Add and Subtract Rational Numbers (Fractions)

What must you have to add and subtract fractions?

• Common numerators
• Different numerators
• Different denominators
• Common denominators

 $\frac{2}{5}+\frac{3}{10}=$  Add and Simplify

•  $\frac{7}{10}$  

•  $\frac{5}{10}$  

•  $\frac{1}{2}$ 

•  $\frac{5}{15}$  

Answer explanation

2/5 is rewritten as 4/10

Subtract and Simplify!

 $\frac{9a}{20}-\frac{a}{4}=$  

•  $\frac{a}{2}$ 

•  $\frac{8a}{16}$  

•  $\frac{4a}{20}$  

•  $\frac{a}{5}$  

Answer explanation

Rewrite a/4 as 5a/20. Subtract and then simplify.

 $\frac{6x}{7}-\frac{2x}{3}=$  Subtract and Simplify

•  $\frac{32x}{21}$  

•  $\frac{4x}{21}$  

•  $\frac{24x}{21}$  

•  $\frac{7}{21x}$  

Answer explanation

Rewrite both with the common denomiator of 21.

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

•  $\frac{5b}{12}$  

•  $-\ \frac{5b}{12}$  

•  $\ \frac{13b}{12}$  

•  $-\frac{13b}{12}$  

 $-\frac{1c}{3}+\left(-\frac{1c}{6}\right)$  Don't forget to simplify.

•  $-\frac{2c}{9}$  

•  $-\frac{1c}{2}$  

•  $\frac{2c}{9}$  

•  $-\frac{3c}{6}$  

 $-\frac{4}{5}+\left(-\frac{3}{8}\right)$  

•  $-\frac{7}{13}$  

•  $-\frac{7}{8}$  

•  $-1\ \frac{7}{40}$  

•  $\frac{17}{40}$  

 $\frac{3}{5}+\left(-\frac{1}{5}\right)$  

•  $\frac{2}{5}$  

•  $\frac{4}{5}$  

•  $-\frac{2}{5}$  

•  $-\frac{4}{5}$  

Answer explanation

Different signs, Subtract.  Keep the sign of the greater number.

 $-\frac{2g}{3}-\frac{g}{9}=$  

•  $\frac{5g}{9}$  

•  $\frac{7g}{9}$ 

•  $-\frac{5g}{9}$  

•   $-\frac{7g}{9}$   

 $-\frac{4}{5}-\left(-\frac{2}{3}\right)=$  

Multiply

•  $-1\ \frac{7}{15}$  

•  $1\ \frac{7}{15}$  

•  $-\frac{2}{15}$  

•  $\frac{2}{15}$