We included **HMH Into Math Grade 3 Answer Key PDF** **Module 13 Lesson 6 Represent and Name Fractions Greater Than 1 **to make students experts in learning maths.

## HMH Into Math Grade 3 Module 13 Lesson 6 Answer Key Represent and Name Fractions Greater Than 1

I Can identify fractions greater than 1 on a number line and write them in fraction form and as mixed numbers.

**Spark Your Learning**

Emilio cuts his pizzas into slices. Each slice is a fourth of a whole pizza. Emilio has 9 slices to sell.

Show all the different amounts of pizza that Emilio can sell. Name each fraction that you show.

Answer:

There are 9 slices.

Each slice is 1/4th of whole pizza.

The different amounts of pizza can be shown as:

1/4, 2/4, 3/4, 4/4, 5/4, 6/4, 7/4, 8/4, 9/4.

– A fraction consists of two numbers (a/b), a numerator and a denominator. The number written at the top is the numerator, and the one written at the bottom is the denominator.

– There are three major types of fractions, named as proper fractions (or the fractions less than one and greater than 0, with numerator less than denominator), improper fractions (or the fractions more than one or equal to one with a numerator greater than or equal to the denominator), and mixed fractions (a combination of a whole number and a proper fraction).

**Turn and Talk** The numerator of a fraction is greater than the denominator. What does that tell you about the fraction?

Answer: Not all the numerators will be less than the denominator in fractions. Sometimes the numerator will be greater than the denominator. If the numerator is greater than the denominator, then the fraction is called an improper fraction.

– Suppose, x/y is an improper fraction, such that x > y. It is, therefore, the improper fraction is always greater than one.

Examples:

13/4; 25/20; 9/5 and so on…

**Build Understanding**

Question 1.

Jasmine has a stack of 7 waffle halves. How many plates can Jasmine fill with 1 whole waffle? Will any waffle halves be left over?

Draw to show the waffles.

A.How many plates do Jasmine fill with whole waffles?

Answer:

Jasmine can fill 2 plates with whole waffles.

The number of waffle halves=7

1 whole waffle=2 parts.

In the stack, there are 7 waffle halves.

We can put 1 part of the waffle in 1st half and another half in the second half-waffle present in the stack.

So we can fill 2 plates.

B. How many halves are left over?

Answer: 5

The total number of waffle halves=7

In that 7 waffle halves, 2 are filled with the help of one whole waffle.

The remaining waffles left are 7-2=5

therefore, 5 halves are leftover.

C. What fraction greater than 1 and mixed number can you write to represent the waffles that Jasmine serves?

________ = _______ wholes + ________ leftover = ________

Answer:

The total number of waffle halves=7

The number of the whole waffles=2

the remaining half waffles=5

The fraction is 7/5. This 7/5 we need to convert a mixed fraction:

There are some steps to follow:

Step 1: Find the whole number

Calculate out how many times the denominator goes into the numerator. To do that, divide 7 by 5 and keep only what is to the left of the decimal point:

7/5=1.400=1

Step 2: Find a new numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

7-(5*1)=2

Step 3: Get a solution

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 7/5 as a mixed number is:

7/5=1 2/5

Connect to Vocabulary

A fraction greater than 1 has a numerator greater than its denominator.

\(\frac{5}{3}\)

Read: five thirds

A mixed number is a number greater than 1 represented by a whole number and a fraction.

Read: four and three eighths

Question 2.

To make a shirt, Luc needs \(\frac{5}{3}\) yards of cloth.

Complete the number line to show thirds.

A. How many thirds are in 1 yard?

Answer:

3 1/3 are there in 1 yard.

From 0 to 1 means completely 1 yard.

In between 0 and 1, there is 1/3, 2/3, 3/3 which is nothing but 1.

So there are 3 1/3 yards are there.

B. How many whole yards does Luc need?

Circle the fraction on the number line that shows this.

Answer:

2 whole yards are needed.

But the fraction is between 1 and 2

C. Circle the section of the number line which represents the amount that Luc still needs.

Answer:

Luc needs 5/3 yards of cloth. It is in between 1 and 2 sections.

D. Write a mixed number to represent \(\frac{5}{3}\).

Answer:

5/3 is an improper fraction

Not all the numerators will be less than the denominator in fractions. Sometimes the numerator will be greater than the denominator. If the numerator is greater than the denominator, then the fraction is called an improper fraction.

– Suppose, x/y is an improper fraction, such that x > y. It is, therefore, the improper fraction is always greater than one

Step 1: Find the whole number

Calculate out how many times the denominator goes into the numerator. To do that, divide 5 by 3 and keep only what is to the left of the decimal point:

5/3=1 which is the quotient

Step 2: Find a new numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

5-(3*1)=2 (remainder)

Step 3: Get a solution

The mixed fraction can be written as a quotient (remainder/divisor)

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 5/3 as a mixed number is: 1 2/3

Question 3.

