# Adding Fractions on a Number Line Rating

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Adding Fractions on a Number Line
CCSS.MATH.CONTENT.4.NF.B.3.A

## Adding Fractions on a Number Line

When we learn how to add fractions, we can use visual methods to understand the process better. In this learning text we are going to use number lines as a visual explanation to get a better understanding.

## Steps to Adding Fractions on a Number Line

We know that a fraction has a top number (numerator) and a bottom number (denominator). Adding fractions is different from adding whole numbers. Let’s look at the steps to take if you want to add two fractions on a number line.

• Firstly, check if the fractions have common or like denominators.
• Secondly, divide the number line (between 0 and 1) into equal parts and label each part; the denominator is the indicator in how many parts the number line will be divided between whole numbers. Then look at the first fraction and circle or highlight it on the number line.
• Finally jump from the highlighted fraction to the right as many times as shown by the numerator of the second fraction. Remember to simplify your answer if possible!

## Adding Fractions on a Number Line – Examples

Let’s look at the examples below and follow the process of adding two fractions on a number line. We are adding here two fractions with a common denominator of eight: $\frac{1}{8}$ and $\frac{5}{8}$. In order to add two fractions using the number line, we divide the number line between zero and one into equal parts and label each part. Then we must find the first fraction on our number line and then jump to the right as many times as the numerator of the fraction we are adding shows. Our added fraction has a numerator of five, so we must jump five times forward. We have land on $\frac{6}{8}$, so $\frac{1}{8}$ add $\frac{5}{8}$ is $\frac{6}{8}$. Now we can simplify our answer if possible. $\frac{6}{8}$ we can simplify to $\frac{3}{4}$ by dividing numerator and denominator by a common factor which is two. Let’s look at another example of adding fractions with a numberline.

This time we have given $\frac{2}{6}$ and $\frac{3}{6}$. Both fractions share the same denominator, which is six. We are going to repeat the same process as above. We divide the number line between zero and one into equal parts and label each part. Then we must find the first fraction on our number line and then jump to the right as many times as the numerator of the fraction we are adding shows. Our added fraction has a numerator of three, so we must jump three times forward. We have land on $\frac{5}{6}$, so $\frac{2}{6}$ add $\frac{3}{6}$ is $\frac{5}{6}$. Now we can simplify our answer if possible. This time we cannot simplify further, so our answer is $\frac{5}{6}$. ## Adding Fractions on a Number Line - Further Practice

Today we learned about adding fractions using a number line. Let’s look at the steps below for a quick review.

Step # What to do
1. Check that the fractions have the same denominators.
2. Divide the number line into equal parts between
0 and 1 as shown by the denominators.
and circle or highlight it.
4. Jump forward to the right as many times as
shown by the numerator to find the sum.

To test your knowledge on adding and subtracting fractions on a number line, have a look at our practice problems, videos and worksheets.

What are numerators and denominators?
What are common denominators?
How can we find common denominators?
How do you add fractions on a number line with the common/like denominators?

## Adding Fractions on a Number Line exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Adding Fractions on a Number Line.
• ### What are the steps to add fractions?

Hints

Before you start adding the fractions, what do you need to check is the same?

Once you have divided your number line into equal parts, what do you need to locate?

Solution

First, check that the fractions you are adding have the same denominator.

Next, divide the number line into equal parts as shown by the denominators.

Then, locate the first fraction on the number line.

Finally, count forward the number of parts shown by the numerator on the second fraction.

• ### How much gas is in the the tank?

Hints

Each interval on the number line goes up in steps of $\frac1 6$. How many jumps will be needed to add $\frac3 6$?

There was already $\frac1 6$ in the tank so start your jumps from there.

Solution
• We are adding $\frac1 6$ + $\frac3 6$, so we start at $\frac1 6$.
• Next, look at the numerator of the fraction we are adding; in $\frac3 6$ the numerator is 3, so we make 3 jumps.
• This gets us to $\frac4 6$.
• So $\frac1 6$ + $\frac3 6$ = $\frac4 6$
• ### Which number lines show the correct way of adding the fractions?

Hints

The number line should be divided into equal parts based on the denominator. What is the denominator in the fractions that Axel and Tank are adding here?

