ 1/3 = 9
So, option C is correct.
Explanation:
The division problem that modeled 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:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-5(2)
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

Lesson 6.4 Answer Key 5th Grade Go Math 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:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-5(3)
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.
Texas Go Math Grade 5 Lesson 6.4 Answer Key 6
Answer:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-6
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.
Texas Go Math Grade 5 Lesson 6.4 Answer Key 7
Answer:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-7
Explanation:
In the above image, we can observe that the 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.

Go Math Lesson 6.4 Answer Key Homework 5th Grade Question 3.
Texas Go Math Grade 5 Lesson 6.4 Answer Key 8
Answer:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-8
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.
Texas Go Math Grade 5 Lesson 6.4 Answer Key 9
Answer:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-9
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.
Texas Go Math Grade 5 Lesson 6.4 Answer Key 10
Answer:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-10
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.

Go Math Lesson 6.4 Homework Answer Key 5th Grade 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?
Texas Go Math Grade 5 Lesson 6.4 Answer Key 11
(A) \(\frac{1}{2}\) ÷ 6
(B) \(\frac{1}{6}\) ÷ 12
(C) \(\frac{1}{6}\) ÷ 2
(D) \(\frac{1}{12}\) ÷ 2
Answer:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-11(1)
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?
Texas Go Math Grade 5 Lesson 6.4 Answer Key 12

(A) 3 ÷ \(\frac{1}{8}\)
(B) 24 ÷ \(\frac{1}{4}\)
(C) 3 ÷ \(\frac{1}{24}\)
(D) 8 ÷ \(\frac{1}{3}\)
Answer:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-12(1)
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.

Go Math 5th Grade Lesson 6.4 Homework Answers 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:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-12(2)
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:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-12(3)
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:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-12(4)
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.

Go Math Grade 5 Lesson 6.4 Answer Key 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:
Texas-Go-Math-Grade-5-Lesson-6.4-Answer-Key-12(5)
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.

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