Question 1122876: 7/5+6/7+8/6
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 7/5 + 6/7 + 8/6
our denominators are 5, 7, and 6
you need to find the least common multiple, or any common multiple if you can't find that.
an easy way to find a common multiple, not necessarily the least common multiple, is to multiple the denominators together.
you will get 5 * 7 * 6 = 210
the recommended way is to break each number down into their prime factors.
for 5, that would be 5
for 7, that would be 7
for 6 that would be 2 * 3.
then multiply by the greatest number of prime factors in each number.
that would be 5 * 7 * 2 * 3 = 210
it turns out the least common multiple is simply 5 * 7 * 6 = 210 for the denominator of the fractions.
here's a reference on how to find the least common multiple.
http://www.math.com/school/subject1/lessons/S1U3L3DP.html
so, your least common denominator is 210.
your fractions are, once again:
7/5 + 6/7 + 8/6
your common denominator is 210.
for 7/5, divide 210 by 5 to get 42.
multiply 7/5 by 42/42 to get 294/210
for 6/7, divide 210 by 7 to get 30
multiply 6/7 by 30/30 to get 180/210
for 8/6, divide 210 by 6 to get 35
multiply 8/6 by 35/35 to get 280/210
now add 294/210 + 180/210 + 280/210
since they all have the same common denominator, then just add the numerators and keep the common denominator on the bottom.
you will get 294 + 180 + 280 = 754 / 210
this fraction can be reduced to 377 / 105 by dividing both numerator and denominator by 2.
it does not appear to be able to be reduced any further.
your final answer is therefore 377 / 105.
to see if this is correct, simply use your calculator to do the following.
in your calculator, enter 7/5 + 6/7 + 8/6 and hit enter to get 3.59047619
enter 377/105 and hit enter to get 3.59047619
since they're the same, you can be sure that 377 / 105 is the same value as 7/5 + 6/7 + 8/6.
this means you did it right.
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