Adding and subtracting fractions

Adding and subtracting fractions

It's very easy to add or subtract fractions with the same denominators.

You just need to keep the denominator in the answer. Then just add or subtract the numerators.

Adding and subtracting fractions with different denominators.

The first thing you want do is to ensure that both denominators become the same.

 $\frac{2}{3}\ +\frac{1}{6}$  
The 3 and 6 are different but you came make them the same by finding the LCM. Just list the multiples of 3 and 6 and the lowest multiple the share in common becomes your new denominator. Then make EQUIVALENT FRACTIONS and work it out.

Multiple Choice

What is the Lowest Common Multiple of 3 and 6?

• 3

• 6

• 9

• 12

 $\frac{2}{3}+\frac{1}{6}=$  

 $\frac{4}{6}+\frac{1}{6}=\ \frac{5}{6}$  

Now both denominators are the same so you can just add the numerators. Remember we KEEP the SAME DENOMINATOR in the answer.

Example (2)     $\frac{19}{21}-\frac{3}{7}$  

Find the LCM of 21 and 7
21: 21, 42, 63
7: 7, 14, 21, 28
The LCM is 21. Therefore both fractions with have the same denominator which is 21.

 $\frac{19}{21}-\frac{3}{7}$  

 $\frac{19}{21}-\frac{9}{21}=\frac{10}{21}$  

We do the same when adding and subtracting mixed numbers. Then we add or subtract the whole after.

Example    $1\frac{1}{2}+1\ \frac{1}{4}$  

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