Decompose Fractions in Multiple Ways

A fraction can be broken into like parts.

The parts add back to the same fraction.

There is more than one way.

Read it: One amount, more than one split

7/12 is 7 pieces of a bar cut into 12. Split them into a part of 6 and a part of 1: 7/12 = 6/12 + 1/12. Split them again as 5 and 2, and 7/12 = 5/12 + 2/12 is right too.

1. Count the pieces in the whole amount: 7 pieces of 1/12.
2. Choose the first part, then count what is left: 6 pieces, then 1 piece.
3. Write each part over the same bottom number: 7/12 = 6/12 + 1/12.

Every part is made of the same 1/12 pieces, so the parts add back to 7/12.

The top numbers of the parts add up to the top number of the whole: 6 + 1 = 7, and 5 + 2 = 7.

The pieces can be split in more than one place, so there is more than one right answer.

Split the top number into parts and keep the bottom number on every part.

11/12 = 3/12 + ___/12 — 8. 11 pieces in all and 3 in the first part, so 8 pieces are left: 8/12.