We included **HMH Into Math Grade 3 Answer Key PDF** **Module 13 Lesson 5 Express Whole Numbers as Fractions **to make students experts in learning maths.

## HMH Into Math Grade 3 Module 13 Lesson 5 Answer Key Express Whole Numbers as Fractions

I Can draw visual models to show how to write fractions that name whole numbers.

**Spark Your Learning**

Mrs. Snow’s class has 8 bags of flour. Each bag weighs \(\frac{1}{4}\) pound.

Show how many 1-pound sacks of flour the class can fill.

Answer:

The number of bags of flour=8

Each bag weights=1/4

To show 1-pound sacks of flour=1/4, 2/4, 3/4, 4/4.

4/4 is equivalent to 1.

**Turn and Talk** How can you write the answer to the problem as a fraction?

Answer: To express the whole number value of 1, you can always use fraction models. In this case, 4/4 represents four equal parts that make up for one whole. Therefore, since both the whole number 1 and 4/4 has the same value, it is equivalent to each other.

**Build Understanding**

Question 1.

Tristan makes circular pans of cornbread and cuts them into thirds.

A. How can you show 1 pan of Tristan’s cornbread cut into thirds? How can you show 2 pans cut into thirds?

Answer:

In one pan, the bread can be divided into thirds as shown in the above diagram

In two pans the bread is divided into thirds.

B. How many thirds are in two pans?

How can you write this amount as a fraction?

Answer: 6 thirds

Explanation:

In the first pan, we divided it into 3 parts.

In the second pan, we divided it into 3 parts.

If we add two pans of thirds:

3/3+3/3

=6/3

=2

Infractions we can write 2/1

To represent the improper fractions we mentioned in the terminology section, which are generally the fraction form we use to display whole numbers, we can take the value of 2 or 2 wholes. In this case, each box represents one whole and it is made up of 1 equal part. Therefore, to represent the value of 2 in this scenario, we can express the whole number 2 as a 2/1 fraction.

C. What whole number does the fraction equal?

= __________

Answer:

To express the whole number value of 1, you can always use fraction models. In this case, 3/3 represents four equal parts that make up for one whole. Therefore, since both the whole number 1 and 3/3 has the same value, it is equivalent to each other.

Question 2.

How can you name the points located on the number line using fractions and whole numbers?

Complete the number line to name the points.

A. How many equal lengths are there from 0 to 1?

Answer:

If we divide the number line into two equal parts, as shown in the figure below, what value does that mid-point hold? Half of what the graduation between 0 and 1 holds. So, the point represents (1-0)/2 = 1/2.

B. What whole number and fraction represent 4 equal lengths?

Answer:

the whole number is 2 and the fraction will be 4/2.

to represent the whole number 2, it can be represented by 4 equal parts that make up 2 wholes. Therefore, the whole number 2 equals 4/2.

C. What whole number and fraction represents 6 equal lengths?

Answer: the whole number is 3 and the fraction will be 6/2.

to represent the whole number 3, it can be represented by 6 equal parts that make up 2 wholes. Therefore, the whole number 3 equals 6/2.

Question 3.

Tim uses 4 tortilla halves to make tortilla chips. Rita uses 9 thirds to make her tortilla chips. How many whole tortillas do they each use?

Draw to show each fraction.

A. What fractions represent Tim’s chips and Rita’s chips? How many whole tortillas does each fraction represent?

Tim: = ________ wholes Rita: = ________ wholes

Answer:

Tim uses 4 halves of tortillas.

Rita uses 9/3 of tortillas.

Now we have to find out the whole.

Tim=4/2

Tim=2

Tim uses 2 wholes.

Rita=9/3

Rita uses 3 whole.

B. How many whole tortillas do they each use?

Answer:

Tim uses 4 halves of tortillas.

Rita uses 9/3 of tortillas.

Now we have to find out the whole.

Tim=4/2

Tim=2

Tim uses 2 wholes.

Rita=9/3

Rita uses 3 whole

Now add both:

Tim+Rita=2+3=5

The whole tortillas they use is 5 tortillas.

**Turn and Talk** Without drawing a picture, what strategy can you use to write \(\frac{18}{6}\) as a whole number?

Answer:

The strategy wants to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.

18/6=3

– Numerator. This is the number above the fraction line. For 18/6, the numerator is 18.

– Denominator. This is the number below the fraction line. For 18/6, the denominator is 6.

