add: $\frac{1}{3} \ + \ \frac{1}{5}$
LCD is just the LCM of the numbers 3 and 5 which is 15. Rewrite both fractions as equivalent fractions with denominator 15:
$\frac{1}{3} \ (\frac{5}{5}) \ + \ \frac{1}{5} \ (\frac{3}{3}) $
= $\frac{5}{5} \ + \ \frac{1}{5}$
= $\frac{8}{15}$
We can also write the addition or subtraction vertically.
subtract: $\frac{5}{6} \ - \ \frac{3}{4}$
Make sure to write your answers in lowest terms or simplified form.
A shorter way to add or subtract fractions is by using the "cross-multiplication" method and the product of the denominators.
add: $\frac{1}{2} \ + \ \frac{4}{7}$
$= \frac{(1 \ x \ 7) \ + \ (4 \ x \ 2)}{2 \ x \ 7}$
$=\frac{7 \ + \ 8}{14} \ = \ \frac{15}{14}$ or $1\frac{1}{14}$
subtract: $\frac{3}{4} \ - \ \frac{1}{6}$
$= \frac{(3 \ x \ 6) \ - \ (1 \ x \ 4)}{4 \ x \ 6}$
$=\frac{18 \ - \ 4}{24} \ = \ \frac{14}{24}$ or $\frac{7}{12}$
add first before subtracting:
$\frac{2}{3} \ + \ \frac{1}{5} \ - \ \frac{5}{6}$
$= \frac{(2 \ x \ 5) \ + \ (1 \ x \ 3)}{3 \ x \ 5} \ - \ \frac{5}{6}$
$= \frac{13}{15} \ - \ \frac{5}{6}$
$= \frac{(13 \ x \ 6) \ + \ (5 \ x \ 15)}{15 \ x \ 6}$
$= \frac{153}{90}$ or $1 \ \frac{7}{10}$
