How do you solve #\frac { 4} { 6} + \frac { 4} { 7}#?

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Answer 1 · 2018-03-05T06:16:19

#26/21 = 1 5/21#

Given: #4/6 + 4/7#

To add these fractions we need to find a common denominator. We want to find the least common multiple (LCM) of the two denominators.

Find the LCM by finding the smallest multiple that is common:
#6: 6, 12, 18, 24, 30, 36, color(red)(42), ...#

#7: 7, 14, 21, 28, 35, color(red)(42), ...#

The LCM is #42#.

Multiply each fraction by a fraction that is #1# that = #42#(LCM) in the denominator:

#4/6 xx 7/7 = 28/42#

#4/7 xx 6/6 = 24/42#

#4/6 + 4/7 = 28/42 + 24/42 = 52/42#

Since both numerator and denominator are divisible by #2#, reduce the fraction: #52/42 -: 2/2 = 26/21#

Put answer in mixed numbers: #26/21 = 1 5/21#