equivalent fractions

Ok so imagine you have 6 things, and you take 3 of those and put them in a separate group:

****** gets split into *** (that's 3 / 6) and the remaining *** (again that's 3 / 6)

similarly you can have 4 things and take 2 of those away to form it's own group

****, ** (2/4) and the remaining ** (also 2/4)

Now looking at both, you have both the same number of groups (2) and that in each case the groups are the same size as the other group(s) (3 in the case of 3/6, 2 in the case of 2/4)

Because there are two equal groups this means that 3 is exactly one half of 6, and 2 is exactly 1 half of 4. This is why they are equivalent fractions. They are both the same fraction of their set of items.

More mathematically if you rewrite the equations using "prime factors" which are numbers only divisible by 1 and theirselves (2 and 3 are prime but 4 is not because 4 is 2 * 2, 5 is prime but 6 is 2 * 3, etc.). You get that

3 / 6 is the same as (3) / (2*3). If you also know that the order of multiplication and division does not matter (the associative property) then you can rewrite it as 3 / 2 / 3 (remember the parentheses around 2*3 means that we are dividing by both 2 and 3) which is (3/3) / 2 or 1 / 2

While with 2 / 4 you get (2) / (2*2) which is 2 / 2 / 2 or (2/2) / 2 which is 1 / 2.

1 / 2 == 1 /2, so they are equivalent.

You can find KA's videos on equivalent fractions here: https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-visualizing-equiv-frac/v/equivalent-amount-of-pizza