How do you simplify #\frac { 4} { 5} + \frac { 7} { 8} #?

Question

Nova Allen · Accepted Answer

See a solution process below:

We need to put each fraction over a common denominator by multiplying each fraction by the appropriate form of #1#: #4/5 = 8/8 xx 4/5 = (8 xx 4)/(8 xx 5) = 32/40# #7/8 = 5/5 xx 7/8 = (5 xx 7)/(5 xx 8) = 35/40# We can now add the numerators of the two fractions over the common denominator. #32/40 + 35/40 = (32 + 35)/40 = 67/40# If necessary, we can convert this improper fraction into a mixed number as follows: #67/40 = (40 + 27)/40 = 40/40 + 27/40 = 1 + 27/40 = 1 27/40#

Cameron Arnold · Answer

undefined To simplify $\frac{4}{5} + \frac{7}{8}$, first find a common denominator, which is the least common multiple (LCM) of 5 and 8, which is 40. Then, rewrite each fraction with the common denominator:

$\frac{4}{5} \times \frac{8}{8} = \frac{32}{40}$

$\frac{7}{8} \times \frac{5}{5} = \frac{35}{40}$

Now, add the fractions together:

$\frac{32}{40} + \frac{35}{40} = \frac{32 + 35}{40} = \frac{67}{40}$

Since the numerator is greater than the denominator, you can simplify by dividing both numerator and denominator by their greatest common divisor, which is 1 in this case:

$\frac{67}{40}$ (no further simplification possible)

So, $\frac{4}{5} + \frac{7}{8} = \frac{67}{40}$.