Toy Train Tracks: Build Fractions from Track Pieces

Break fractions and mixed numbers into sums in more than one way.

One piece at a time

One loop of track is 1 whole. Each small track piece is a unit fraction of the loop.

A loop of track is made of 6 equal pieces. Nia builds 4/6 of the loop using only 1/6 pieces. Which sum shows her track?

A. 1/4 + 1/4 + 1/4 + 1/4B. 4/6 + 1/6C. 1/6 + 1/6 + 1/6 + 1/6D. 1/6 + 1/6 + 1/6

The number line shows one loop of track from 0 to 1, marked in tenths. The point shows where Omar's track ends, at 7/10.

7/10 is pieces that are each 1/10 of the loop.
7/10 = 4/10 + /10
7/10 = 5/10 + /10

Many ways to build

There is more than one way to break apart a fraction. Every piece in a sum has the same denominator.

Theo needs a track that is 6/8 of a loop. Write the missing numerator to show four ways he can build it.

6/8 = 2/8 + /8
6/8 = 3/8 + /8
6/8 = 1/8 + 1/8 + /8
6/8 = 2/8 + 2/8 + /8

Kayla wants a track that is 5/6 of a loop. Circle every sum that equals 5/6.

A loop is made of 12 equal pieces. Match each track length to a sum that builds it.

Ana is building a track that is 9/10 of a loop. Find the missing piece in each way she tries.

9/10 = 2/10 + 2/10 + 2/10 + /10
9/10 = 4/10 + 4/10 + /10
9/10 = 5/10 + /10

Tracks longer than one loop

A track can be more than one loop long. Break each mixed number into wholes and fractions. One whole loop of fourths is 4/4.

Leo's track is 1 3/4 loops long. Each loop is made of 4 equal pieces.

1 3/4 = 1 + /4
1 3/4 = /4 + 3/4
1 3/4 = 4/4 + 1/4 + 1/4 + /4

Ruby's track is 2 2/6 loops long. Each loop is made of 6 equal pieces, so one whole loop is 6/6.

2 2/6 = 1 + 1 + /6
2 2/6 = /6 + 6/6 + 2/6
2 2/6 = 6/6 + 6/6 + 1/6 + /6

Dev's track is 1 2/5 loops long. Which sum is not equal to 1 2/5?

A. 1 + 2/5B. 1 + 1/5 + 2/5C. 5/5 + 1/5 + 1/5D. 1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 2/5

10.

Each loop is made of 8 equal pieces. Sort each sum by the length of track it builds.

11.

Jamal says the only way to build 4/5 of a loop is 1/5 + 1/5 + 1/5 + 1/5. Write two other ways to show 4/5 as a sum of fifths. Explain how you know each sum equals 4/5.