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

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Answer 1 · 2016-08-04T21:14:22

$1/21$

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

$color(brown)("Fact 1")$
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 $ul("does change the way it looks")$ .

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

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

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

$=15/21-14/21$

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

How do you simplify 5/7 - 2/35/7 - 2/3?