Into Math Grade 5 Module 11 Lesson 1 Answer Key Relate Multiplication and Division of Fractions

We included HMH Into Math Grade 5 Answer Key PDF Module 11 Lesson 1 Relate Multiplication and Division of Fractions to make students experts in learning maths.

HMH Into Math Grade 5 Module 11 Lesson 1 Answer Key Relate Multiplication and Division of Fractions

I Can divide a whole number by a unit fraction or a unit fraction by a whole number using a related multiplication equation.

Spark Your Learning

Josiah buys six packages of ground beef. How many \(\frac{1}{4}\)-pound hamburgers can Josiah make from the six packages?

A classmate began solving this problem by using a visual fraction model. How can you complete the model and use it to solve the problem?

Answer:

24 packages,

Explanation:
Given Josiah buys six packages of ground beef.
Number of \(\frac{1}{4}\)-pound hamburgers can Josiah make from the six packages are drawn a visual fraction model  above and 6 ÷ \(\frac{1}{4}\) = 6 X 4 = 24 packages.

Turn and Talk How can you model this problem with a division equation? How can you model this problem with a multiplication equation?
Answer:
Division equation:
6 ÷ \(\frac{1}{4}\) = 24,
Multiplication equation:
6 X 4 = 24,

Explanation:
Given Josiah buys six packages of ground beef.
Number of \(\frac{1}{4}\)-pound hamburgers can Josiah make from the six packages
Division equation:
6 ÷ \(\frac{1}{4}\) = 24,
Multiplication equation:
6 X 4 = 24.

Build Understanding

Question 1.
Josiah has 3 pounds of potato salad for his cookout. He divides the potato salad into \(\frac{1}{4}\)-pound servings. How many \(\frac{1}{4}\)-pound servings does Josiah have?
A. Write an equation to model the situation. ___________
Represent the equation by drawing rectangles as a visual model.
Answer:
3 ÷ \(\frac{1}{4}\),

Explanation:
Given Josiah has 3 pounds of potato salad for his cookout.
He divides the potato salad into \(\frac{1}{4}\)-pound servings. Number of \(\frac{1}{4}\)-pound servings does
Josiah have equation is 3 ÷ \(\frac{1}{4}\) and
Represented the equation by drawing rectangles as a visual model as shown above.

B. How many rectangles did you draw to represent the dividend?
Answer:
3 rectangles,

Explanation:
3 rectangles I have drawn to represent the dividend.

C. How did you represent the divisor in your visual fraction model?
Answer:
Each 1 dividend is divided by fourths,

Explanation:
To represent the divisor \(\frac{1}{4}\) in my visual fraction model I divided each 1 dividend into 4 parts.

D. How does your visual fraction model represent the quotient?
Answer:
12 parts of \(\frac{1}{4}\),

Explanation:
12 parts of \(\frac{1}{4}\) with cream color in my visual fraction model represent the quotient.

E. How many \(\frac{1}{4}\)-pound servings of potato salad does Josiah have?
Answer:
12 servings,

Explanation:
12 – \(\frac{1}{4}\)-pound servings of potato salad does Josiah have.

F. How can you use a multiplication equation to represent your visual fraction model?
3 ÷ \(\frac{1}{4}\) = ____________
Answer:
Multiplication equation:
3 X 4 = 12,

Explanation:
Multiplication equation to represent my visual fraction model
3 ÷ \(\frac{1}{4}\)  is 3 X 4 = 12.

Turn and Talk For Part E, how can you use the relationship between multiplication and division to show that your answer is correct?
Answer:
Both have same value 12,

Explanation:
The relationship between multiplication and division to show that your answer is correct is in multiplication it is 3 X 4 = 12 and in division also it is 3 ÷ \(\frac{1}{4}\) we get 12 only and
Multiplication and division are closely related, given that division is the inverse operation of multiplication.
When we divide, we look to separate into equal groups, while multiplication involves joining equal groups.

Step It Out

Question 2.
At Josiah’s cookout, 4 friends share \(\frac{1}{3}\) of a watermelon equally. What fraction of the whole watermelon does each friend get?

A. Write an equation to represent the problem.
Answer:
\(\frac{1}{3}\) ÷ 4,

Explanation:
Given at Josiah’s cookout, 4 friends share \(\frac{1}{3}\) of a watermelon equally. The fraction of the whole
watermelon does each friend get the equation to represent the problem is \(\frac{1}{3}\) ÷ 4.

B. Draw a visual model to represent the equation.

• The rectangle represents the whole watermelon. Divide the rectangle to represent the dividend.
• Divide the dividend to represent the divisor.
• Divide the other sections in the same way.
• Shade the part that each friend gets.

Answer:

Explanation:
Drawn a visual model to represent the equation.

• The rectangle represents the whole watermelon.
  Divided the rectangle to represent the dividend as \(\frac{1}{3}\)
• Divided the dividend to represent the divisor.
• Divided the other sections in the same way.
• Shaded the part \(\frac{1}{12}\) that each friend gets.

C. What fraction of the whole watermelon does each friend get?
Answer:
\(\frac{1}{12}\) fraction,

Explanation:
When \(\frac{1}{3}\) ÷ 4 =
\(\frac{1}{3}\)  X \(\frac{1}{4}\) =
\(\frac{1}{3 X 4}\) = \(\frac{1}{12}\) fraction
of the whole does each friend get.

