Fractions Review

What are equivalent fractions? They are fractions with different numbers that represent the same amount.

To find equivalent fractions, multiply the top number (numerator) and the bottom number (denominator) by the same amount

In order to add fractions, they need to have the same denominator. Then we just add the numerators and keep the same denominator.

For example:

If we have fractions with different denominators, we need to find an equivalent fraction first and convert the fraction so it has the same denominator.

 $\frac{1}{2}+\frac{1}{4}$  

Our fractions don't have the same denominator, so we need to change 1/2 so that it has a denominator of 4. 

Now that we found an equivalent fraction and made the denominators the same, we can add the numerators

 $\frac{1}{2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}$  

Subtracting fractions is the same as adding fractions. The only difference is we subtract the numerators.

Note: WE STILL NEED TO HAVE THE SAME DENOMINATORS BEFORE WE CAN SUBTRACT

 $\frac{7}{8}-\frac{2}{8}=\frac{5}{8}$  

 $\frac{1}{2}-\frac{3}{4}$  

We need to convert 1/2 so that it has a denominator of 4. 

 $\frac{1}{2}\times\frac{2}{2}=\frac{2}{4}$  

So  $\frac{1}{2}-\frac{3}{4}=\frac{2}{4}-\frac{3}{4}=-\frac{1}{4}$  

To multiply fractions, just multiply the numerators to get the new numerator, and the denominators to get the new denominator.

For example: $\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}$  

 $\frac{2}{3}\times\frac{5}{8}=\frac{10}{24}$  

Dividing fractions is the same as multiplying fractions, but with one extra step.

First we need to flip the second fraction around.

Then we multiply as we did before.

 $\frac{1}{2}\div\frac{1}{4}$  

We flip the second fraction around and change the divide to multiply

 $\frac{1}{2}\div\frac{1}{4}=\frac{1}{2}\times\frac{4}{1}=\frac{4}{2}=2$  

 $\frac{1}{2}\div\frac{3}{8}$  

Flip the second fraction and multiply:

 $\frac{1}{2}\div\frac{3}{8}=\frac{1}{2}\times\frac{8}{3}=\frac{8}{6}$  

Once we get our answer to our fraction problem, we want to try and simplify our fraction as much as possible. We do this by dividing the top and bottom numbers by the same amount.

For example:

We use fractions in every day life for things like measuring ingredients in cooking to measuring things using tools.

Knowing how to add, subtract, multiply and divide fractions are useful tools to help us with our measurements.