Decomposing fractions review

CCSS Math: 4.NF.B.3, 4.NF.B.3b
Review the basics of decomposing fractions, and try some practice problems.

Decomposing fractions

To decompose a number, we break it into smaller parts.
We can decompose 5454 into 50+450+4.
Fractions, like all numbers, can be decomposed in many ways.
Here are a few possible ways to decompose 77 :
  • 2+52+5
  • 4+2+14+2+1
  • 6+16+1
  • 1+2+3+11+2+3+1

Example 1: Tape diagram

Let's decompose 59\dfrac59.
One way we can decompose 59\dfrac59 is 29+39\goldD{\dfrac29}+\greenD{\dfrac39}:
29+39=2+39=59\goldD{\dfrac29}+\greenD{\dfrac39}=\dfrac{\goldD2+\greenD3}9=\dfrac59
Another way we can decompose 59\dfrac59 is 19+29+29\purpleD{\dfrac19}+\redD{\dfrac29}+\tealD{\dfrac29}:
19+29+29=1+2+29=59\purpleD{\dfrac19}+\redD{\dfrac29}+\tealD{\dfrac29}=\dfrac{\purpleD1+\redD2+\tealD2}9=\dfrac59

Example 2: Number line

How can we decompose 64\dfrac64?
One way we can decompose 64\dfrac64 is 14+14+14+14+14+14\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}:
14+14+14+14+14+14=1+1+1+1+1+14=64\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}+\purpleD{\dfrac14}=\dfrac{\purple1+\purple1+\purple1+\purple1+\purple1+\purple1}4=\dfrac64
Another way we can decompose 64\dfrac64 is 34+34\blueD{\dfrac34}+\blueD{\dfrac34}:
34+34=3+34=64\blueD{\dfrac34}+\blueD{\dfrac34}=\dfrac{\blueD3+\blueD3}4=\dfrac64
Want to learn more about decomposing fractions? Check out this video.

Practice

Problem 1
Which of these sums equal 1410\dfrac{14}{10} ?
Choose all answers that apply:
Choose all answers that apply:

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