D. What related multiplication equation can you write to represent the problem? Explain.
Answer:
Multiplication equation :
\(\frac{1}{3}\)  X \(\frac{1}{4}\) = \(\frac{1}{12}\),

Explanation:
4 friends shared \(\frac{1}{3}\) of a watermelon equally.
The fraction of the whole watermelon does each friend gets and the multiplication equation is \(\frac{1}{3}\)  X \(\frac{1}{4}\) = \(\frac{1}{12}\).

Check Understanding

Represent the situation with a visual model. Then write a division equation and a related multiplication equation.

Question 1.
Josiah serves \(\frac{1}{2}\) pound of macaroni salad equally to 6 guests. What fraction of a pound does each guest get?
Answer:

Division equation:
\(\frac{1}{2}\) ÷ 6,
Multiplication equation:
\(\frac{1}{2}\) X \(\frac{1}{6}\),
\(\frac{1}{12}\) fraction of a pound,

Explanation:
Given Josiah serves \(\frac{1}{2}\) pound of macaroni salad equally to 6 guests.
The fraction of a pound does each guest gets represented the situation with a visual model above,
Division equation:
\(\frac{1}{2}\) ÷ 6,
Multiplication equation:
\(\frac{1}{2}\) X \(\frac{1}{6}\),
So solving \(\frac{1}{2}\) X \(\frac{1}{6}\) =
\(\frac{1}{2 X 6}\) = \(\frac{1}{12}\) fraction of pound does each guest get.

On Your Own

Question 2.
The container of milk is divided equally into 8 glasses. How much milk should be poured into each glass?

Answer:

Division equation:
\(\frac{1}{2}\) ÷ 8,
Multiplication equation:
\(\frac{1}{2}\) X \(\frac{1}{8}\), \(\frac{1}{16}\) gallon,

Explanation:
Given the container of milk is divided equally into 8 glasses.
Milk should be poured into each glass, represented the situation with a visual model above,
Division equation:
\(\frac{1}{2}\) ÷ 8,
Multiplication equation:
\(\frac{1}{2}\) X \(\frac{1}{8}\),
So solving \(\frac{1}{2}\) X \(\frac{1}{8}\) =
\(\frac{1}{2 X 8}\) = \(\frac{1}{16}\) gallon of milk into each glass.

Divide. Write a related multiplication equation to solve.

Question 3.
8 ÷ \(\frac{1}{12}\) = n
Answer:
n= 8 X 12 = 96,

Explanation:
Given 8 ÷ \(\frac{1}{12}\) = n,
The multiplication equation is
n = 8 X 12 = 96.

Question 4.
n = 4 ÷ \(\frac{1}{8}\)
Answer:
n = 4 X 8 = 32,

Explanation:
Given n = 4 ÷ \(\frac{1}{8}\),
The multiplication equation is
n = 4 X 8 = 32.

Question 5.
\(\frac{1}{10}\) ÷ 3 = n
Answer:
n = \(\frac{1}{30}\),

Explanation:
Given n = \(\frac{1}{10}\) ÷ 3,
The multiplication equation is
n = \(\frac{1}{10}\) X \(\frac{1}{3}\),
n = \(\frac{1}{10 X 3}\) = \(\frac{1}{30}\).

Question 6.
6 ÷ \(\frac{1}{5}\) = n
Answer:
n = 6 X 5 = 30,

Explanation:
Given n = 6 ÷ \(\frac{1}{5}\),
The multiplication equation is
n = 6 X 5 = 30.

Question 7.
n = \(\frac{1}{5}\) ÷ 6
Answer:
n = \(\frac{1}{30}\),

Explanation:
Given n = \(\frac{1}{5}\) ÷ 6,
The multiplication equation is
n = \(\frac{1}{5}\) X \(\frac{1}{6}\),
n = \(\frac{1}{5 X 6}\) = \(\frac{1}{30}\).

Question 8.
n = \(\frac{1}{9}\) ÷ 7
Answer:
n = \(\frac{1}{63}\),

Explanation:
Given n = \(\frac{1}{9}\) ÷ 7
The multiplication equation is
n = \(\frac{1}{9}\) X \(\frac{1}{7}\),
n = \(\frac{1}{9 X 7}\) = \(\frac{1}{63}\).

Question 9.
Critique Reasoning Lulu says that when you divide any whole number by a unit fraction, the quotient is always another whole number that is less than the dividend. Is Lulu correct? Explain.
Answer:
Lulu is incorrect,

Explanation:
When a whole number is divided by a unit fraction, the quotient is a whole number greater than the dividend.
As Lulu says that when we divide any whole number by a unit fraction, the quotient is always another whole number that is less than the dividend. So Lulu is incorrect.
Example if 10 is divided into \(\frac{1}{2}\) parts it becomes 10 X 2 = 20 parts it is greater than 10.

Question 10.
Use Tools Four friends divide \(\frac{1}{2}\) of an apple pie equally. What fraction of the pie does each friend get? Describe how you could divide a circle to find the answer.
Answer:
\(\frac{1}{8}\) of the pie,

Explanation:
Given four friends divide \(\frac{1}{2}\) of an apple pie equally. The fraction of the pie does each friend gets is
\(\frac{1}{2}\) ÷ 4 =
\(\frac{1}{2}\) X \(\frac{1}{4}\)  =
\(\frac{1}{2 X 4}\) = \(\frac{1}{8}\).
Drawn a circle and divided it first by \(\frac{1}{2}\) then
\(\frac{1}{2}\) parts into 4 we will get \(\frac{1}{8}\) of the pie does each friend will get.

I’m in a Learning Mindset!

When I get stuck, how can I use different strategies to divide fractions?
Answer:
Use Visual models or follow steps to divide,

Explanation:
When I get stuck i use visual models to divide
fractions or Follow these steps: