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Decomposing fractions review

Review the basics of decomposing fractions, and try some practice problems.

Decomposing fractions

To decompose a number, we break it into smaller parts.
Fractions, like all numbers, can be decomposed in many ways.

Example 1: Tape diagram

Let's decompose 59.
A tape diagram divided into 9 equal parts. Five parts are shaded.
One way we can decompose 59 is 29+39:
A tape diagram divided into 9 equal parts with 5 parts shaded. The first two parts are shaded orange. The next three parts are shaded green.
29+39=2+39=59
Another way we can decompose 59 is 19+29+29:
A tape diagram divided into 9 equal parts with 5 parts shaded. The first part is shaded purple. The next two parts are shaded pink. The next two parts are shaded green.
19+29+29=1+2+29=59

Example 2: Number line

How can we decompose 64?
A number line labeled 0 to 2 with tick marks every one-fourth unit. Tick marks 0, 1, and 2 are labeled. A point labeled six-fourths appears two tick marks to the right of 1.
One way we can decompose 64 is 14+14+14+14+14+14:
A number line labeled 0 to 2 with tick marks every one-fourth unit. Tick marks 0, 1, and 2 are labeled. A point labeled six-fourths appears two tick marks to the right of 1. An arrow begins at 0 and moves right one tick mark six times, ending two tick marks to the right of 1. The arrow is labeled one-fourth plus one-fourth plus one-fourth plus one-fourth plus one-fourth plus one-fourth.
14+14+14+14+14+14=1+1+1+1+1+14=64
Another way we can decompose 64 is 34+34:
A number line labeled 0 to 2 with tick marks every one-fourth unit. Tick marks 0, 1, and 2 are labeled. A point labeled six-fourths appears two tick marks to the right of 1. An arrow begins at 0 and moves right three tick marks and then moves right three tick marks, ending two tick marks to the right of 1. The arrow is labeled three-fourths plus three-fourths.
34+34=3+34=64
Want to learn more about decomposing fractions? Check out this video.

Practice

Problem 1
Which of these sums equal 1410 ?
Choose all answers that apply:

Want to try more problems like this? Check out this exercise.

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