Nisa’s egg cartons each hold 8 eggs. Nisa has 17 eggs. How many cartons of eggs does Nisa fill?

A. Draw to show the eggs in Nisa’s cartons.

Answer:

The total number of eggs Nisa has=17

The number of eggs egg carton hold=8

The number of cartons of eggs does Nisa fill=X

X=17/8

X=2.125

B. How many whole cartons does Nisa fill completely?

Answer:

In each carton, 8 eggs will be filled

There are 17 eggs are there.

16 eggs will be filled in 2 cartons. And the remaining egg will be placed in the third carton.

Therefore, 2 whole cartons Nisa filled completely.

C. How many eggs are left over? What fraction of a carton is left over?

Answer: 1 egg left over.

The fraction of carton =1/8

In each carton, 8 eggs will be filled.

The remaining egg will be placed in the new carton.

D. Write the number of cartons Nisa fills as a mixed number. Nisa fills _________ cartons of eggs.

Answer:

The fraction is 17/8 which is an improper fraction.

Not all the numerators will be less than the denominator in fractions. Sometimes the numerator will be greater than the denominator. If the numerator is greater than the denominator, then the fraction is called an improper fraction.

– Suppose, x/y is an improper fraction, such that x > y. It is, therefore, the improper fraction is always greater than one

Step 1: Find the whole number

Calculate out how many times the denominator goes into the numerator. To do that, divide 17 by 8 and keep only what is to the left of the decimal point:

17/8=2 which is the quotient

Step 2: Find a new numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

17-(8*2)=1 (remainder)

Step 3: Get a solution

The mixed fraction can be written as a quotient (remainder/divisor)

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 17/8 as a mixed number is: 2 1/8

Therefore, Nisa fills 2 1/8 cartons of eggs.

**Turn and Talk** How many more eggs does Nisa need to fill her partly-filled carton? Explain how you know.

Answer: 7 eggs Nisa need to fill her partly-filled carton.

Explanation:

We already know that each carton can be filled with 8 eggs and Nisa has 17 eggs.

In 2 whole cartons, 16 eggs are filled completely and the remaining egg is filled in the next carton. Out of 8 places, 1 place is filled with one egg and the remaining 7 need to fill.

**Check Understanding**

Question 1.

Shel has \(\frac{11}{8}\) pizzas to sell. How much pizza does he have?

Write the mixed number. __________ pizzas

Answer:

11/8 is an improper fraction.

Not all the numerators will be less than the denominator in fractions. Sometimes the numerator will be greater than the denominator. If the numerator is greater than the denominator, then the fraction is called an improper fraction.

– Suppose, x/y is an improper fraction, such that x > y. It is, therefore, the improper fraction is always greater than one

Step 1: Find the whole number

Calculate out how many times the denominator goes into the numerator. To do that, divide 11 by 8 and keep only what is to the left of the decimal point:

11/8=1 which is the quotient

Step 2: Find a new numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

11-(8*1)=3 (remainder)

Step 3: Get a solution

The mixed fraction can be written as a quotient (remainder/divisor)

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 11/8 as a mixed number is: 1 3/8

Question 2.

Mae swims \(\frac{1}{2}\) mile each day. How many miles does Mae swim in 5 days? Complete the number line to show the distance and write the distance as a mixed number.

Mae swims _______ miles.

Answer:

The miles Mae swims each day=1/2

The number of miles does Mae swim in 5 days=X

For 1 day 1/2 mile; for 5 days X mile.

X=5/2 mile

5/2 is an improper fraction.

Not all the numerators will be less than the denominator in fractions. Sometimes the numerator will be greater than the denominator. If the numerator is greater than the denominator, then the fraction is called an improper fraction.

– Suppose, x/y is an improper fraction, such that x > y. It is, therefore, the improper fraction is always greater than one

Step 1: Find the whole number

Calculate out how many times the denominator goes into the numerator. To do that, divide 5 by 2 and keep only what is to the left of the decimal point:

5/2=2 which is the quotient

Step 2: Find a new numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

5-(2*2)=1 (remainder)

Step 3: Get a solution

The mixed fraction can be written as a quotient (remainder/divisor)

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer.5/2 as a mixed number is: 2 1/2

**On Your Own**

Question 3.

**Use Repeated Reasoning** The square represents 1 whole and each triangle represents \(\frac{1}{2}\) of a whole. How would you represent 3\(\frac{1}{2}\)?

Answer:

3\(\frac{1}{2}\): It is in mixed form. Now convert it into fraction form.

3 1/2 can be written as 7/2

Explanation:

– we multiply the whole number by the denominator.

3*2=6

– Then, we add the numerator to the answer we got.

6+1=7

– finally, to get the solution, we keep the original denominator and make the numerator the answer. Thus, 3 1/2 as an improper fraction is 7/2.

Question 4.

