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

2 Answers
May 12, 2018

#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.

May 12, 2018

#(-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#