Fractions Review

Fractions Review

Equivalent Fractions

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

Finding equivalent fractions

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

PRACTICE QUESTIONS

Multiple Select

Which 2 fractions are equivalent to  $\frac{1}{2}$  

•  $\frac{2}{4}$  

•  $\frac{2}{6}$  

•  $\frac{3}{6}$  

•  $\frac{3}{8}$  

Multiple Select

Which 2 fractions are equivalent to  $\frac{1}{4}$  

•  $\frac{2}{4}$  

•  $\frac{2}{8}$  

•  $\frac{3}{12}$  

•  $\frac{4}{12}$  

Adding fractions with same denominators

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:

 $\frac{1}{8}+\frac{3}{8}=\frac{4}{8}$  

Adding fractions with different denominators

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.

For example

 $\frac{1}{2}+\frac{1}{4}$  

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

We know that if we multiply 2 x 2, we get 4, so we also have to multiply the top number by 2.
 $\frac{1}{2}\times\frac{2}{2}=\frac{2}{4}$  

Example continued

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

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

PRACTICE QUESTIONS

Multiple Choice

 $\frac{2}{4}+\frac{1}{4}$  

•  $\frac{1}{4}$  

•  $\frac{2}{4}$  

•  $\frac{3}{4}$  

•  $\frac{4}{4}$  

Multiple Choice

 $\frac{3}{8}+\frac{2}{8}$  

•  $\frac{2}{8}$  

•  $\frac{3}{8}$  

•  $\frac{4}{8}$  

•  $\frac{5}{8}$  

Multiple Choice

 $\frac{1}{2}+\frac{3}{4}$  

•  $\frac{3}{4}$  

•  $\frac{4}{4}$  

•  $\frac{5}{4}$  

•  $\frac{6}{4}$  

Multiple Choice

 $3\ \frac{1}{2}+2\ \frac{3}{8}$  

•  $5\ \frac{1}{8}$  

•  $5\ \frac{5}{8}$  

•  $5\ \frac{7}{8}$  

•  $6\ \frac{1}{8}$  

Subtracting fractions

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

Example

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

Example 2

 $\frac{1}{2}-\frac{3}{4}$  

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

PRACTICE QUESTIONS

Multiple Choice

 $\frac{3}{4}-\frac{2}{4}$  

•  $\frac{1}{4}$  

•  $\frac{2}{4}$  

•  $\frac{3}{4}$  

•  $\frac{4}{4}$  

Multiple Choice

 $\frac{3}{8}-\frac{6}{8}$  

•  $-\frac{1}{8}$  

•  $-\frac{3}{8}$  

•  $-\frac{5}{8}$  

•  $-\frac{7}{8}$  

Multiple Choice

 $\frac{1}{2}-\frac{1}{4}$  

•  $\frac{1}{4}$  

•  $-\frac{1}{4}$  

•  $\frac{1}{2}$  

•  $-\frac{1}{2}$  

Multiple Choice

 $3\ \frac{7}{8}-2\ \frac{1}{4}$  

•  $1\ \frac{1}{8}$  

•  $1\ \frac{1}{4}$  

•  $1\ \frac{3}{8}$  

•  $1\ \frac{5}{8}$  

Multiplying fractions

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

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

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

PRACTICE QUESTIONS

Multiple Choice

 $\frac{1}{8}\times\frac{7}{8}$  

•  $\frac{7}{8}$  

•  $\frac{7}{48}$  

•  $\frac{7}{64}$  

•  $\frac{8}{64}$  

Multiple Choice

 $\frac{1}{2}\times\frac{3}{4}$  

•  $\frac{3}{2}$  

•  $\frac{3}{4}$  

•  $\frac{3}{6}$  

•  $\frac{3}{8}$  

Multiple Choice

 $\left(-\frac{2}{3}\right)\left(\frac{6}{7}\right)$  

•  $\frac{12}{21}$  

•  $-\frac{12}{21}$  

•  $\frac{8}{10}$  

•  $-\frac{8}{10}$  

Dividing fractions

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.

For example

 $\frac{1}{2}\div\frac{1}{4}$  

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

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

Another example

 $\frac{1}{2}\div\frac{3}{8}$  

Flip the second fraction and multiply:

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

PRACTICE QUESTIONS

Multiple Choice

 $\frac{7}{8}\div\frac{1}{2}$  

•  $\frac{7}{4}$  

•  $\frac{14}{16}$  

•  $\frac{7}{16}$  

•  $\frac{14}{8}$  

Multiple Choice

 $\frac{7}{4}\div\frac{1}{3}$  

•  $\frac{21}{4}$  

•  $\frac{14}{16}$  

•  $\frac{7}{16}$  

•  $\frac{14}{8}$  

Multiple Choice

 $\frac{1}{2}\div\frac{4}{3}$  

•  $\frac{4}{6}$  

•  $\frac{3}{8}$  

•  $\frac{4}{8}$  

•  $\frac{6}{10}$  

Simplifying Fractions

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:

 $\frac{4}{8}\div\frac{4}{4}=\frac{1}{2}$  

PRACTICE QUESTIONS

Simplify our answers to previous questions

Multiple Choice

Simplify:

 $\frac{3}{9}$  

•  $-\frac{4}{7}$  

•  $\frac{1}{3}$  

•  $\frac{2}{5}$  

•  $-\frac{3}{8}$  

Multiple Choice

Simplify:

 $\frac{4}{10}$  

•  $-\frac{4}{7}$  

•  $\frac{1}{3}$  

•  $\frac{2}{5}$  

•  $-\frac{3}{8}$  

Multiple Choice

Simplify:

 $-\frac{6}{16}$  

•  $-\frac{4}{7}$  

•  $\frac{1}{3}$  

•  $\frac{2}{5}$  

•  $-\frac{3}{8}$  

Multiple Choice

Simplify:

 $-\frac{12}{21}$  

•  $-\frac{4}{7}$  

•  $\frac{1}{3}$  

•  $\frac{2}{5}$  

•  $-\frac{3}{8}$  

Conclusion

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.