**Use Structure** Jerry has 14 lemons that are packed in bags of 6 lemons. How many bags of lemons does Jerry have? Write a mixed number.

Answer:

The number of lemons Jerry has=14+6=20

The number of bags=X

Suppose, in each bag 6 lemons are there then the value of X is:

X=20/6

X=10/3 which is an improper fraction.

now, this 10/3 should convert into the mixed form:

Not all the numerators will be less than the denominator in fractions. Sometimes the numerator will be greater than the denominator. If the numerator is greater than the denominator, then the fraction is called an improper fraction.

– Suppose, x/y is an improper fraction, such that x > y. It is, therefore, the improper fraction is always greater than one

Step 1: Find the whole number

Calculate out how many times the denominator goes into the numerator. To do that, divide 10 by 3 and keep only what is to the left of the decimal point:

10/3=3 which is the quotient

Step 2: Find a new numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

10-(3*3)=1 (remainder)

Step 3: Get a solution

The mixed fraction can be written as a quotient (remainder/divisor)

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer.10/3 as a mixed number is: 3 1/3

Question 5.

Nya needs string that is nine-sixths feet long. Complete the number line to show the length of string that Nya needs.

Write a mixed number. Nya needs ________ feet of string.

Answer:

9/6 =3/2 which is an improper fraction.

Not all the numerators will be less than the denominator in fractions. Sometimes the numerator will be greater than the denominator. If the numerator is greater than the denominator, then the fraction is called an improper fraction.

– Suppose, x/y is an improper fraction, such that x > y. It is, therefore, the improper fraction is always greater than one

Step 1: Find the whole number

Calculate out how many times the denominator goes into the numerator. To do that, divide 3 by 2 and keep only what is to the left of the decimal point:

3/2=1 which is the quotient

Step 2: Find a new numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

3-(2*1)=1 (remainder)

Step 3: Get a solution

The mixed fraction can be written as a quotient (remainder/divisor)

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer.3/2 as a mixed number is: 1 1/2

She needs 1 1/2 feet of string.

**Write the fraction as a mixed number.**

Question 6.

\(\frac{5}{4}\)

Answer:

5/4 is an improper fraction.

Not all the numerators will be less than the denominator in fractions. Sometimes the numerator will be greater than the denominator. If the numerator is greater than the denominator, then the fraction is called an improper fraction.

– Suppose, x/y is an improper fraction, such that x > y. It is, therefore, the improper fraction is always greater than one

Step 1: Find the whole number

Calculate out how many times the denominator goes into the numerator. To do that, divide 5 by 4 and keep only what is to the left of the decimal point:

5/4=1.2500=1

Step 2: Find a new numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

5-(4*1)=1

Step 3: Get a solution

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 5/4 as a mixed number is: 1 1/4

Question 7.

\(\frac{7}{3}\)

Answer:

7/3 is an improper fraction

Not all the numerators will be less than the denominator in fractions. Sometimes the numerator will be greater than the denominator. If the numerator is greater than the denominator, then the fraction is called an improper fraction.

– Suppose, x/y is an improper fraction, such that x > y. It is, therefore, the improper fraction is always greater than one

Step 1: Find out the whole number

Calculate out how many times the denominator goes into the numerator. To do that, divide 7 by 3 and keep only what is to the left of the decimal point:

7/3=2.333=2

Step 2: Find a new numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

7-(3*2)=1

Step 3: Get a solution

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 7/3 as a mixed number is: 2 1/3

Question 8.

\(\frac{10}{8}\)

Answer:

10/8 is an improper fraction

Not all the numerators will be less than the denominator in fractions. Sometimes the numerator will be greater than the denominator. If the numerator is greater than the denominator, then the fraction is called an improper fraction.

– Suppose, x/y is an improper fraction, such that x > y. It is, therefore, the improper fraction is always greater than one

Step 1: Find out the whole number

Calculate out how many times the denominator goes into the numerator. To do that, divide 10 by 8 and keep only what is to the left of the decimal point:

10/8=1

Step 2: Find a new numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

10-(8*1)=2

Step 3: Get a solution

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 10/8 as a mixed number is: 1 2/8

Question 9.

\(\frac{9}{4}\)

Answer:

9/4 is an improper fraction.

Not all the numerators will be less than the denominator in fractions. Sometimes the numerator will be greater than the denominator. If the numerator is greater than the denominator, then the fraction is called an improper fraction.

– Suppose, x/y is an improper fraction, such that x > y. It is, therefore, the improper fraction is always greater than one

Step 1: Find out the whole number

Calculate out how many times the denominator goes into the numerator. To do that, divide 9 by 4 and keep only what is to the left of the decimal point:

9/4=2

Step 2: Find a new numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

9-(4*2)=1

Step 3: Get a solution

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 9/4 as a mixed number is: 2 1/4

**I’m in a Learning Mindset!**

Is there anything still unclear to me about mixed numbers after finishing this lesson? Explain.

Answer: