How do you simplify #5/7 - 2/3#?

Question

Eva Abramson · Accepted Answer

#1/21#

#color(blue)("Two very important facts")#

#color(brown)("Fact 1")# You can not #ul("directly")# add or subtract counts in fractions unless their 'size' indicators are the same.

#("count")/("size indicator")->("numerator")/("denominator")#

"................................................................................................"

#color(brown)("Fact 2")# Multiplying by 1 does not change the intrinsic value of something.

Multiply by 1 in some different form does not change the intrinsic value but #ul("does change the way it looks")#.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Answering your question")#

#color(brown)((5/7xx1)-(2/3xx1))color(blue)(" "->" "(5/7xx3/3)-(2/3xx7/7)#

#=(5xx3)/(7xx3) - (2xx7)/(3xx7)#

#=15/21-14/21#

#(15-14)/21 = 1/21#

Eva Adamson · Answer

undefined To simplify $ \frac{5}{7} - \frac{2}{3} $, you need to find a common denominator, which is the least common multiple (LCM) of 7 and 3, which is 21. Then, rewrite each fraction with the common denominator and subtract them.

$ \frac{5}{7} - \frac{2}{3} = \frac{5 \cdot 3}{7 \cdot 3} - \frac{2 \cdot 7}{3 \cdot 7} = \frac{15}{21} - \frac{14}{21} = \frac{15 - 14}{21} = \frac{1}{21} $

So, $ \frac{5}{7} - \frac{2}{3} $ simplifies to $ \frac{1}{21} $.