Question

How do you evaluate `\frac { 3} { 8} + \frac { 5} { 7}`?

Answer 1

We find a common multiple of both denominators and then add them.

Explanation:

The two denominators are 7 and 8. We want to find the lowest common multiple of these numbers. In this case, we just multiply them together.
`7xx8=56` which is the lowest common multiple. Then we need to multiply both numerators by the opposite denominators and divide them by the lowest common multiple. Algebraically, this looks like
`frac{a}{b}+frac{c}{d}=frac{ad+bc}{bd}`
For this equation, it looks like `frac{3}{8}+frac{5}{7}=frac{3xx7+5xx8}{7xx8}=frac{21+40}{56}=frac{61}{56}`