Using models to add and subtract fractions

How to add fractions

Before we begin this chapter, make sure you’ve got a good grip on prime factorization and divisibility rules.

When adding fractions, the first thing you’ll have to do is make sure you have common denominators. This means that the number at the bottom of your fractions have to be the same. If your denominators aren’t the same, you’ll have to convert them so that they are.

You can get common denominators by taking the LCM (least common multiple) of the numbers in your denominator. Then you’ll be able to add the numerators as you would with regular numbers when you carry out addition.

How to subtract fractions

When subtracting fractions, you’ll also have to make sure that the denominators are the same. After you’ve found the common factors for the denominators, you can once again carry out subtraction.

Let’s try out practice problems to see how this works. We’ll demonstrate the concept using models to add fractions and using models to subtract fractions. This means you’ll learn how to visually add and subtract fractions.

Example problems

Question 1:

Use a number line to calculate. Write the answer in lowest terms.

57+17\frac{5}{7} + \frac{1}{7}

Solution:

So let’s first draw the number line. Look at it and you see the number line from 0 to 1 is divided into 7 sections. This is because we are dealing with a denominator of 7

Divide 0 to 1 into 7 intervals becuase of a denominator of 7
Divide 1 into 7 intervals (denominator = 7)

If the denominator is 7, one way to represent 1 in fraction form is 77\frac{7}{7} = 1. With the number line in 7 sections, we can calculate 57+17\frac{5}{7} + \frac{1}{7} on the number line:

Look at 57\frac{5}{7}, it is on this location of the number line

Locate the position of 5/7 in the area of 1 divided into 7 small segments.
Locate five seventh on the seven small segments

And we are adding 17\frac{1}{7}, and that’s the result

Add one seventh into the previous fraction of five seventh.
Add one seventh to the previous fraction

And our final answer is 67\frac{6}{7}

Question 2:

Use a number line to calculate. Write the answer in lowest terms.

2818\frac{2}{8} - \frac{1}{8}

Solution:

So, let’s draw the number line again. Look at it and you’ll see the number line from 0 to 1 is divided into 8 sections. This is because we are dealing with a denominator of 8

Divide one into 8 small segments because of a denominator of 8.
Divide 1 into 8 segments (denominator = 8)

If the denominator is 8, one way to represent 1 in fraction form is 88\frac{8}{8} = 1. With the number line in 8 sections, we can calculate 2818\frac{2}{8} - \frac{1}{8} on the number line:

Look at 28\frac{2}{8}, it is on this location of the number line

Look at the location of two eighth on the intervals between 0 and 1.
Locate two eighth

And we are subtracting 18\frac{1}{8}, and that’s the result

Subtract one eighth from the previous fraction.
Subtract one eighth

And our answer is 18\frac{1}{8}

Question 3:

Write the addition or subtraction statement for the diagram. Write the answer in the lowest terms.

A diagram with areas divided into small segments
Diagram provided for statement

Solution:

We see the plus sign. So we are dealing with an addition. Each of the large rectangles represents a fraction. Each rectangle is divided into 20 sections. So 20 is the denominator. The shaded area represents the nominator.

So the first box:

Representation of fractions according to the diagram provided
Representation in fraction form

It represents 1020\frac{10}{20}

And the second box:

Another representation in fractions according the the diagram provided
Fraction representation

It represents 220\frac{2}{20}

So,

1020+220=1220\frac{10}{20} + \frac{2}{20} = \frac{12}{20}

Addition of two fractions
Addition of two fractions

The question asks us to write the answer in the lowest terms. So, we need to look for the common factor of 12 and 20 in order to simplify the answer. Turns out 4 is the common factor. So, we’ll divide 4 to the answer,

12÷420÷4=35\frac{12 \div 4}{20 \div 4} = \frac{3}{5}

So

35\frac{3}{5}

is the final answer.

Question 4:

Write the addition or subtraction statement for the diagram. Write the answer in the lowest terms.

Addition or subtraction statement for the diagram.
Statement for diagram of addition or subtraction

Solution:

We see the minus sign. So we are dealing with a subtraction. Each of the rectangles represents a fraction. Each box is divided into 6 sections. So 6 is the denominator. The shaded area represents the nominator

So the first box:

The fraction of the first box provided in the diagram
Fraction of the first box

It represents 46\frac{4}{6}

And the second box:

The fraction of the first box provided in the diagram
Fraction of the second box

It represents 26\frac{2}{6}

So,

4626=26\frac{4}{6} - \frac{2}{6} = \frac{2}{6}

Subtraction of two fractions provided in the diagram
Subtraction of two fractions

The question asks us to write the answer in the lowest terms. So, we need to look for the common factor of 2 and 6 in order to simplify the answer. Turns out 2 is the common factor. So, we divide 2 to the answer,

2÷26÷2=13\frac{2 \div 2}{6 \div 2} = \frac{1}{3}

So

13\frac{1}{3}

is the final answer.

Want to see an interactive diagram to see more of how to subtract fractions using a number line? Try this one out!

Next up, learn how to multiply whole numbers and fractions, and divide fractions with whole numbers. You can also learn how to multiply proper fractions.

Using models to add and subtract fractions

In this section, we will write addition or subtraction statements involving fractions for given diagrams. We were introduced to addition and subtraction statements in previous sections. In this section, we will also be asked to use diagrams to solve word problems involving the addition and subtraction of fractions.

Lessons

  • 2.
    Write the addition or subtraction statement for the diagram. Write the answer in the lowest terms.
    Using models to add and subtract fractions
  • 3.
    Use a number line to calculate. Write the answer in lowest terms.
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Using models to add and subtract fractions

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