Question

How do you find `3/5-3/7-1/14-2/7xx3/8`?

Answer 1

`3/5-3/7-1/14-2/7*3/8 = -1/140`

Explanation:

The expression is `3/5-3/7-1/14-2/7*3/8`

Let's start with the most complicated term, the last one,
`2/7*3/8=(2*3)/(7*8)=3/28`
(multiply numerators together and denominators together)

Our expression, therefore, can be written:
`3/5-3/7-1/14-3/28`

Here we need the least common denominator, which we find by factorising the denominators:
`5=5, 7=7, 14=2*7, 28=2*2*7`
Our denominator, therefore, is `2*2*5*7=140`

Expanding the terms so they all have the same denominator, gives:

`3/5-3/7-1/14-3/28=(3*28-3*20-1*10-3*5)/140`

`(84-60-10-15)/140=-1/140`

which is our solution.

Answer 2

`(-1)/140`

Explanation:

Count the number of terms first.
Each term will simplify to a single answer.
Do any multiplication or divisions before the additions and subtractions.

`3/5-3/7-1/14color(blue)(-cancel2/7xx3/cancel8^4)" "larr` there are `4` terms

`3/5-3/7-1/14color(blue)(-3/28)" "larr` add the fractions.

`7 and 14` are factors of `28`. The LCM of `28 and 5 " is "140`

Find equivalent fractions which have a denominator of `140`

`3/5-3/7-1/14-3/28`

`=(84-60-10-15)/140`

`=-1/140`