# MPM1D – Fractions and LCM 2017-09-11

On Friday I gave you a page of work to refresh your math brain. We spent today looking at a bunch of those questions, and then talking about adding and subtracting fractions.

The big idea today is that fractions must have the same denominator (bottom number) if we’re going to add them together. If they’re different, we have to adjust one or more of the fractions so they do match (we use equivalent fractions to do this).

We looked back at finding Least Common Multiples (LCMs) using factor trees to help us. For example, finding the LCM of 18 and 15 we have:

$18 = 2 \times 3 \times 3$

$15 = 3 \times 5$

The LCM of 15 and 18 is the collection of all the factors from each number, removing duplicates. In this case,

$LCM(15,18) = 2 \times 3 \times 3 \times 5$

We got two 3s from 18, so we didn’t get any extra from the 15 (there was only a single 3 there).

When fractions have the same denominator, we can add or subtract them just by adding or subtracting the numerators:

$\frac{3}{8}+\frac{6}{8} = \frac{3+6}{8} = \frac{9}{8}$

# More

If you want some more details and a little bit different approach to finding the prime factorization, check out this page at Purple Math about LCM and GCF: http://www.purplemath.com/modules/lcm_gcf.htm