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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 start fraction, 5, divided by, 9, end fraction.
A tape diagram divided into 9 equal parts. Five parts are shaded.
One way we can decompose start fraction, 5, divided by, 9, end fraction is start color #e07d10, start fraction, 2, divided by, 9, end fraction, end color #e07d10, plus, start color #1fab54, start fraction, 3, divided by, 9, end fraction, end color #1fab54:
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.
start color #e07d10, start fraction, 2, divided by, 9, end fraction, end color #e07d10, plus, start color #1fab54, start fraction, 3, divided by, 9, end fraction, end color #1fab54, equals, start fraction, start color #e07d10, 2, end color #e07d10, plus, start color #1fab54, 3, end color #1fab54, divided by, 9, end fraction, equals, start fraction, 5, divided by, 9, end fraction
Another way we can decompose start fraction, 5, divided by, 9, end fraction is start color #7854ab, start fraction, 1, divided by, 9, end fraction, end color #7854ab, plus, start color #e84d39, start fraction, 2, divided by, 9, end fraction, end color #e84d39, plus, start color #01a995, start fraction, 2, divided by, 9, end fraction, end color #01a995:
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.
start color #7854ab, start fraction, 1, divided by, 9, end fraction, end color #7854ab, plus, start color #e84d39, start fraction, 2, divided by, 9, end fraction, end color #e84d39, plus, start color #01a995, start fraction, 2, divided by, 9, end fraction, end color #01a995, equals, start fraction, start color #7854ab, 1, end color #7854ab, plus, start color #e84d39, 2, end color #e84d39, plus, start color #01a995, 2, end color #01a995, divided by, 9, end fraction, equals, start fraction, 5, divided by, 9, end fraction

Example 2: Number line

How can we decompose start fraction, 6, divided by, 4, end fraction?
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 start fraction, 6, divided by, 4, end fraction is start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab:
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.
start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, equals, start fraction, start color #9d38bd, 1, end color #9d38bd, plus, start color #9d38bd, 1, end color #9d38bd, plus, start color #9d38bd, 1, end color #9d38bd, plus, start color #9d38bd, 1, end color #9d38bd, plus, start color #9d38bd, 1, end color #9d38bd, plus, start color #9d38bd, 1, end color #9d38bd, divided by, 4, end fraction, equals, start fraction, 6, divided by, 4, end fraction
Another way we can decompose start fraction, 6, divided by, 4, end fraction is start color #11accd, start fraction, 3, divided by, 4, end fraction, end color #11accd, plus, start color #11accd, start fraction, 3, divided by, 4, end fraction, end color #11accd:
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.
start color #11accd, start fraction, 3, divided by, 4, end fraction, end color #11accd, plus, start color #11accd, start fraction, 3, divided by, 4, end fraction, end color #11accd, equals, start fraction, start color #11accd, 3, end color #11accd, plus, start color #11accd, 3, end color #11accd, divided by, 4, end fraction, equals, start fraction, 6, divided by, 4, end fraction
Want to learn more about decomposing fractions? Check out this video.

Practice

Problem 1
Which of these sums equal start fraction, 14, divided by, 10, end fraction ?
Choose all answers that apply:
Choose all answers that apply:

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

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