We included **HMH Into Math Grade 3 Answer Key PDF** **Module 13 Lesson 4 Represent and Name Fractions on a Number Line **to make students experts in learning maths.

## HMH Into Math Grade 3 Module 13 Lesson 4 Answer Key Represent and Name Fractions on a Number Line

I Can identify, describe, represent, and locate fractions on a number line.

**Spark Your Learning**

Michaela works for the Park Service. Her job is to place trail markers on the trail from the Ranger Station to Baldy Mountain. The markers should be placed at locations that mark \(\frac{1}{4}\), \(\frac{2}{4}\), \(\frac{3}{4}\), and \(\frac{4}{4}\) of the distance from the Ranger Station to Baldy Mountain.

Show each of Michaela’s markers on the number line. Label the distance of each marker from the Ranger Station.

Answer:

First, we have to know the representation of fractions on a number line.

Representing fractions on a number line means that we can plot fractions on a number line, which is similar to plotting whole numbers and integers. Fractions represent parts of a whole. So, fractions on the number line are represented by making equal parts of a whole i.e. 0 to 1, and the number of those equal parts would be the same as the number written in the denominator of the fraction.

**Turn and Talk** Trace the number line on a sheet of paper and fold the paper to show the trail marker locations. How do the folds on your paper number line compare to the labels on your drawing?

Answer:

**Build Understanding**

Question 1.

On the way to school, Leo stops at Blackberry Pond. What fraction of the 1-mile distance to school has Leo gone?

Complete the fractions on the number line.

A. Into how many equal lengths is the whole mile divided?

Answer:

To plot fractions on the number line, follow the steps given below:

Step 1: Draw a number line of a suitable length.

Step 2: check the fractions once. If the given fraction is a proper fraction then mark points 0 and 1 on the number line. If it is an improper fraction, then we have to convert it into a mixed fraction, and then mark two integers between those the given fraction lies.

Step 3: Draw an equal number of parts of the numbers marked in step 2 which will be equal to the denominator of the fraction.

Step 4: Starting from the left point, count forward the number of parts shown by the numerator.

Step 5: Mark the point on the line.

In the above problem, Leo walked up to the blackberry pond and he stopped there. If he walks about 2 more steps then he reached the school.

– If we add 1/6 to every next number he reaches the school within one mile.

B. Which part of a fraction shows the number of equal lengths in the whole, the numerator or the denominator? Which part of the fraction shows the number of equal lengths you are counting?

Answer:

The last part will show the number of equal lengths in the whole.

1 is represented as a whole which is 6/6.

1/6 shows the number of equal lengths.

1 is numerator and 6 is the denominator.

When I was counting the fraction shows the equal length is 1/6 every time.

C. Locate and draw a point on the number line to show the distance from Leo’s home to Blackberry Pond.

Answer:

To plot fractions on the number line, follow the steps given below:

Step 1: Draw a number line of a suitable length.

Step 2: check the fractions once. If the given fraction is a proper fraction then mark points 0 and 1 on the number line. If it is an improper fraction, then we have to convert it into a mixed fraction, and then mark two integers between those the given fraction lies.

Step 3: Draw an equal number of parts of the numbers marked in step 2 which will be equal to the denominator of the fraction.

Step 4: Starting from the left point, count forward the number of parts shown by the numerator.

Step 5: Mark the point on the line.

D. What fraction represents 1 equal length of the whole? What fraction names the distance from Leo’s home to Blackberry Pond?

Answer:

1 is represented as a whole infraction.

the fraction 6/6 represents 1 equal length of the whole.

the fraction names the distance from Leo’s home to Blackberry pond

The starting point is 0 and from there one-sixths, two-sixths, and up to 4/6.

For every step, we are adding 1/6.

Question 2.

What fraction does point A show?

A. Into how many equal lengths is the distance from 0 to 1 divided?

Answer: Representing fractions on a number line means that we can plot fractions on a number line, which is similar to plotting whole numbers and integers. Fractions represent parts of a whole. So, fractions on the number line are represented by making equal parts of a whole i.e. 0 to 1, and the number of those equal parts would be the same as the number written in the denominator of the fraction.

The distance from 0 to 1 is divided into 4 equal increments.

The third mark represents 3/4 because it is 3/4 of the distance from 0 to 1.

The point represents the fraction 3/4.

B. How many equal lengths are being counted?

Answer: There are four equal lengths.

Start from 0 to 1

0/4, 1/4, 2/4, 3/4, 4/4.

C. What is the fraction?

Answer: A fraction represents a numerical value, which defines the parts of a whole. Generally, the fraction can be a portion of any quantity out of the whole thing and the whole can be any specific things or value. The basics of fractions explain the top and bottom numbers of a fraction. The top number represents the number of selected or shaded parts of a whole whereas the bottom number represents the total number of parts.

Properties of fraction:

Similar to real numbers and whole numbers, a fractional number also holds some of the important properties. They are:

– Commutative and associative properties hold true for fractional addition and multiplication.

– The identity element of fractional addition is 0, and fractional multiplication is 1.

– The multiplicative inverse of a/b is b/a, where a and b should be non zero elements.

– Fractional numbers obey the distributive property of multiplication over addition.

Question 3.

Enya and Kat walk from home to the local history museum. When they are \(\frac{1}{3}\) of the way to the museum, they stop at the library. They stop again to read their library books at the park when they are \(\frac{2}{3}\) of the way to the museum. Complete the number line to show how to represent these distances.

