Fractions and Multiplcation

Question

Arelli and daniel each have 1 pan of lasagna. Arelli ate 1/3 of her lasagna. Daniel cut his pan into sixths and are the same amount as Arelli. How many sixths did daniel eat?

Prove that the Two fractions are equivalent using multiplication:

(_/_) = (_/_) X ( _ / _ ) = (_/_)

Answer 1

You're looking for an equivalent fraction to 1/3 that has a denominator of 6 instead of 3.

1/3 = x/6

If you cross-multiply you'll get 3x = 6, so x = 2. The equivalent fraction is 2/6.

You can check by reducing back to lowest terms (divide numerator and denominator by 2).

Answer 2

(1 / 3) = (1 / 3)(2 / 2) = (2 / 6)