Expert: Josh - 8/28/2008

Question
Add and simplify
7/10 + 5/8 + 7/20

Answer
Aimee,

To add fractions together you need to know about "common denominators". Please look up "least common multiple" or "lowest common multiple" (LCM) on a search engine to find out more.

In this question, 40 is the LCM of 10, 8 and 20. That is to say, 40 is the smallest integer divisible by 8, 10 and 20.

Note that 8x5=40, 10x4=40 and 20x2=40.
Also, 4/4, 5/5 and 2/2 are all identical to 1.
So, we can multiply (7/10) by (4/4) without changing the ratio represented by the fraction. We get (7/10)x(4/4) = (7x4)/(10x4) = 28/40.

Similarly, we can multiply (5/8) by (5/5) to get (5x5)/(8x5)=25/40 without changing the ratio represented by the fraction (5/8).

We do the same, multiplying (7/20) by (2/2) to get 14/40.

The whole point is to ensure that they all have the SAME denominator.

7/10 + 5/8 + 7/20      is the same as
28/40 + 25/40 + 14/40  which we can write as
(28+25+14)/40          this simplifies to
67/40

Check out some websites, look at some examples and practice heaps if you are new to this. Good luck!