The friends added $\frac1 9$ and $\frac6 9$. There are two ways to add these fractions, depending on which order they are added.

To add $\frac1 9$ and $\frac6 9$, the friends could start at $\frac1 9$ and make 6 jumps, or they could start at $\frac6 9$ and make 1 jump.

Solution
• There are two correct options to add $\frac1 9$ + $\frac6 9$.
• Both correct options have the number line divided into 9 equal parts because the denominators in $\frac1 9$ + $\frac6 9$ are 9.
• To solve starting with the smaller fraction: $\frac1 9$ + $\frac6 9$, start at $\frac1 9$ and jump forward 6.
• To solve starting with the larger fraction: $\frac6 9$ + $\frac1 9$, start at $\frac6 9$ and jump forward 1.

Hints

To add the fractions on a number line, first partition the number line to the number of parts that is in the denominator.

Find the first fraction on the number line, then count forward by the numerator of the second fraction.

Can you simplify your answer by dividing the numerator and denominator by the same factor?

Solution
• $\frac2 8$ + $\frac2 8$ = $\frac1 2$.
Start on $\frac2 8$, count forward by two, which takes you to $\frac4 8$. $\frac4 8$ can be simplified to $\frac1 2$ by dividing both the numerator (4) and the denominator (8) by 4.
• $\frac3 6$ + $\frac1 6$ = $\frac2 3$.
Start on $\frac3 6$, count forward by one, which takes you to $\frac4 6$. $\frac4 6$ can be simplified to $\frac2 3$ by dividing both the numerator (4) and the denominator (6) by 2.
• $\frac1 7$ + $\frac3 7$ = $\frac4 7$.
Start on $\frac1 7$, count forward by three, which takes you to $\frac4 7$. This cannot be simplified any further.
• $\frac3 5$ + $\frac2 5$ = 1.
Start on $\frac3 5$, count forward by two, which takes you to $\frac5 5$. $\frac5 5$ can be simplified to 1 by dividing both the numerator (5) and the denominator (5) by 5.
• ### Add the fractions on the number line.

Hints

Start by locating the first fraction in the equation on the number line.

How many parts do you need to jump forward?

The numerator in the second fraction ($\frac4 7$) is 4, so jump forward 4 parts.

Solution
• Start at $\frac2 7$
• As we are adding $\frac4 7$, look at the numerator of that fraction.
• The numerator of $\frac4 7$ is 4, so we make 4 jumps forward.
• This gets us to $\frac6 7$.
• So $\frac2 7$ + $\frac4 7$ = $\frac6 7$.
• ### Adding and simplifying fractions.

Hints

To simplify a fraction, divide the numerator and denominator by the same factor, in this example $\frac{4}{10}$ is simplified to $\frac2 5$ by dividing both by 2.

Sometimes it may be a fraction in the question that has already been simplified and needs expanding. For example, $\frac1 3$ can be expanded by multiplying both the numerator and denominator by 2 to get $\frac2 6$.

Solution

1) This answer is correct. $\frac3 8$ + $\frac3 8$ = $\frac6 8$. Divide numerator and denominator by 2 to get $\frac3 4$.

2) This answer is correct. $\frac4 9$ + $\frac1 3$ = $\frac7 9$. First expand $\frac1 3$ by multiplying the numerator and denominator by 3 to get $\frac3 9$. $\frac4 9$ + $\frac3 9$ = $\frac7 9$.

3) This answer is incorrect. $\frac2 6$ + $\frac2 6$ = $\frac4 6$. Divide numerator and denominator by 2 to get $\frac2 3$.

4) This answer is incorrect. $\frac{4}{10}$ + $\frac{4}{10}$ = $\frac{8}{10}$. Divide numerator and denominator by 2 to get $\frac4 5$.

5) This answer is correct. $\frac{3}{12}$ + $\frac{5}{12}$ = $\frac{8}{12}$. Divide numerator and denominator by 4 to get $\frac2 3$.

6) This answer is correct. $\frac{1}{16}$ + $\frac{1}{16}$ + $\frac{2}{16}$ = $\frac{4}{16}$. Divide numerator and denominator by 4 to get $\frac1 4$.