– Improper fraction. This is a fraction where the numerator is greater than the denominator.

**Check Understanding**

Question 1.

Each circle is 1 whole. Write a whole number and a fraction for the parts that are shaded.

_________ =

Answer:

First, it is important to note the meaning of whole numbers. It refers to the “natural” state of numbers that do not involve fractions, decimals, or negatives. The list of whole numbers can include, 0, 1, 2, 3, 4, 5, 6, and so on…

– Numerator: This is the top part of the fraction. It represents a number of equal parts and also indicates whether the value of the fraction is smaller or larger than the value of 1.

– Denominator: This is displayed below the fraction line. It is a non-zero integer and it shows how many of the equal parts can make up a whole.

– Proper Common Fractions: This is used to classify fractions with an absolute value less than 1 but greater than -1

– Improper Common Fractions: This is particularly important for learning about expressing whole numbers in fraction form. The numerator of this type of fraction is usually a larger value than the denominator. The absolute value of this fraction is greater than or equal to 1. However, it is possible to have a negative number for either the top or bottom of the fraction, making it less than 1.

=6/6+6/6

=6+6/6.

12/6 is an improper fraction.

to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.

12/6=2

2 is the whole number and 6/12 is the fraction.

**On Your Own**

Question 2.

Use Tools Peter uses 8 one-half fraction circle pieces to make whole circles. Show the whole circles that Peter makes.

Peter makes _________ whole circles.

Answer:

Question 3.

Circle the fraction on the number line that is the same as 1 whole. Draw a box around the fraction that is the same as 2 wholes.

Answer:

If we divide the number line into two equal parts, as shown in the figure below, what value does that mid-point hold? Half of what the graduation between 0 and 1 holds. So, the point represents (1-0)/4 = 1/4.

the whole number is 1 and the fraction will be 4/4.

to represent the whole number 1, it can be represented by 4 equal parts that make up 4 wholes. Therefore, the whole number 1 equals 4/4.

the whole number is 2 and the fraction will be 4/2.

to represent the whole number 2, it can be represented by 4 equal parts that make up 2 wholes. Therefore, the whole number 2 equals 4/2.

**Each square is 1 whole. Write a whole number and a fraction for the parts that are shaded.**

Question 4.

Answer:

To express the whole number value of 1, you can always use fraction models. In this case, 4/4 represents four equal parts that make up for one whole. Therefore, since both the whole number 1 and 4/4 has the same value, it is equivalent to each other.

4/4+4/4+4/4

=4+4+4/4

=12/4

=3

Infractions, we can write as 3/1.

To represent the improper fractions we mentioned in the terminology section, which are generally the fraction form we use to display whole numbers, we can take the value of 3 or 3 wholes. In this case, each box represents one whole and it is made up of 1 equal part. Therefore, to represent the value of 3 in this scenario, we can express the whole number 3 as a 3/1 fraction.

Question 5.

Answer:

To express the whole number value of 1, you can always use fraction models. In this case, 8/8 represents eight equal parts that make up for one whole. Therefore, since both the whole number 1 and 8/8 has the same value, it is equivalent to each other.

8/8+8/8

=8+8/8

=16/8

=2

Infractions, we can write as 2/1.

To represent the improper fractions we mentioned in the terminology section, which are generally the fraction form we use to display whole numbers, we can take the value of 2 or 2 wholes. In this case, each box represents one whole and it is made up of 1 equal part. Therefore, to represent the value of 2 in this scenario, we can express the whole number 2 as a 2/1 fraction.

Question 6.

**Reason** Belle runs 16 times around a track that measures \(\frac{1}{4}\) mile long. Write a fraction that shows the distance that Belle runs. How many whole miles does Belle run?

Answer: 4 miles

The number of times belle rune=16

The miles measure=1/4

The fraction distance that belle runs=X

The number of miles=Y

For 1 time, she ran 1/4 miles.

For 16 times, we need to find out.

The fraction means X value is 4/1

To represent the improper fractions we mentioned in the terminology section, which are generally the fraction form we use to display whole numbers, we can take the value of 4 or 4 wholes. In this case, each box represents one whole and it is made up of 1 equal part. Therefore, to represent the value of 4 in this scenario, we can express the whole number 4 as a 4/1 fraction.

**I’m in a Learning Mindset!**

How is solving fraction problems different when I work with a partner?

Answer: It is a good way to practise addition and subtraction.