How do you simplify #30/80 + 40/100#?

1 Answer
Mar 24, 2018

Answer:

Find a common denominator and divide out common factors.

Explanation:

# 80 = 2 xx 2 xx2 xx2 xx 5#
# 30 = 3 xx2 xx 5#

The common factors of # 2 xx 5# can be divided out leaving

# 30/80 = 3/8#

# 100 = 2xx 2 xx xx 5 xx 5 #
# 40 = 2 xx 2 xx 2 xx 5#

The common factors of # 2 xx 5 # can be divided out leaving

# 40/100 = 4/10#

8 and 10 have a common multiply of 40

# 8 = 2 xx 2 xx2 #
# 10 = 2 xx 5 #

The unique factors are # 2 xx 2 xx 2 xx 5 = 40#
( the factor of 2 in ten is a repeat of the 3 factors of 2 in 8)

Now change both fractions to a faction with a denominator of 40

# (3 xx 5)/( 8 xx 5) + (4 xx 4)/( 10xx 4) = 15/40 + 16 /40#

These fractions can be added giving

# 15/40 + 16/40 = 31/40#

there are no common factors between 31 and 40 so #31/40# is the final answer.