Answer:

To plot fractions on the number line, follow the steps given below:

Step 1: Draw a number line of a suitable length.

Step 2: check the fractions once. If the given fraction is a proper fraction then mark points 0 and 1 on the number line. If it is an improper fraction, then we have to convert it into a mixed fraction, and then mark two integers between those the given fraction lies.

Step 3: Draw an equal number of parts of the numbers marked in step 2 which will be equal to the denominator of the fraction.

Step 4: Starting from the left point, count forward the number of parts shown by the numerator.

Step 5: Mark the point on the line.

The above-given question Enya and Kat walk from home to the local history museum.

On the way to the museum is 1/3. And from there they stopped at the library and read library books at the park that is 2/3. We need to represent these ways on the number line. The number line is drawn below:

**Turn and Talk** On a number line, what does the length between each whole number represent? What does the length between each mark represent? How do you know?

Answer:

The length between each whole number represents is 3/3 is nothing but 1.

The length between each mark represents 1/3.

**Check Understanding**

Question 1.

Complete the number line. Label the fractions. Locate and draw a point on the number line to show \(\frac{5}{8}\).

Answer:

To plot fractions on the number line, follow the steps given below:

Step 1: Draw a number line of a suitable length.

Step 2: check the fractions once. If the given fraction is a proper fraction then mark points 0 and 1 on the number line. If it is an improper fraction, then we have to convert it into a mixed fraction, and then mark two integers between those the given fraction lies.

Step 3: Draw an equal number of parts of the numbers marked in step 2 which will be equal to the denominator of the fraction.

Step 4: Starting from the left point, count forward the number of parts shown by the numerator.

Step 5: Mark the point on the line.

Write the fractions that name points E and F

Question 2.

point E

Answer:

To plot fractions on the number line, follow the steps given below:

Step 1: Draw a number line of a suitable length.

Step 2: check the fractions once. If the given fraction is a proper fraction then mark points 0 and 1 on the number line. If it is an improper fraction, then we have to convert it into a mixed fraction, and then mark two integers between those the given fraction lies.

Step 3: Draw an equal number of parts of the numbers marked in step 2 which will be equal to the denominator of the fraction.

Step 4: Starting from the left point, count forward the number of parts shown by the numerator.

Step 5: Mark the point on the line.

By applying all those steps we can continue the number line by pointing E and F.

The complete number line is shown below:

The point E represents 3/6.

Question 3.

point F

Answer:

The point F represents 4/6.

By using the above number line we can write the point F fraction.

**On Your Own**

Question 4.

**Use Tools** Reese’s poster is \(\frac{2}{4}\) yard wide. Complete the number line. Label the fractions. Locate and draw a point on the number line to show the width of Reese’s poster.

Answer:

To plot fractions on the number line, follow the steps given below:

Step 1: Draw a number line of a suitable length.

Step 2: check the fractions once. If the given fraction is a proper fraction then mark points 0 and 1 on the number line. If it is an improper fraction, then we have to convert it into a mixed fraction, and then mark two integers between those the given fraction lies.

Step 3: Draw an equal number of parts of the numbers marked in step 2 which will be equal to the denominator of the fraction.

Step 4: Starting from the left point, count forward the number of parts shown by the numerator.

Step 5: Mark the point on the line.

The whole length is 4/4

The length in each mark represents 1/4 to next fraction.

Question 5.

Abe marks points H and l on the number line. Write the fraction that names each point.

Answer:

To plot fractions on the number line, follow the steps given below:

Step 1: Draw a number line of a suitable length.

Step 2: check the fractions once. If the given fraction is a proper fraction then mark points 0 and 1 on the number line. If it is an improper fraction, then we have to convert it into a mixed fraction, and then mark two integers between those the given fraction lies.

Step 3: Draw an equal number of parts of the numbers marked in step 2 which will be equal to the denominator of the fraction.

Step 4: Starting from the left point, count forward the number of parts shown by the numerator.

Step 5: Mark the point on the line.

Question 6.

Reason Izzy marks a number line to show eighths. What is the fraction that is located halfway between \(\frac{6}{8}\) and \(\frac{8}{8}\)? Explain.

Answer:

To plot fractions on the number line, follow the steps given below:

Step 1: Draw a number line of a suitable length.

Step 2: check the fractions once. If the given fraction is a proper fraction then mark points 0 and 1 on the number line. If it is an improper fraction, then we have to convert it into a mixed fraction, and then mark two integers between those the given fraction lies.

Step 3: Draw an equal number of parts of the numbers marked in step 2 which will be equal to the denominator of the fraction.

Step 4: Starting from the left point, count forward the number of parts shown by the numerator.

Step 5: Mark the point on the line.

the whole length of the fraction is 8/8 nothing but 1.

The length between each mark represents 1/8.

**I’m in a Learning Mindset!**

Would drawing my own diagrams help me better understand how to place fractions on a number line?

Answer: yes

Explanation:

For more clarification we can draw number lines step by step:

1. To represent fractions on a number line, you may follow these steps. Draw a number line with whole numbers.

2. Draw a second number line with the same scale, but with half integers in between the whole numbers. This is where the fractional numbers are placed.

3. To draw a third number line, connect the points from the first two number lines, so that the fractional numbers are represented.

4. And moreover, you can also use a graphical representation of a fraction which is known as a fraction bar or fraction sign.

5. And many other options are there to place fractions on the number line, not only on the number line we can use rectangular grids too.