How do you simplify 2/3 + 1/5 - 1/2?

1 Answer
Aug 2, 2016

11/30

Explanation:

color(blue)("Considering the common denominator")

5 will be a factor of any number (apart from 0) that end in 5 or 10
Unfortunately a number ending with 5 can not be divided exactly by 2. So the common denominator has to be a one of the 'tens'

Note that 3xx10 = 30 => the common factor is 30
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Method of changing to equivalent fractions")

Multiply a number by 1 and you do not change its value. You can however change the way it looks.
Example: 3xx1 -= 3xx5/5 -=15/5

The inherent value is still three but it looks different.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Answering the question")

Write as: (2/3xx10/10)+(1/5xx6/6)-(1/2xx15/15)

( (2xx10)/(3xx10) )+((1xx6)/(5xx6))-((1xx15)/(2xx15))

20/30+6/30-15/30

color(brown)("You can now directly add/subtract the top numbers")

(20+6-15)/30 =11/30