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*Contributor: Elephango Editors. Lesson ID: 12778*

What is 12/30 - 3/90? That may look complicated, but if you know your common denominators, you can solve this in a fraction of the time! Learn these 3 simple steps and you'll be "cooking" in no time!

categories

subject

Math

learning style

Kinesthetic, Visual

personality style

Beaver

Grade Level

Intermediate (3-5)

Lesson Type

Quick Query

We can’t subtract two denominators when they do not have anything in common.

- So, how do we subtract fractions with unlike denominators, like
^{9}⁄_{28}-^{13}⁄_{56}?

*Fractions* tell us how many parts are in a whole.

When fractions have different *denominators*, the whole has been split into a different number of parts. Therefore, the parts will be different sizes.

When the parts are not the same size, we cannot subtract two fractions.

For example, look at the difference between ^{1}/_{2} and ^{1}/_{5}:

In the first model, the whole is split into 2 equal parts. In the other model, the whole is split into 5 equal parts. It is pretty clear that these parts are not the same size because of those denominators.

This is why the fractions cannot be subtracted with unlike denominators - they need to share a common denominator.

To subtract fractions with unlike denominators, we can follow three easy steps:

**Step One**

Find a common denominator. Multiply the numerators by the same factor you used to find the common denominator.

**Step Two**

Subtract the numerators. Keep the denominator the same.

**Step Three**

Simplify the fraction if needed.

Take a moment to put these steps into practice. Look at the example below:

- What is
^{1}/_{2}-^{1}/_{5}?

**Step One**

Find common denominator.

To find the common denominator, we need to find the least common multiple of the two denominators. The least common multiple between 2 and 5 is 10.

Both 2 and 5 can be multiplied by other numbers to equal 10. Also, both numbers can reach 10 by skip counting.

- How do we change the fractions so that both share the denominator of 10?

We will multiply the top and the bottom of each fraction by the factor needed to make the denominator 10.

For example, to change the denominator in ½ to 10, we will need to multiply the top and the bottom by 5:

1 | x | 5 | = | 5 | |

2 | x | 5 | = | 10 |

- For
^{1}/_{5}, what can you multiply the denominator of 5 by to get 10?

2! Multiply the top and bottom by 2.

1 | x | 2 | = | 2 | |

5 | x | 2 | = | 10 |

Now, both fractions have a common denominator. You are ready for the next step.

**Step Two**

Subtract the numerators. Keep the denominators the same.

Look at the fraction model now. Now that ½ and ^{1}/_{5} have the same denominator, it is easy to subtract:

5 | - | 2 | = | 3 | |

10 | 10 | = | 10 |

**Step Three **

Simplify the fraction if needed.

^{3}/_{10} is in its simplest form. The numerator and denominator cannot be divided by a shared factor. We do not need to simplify the fraction.

So, ^{1}/_{2} - ^{1}/_{5} = ^{3}/_{10}

You have learned how to use a pencil and paper to subtract fractions with unlike denominators. You have also used models to visualize subtraction problems.

Now, use your new strategies to complete the practice problems and activities in the *Got It? *section.