# Adding Fractions on a Number Line

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

## How to Add Fractions on a Number Line

• First, check that the fractions have like, or common, denominators.
• Next, divide the number line into equal parts between whole numbers as shown by the denominators.
• Then, locate the first fraction on the number line.
• Finally, jump forward the number of parts as shown by the numerator of the second fraction to find the sum.

Remember to simplify the fraction if you can.

## 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 $\frac1 4$.