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Lesson 1: Decomposing fractions

# 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 $\frac{5}{9}$.
One way we can decompose $\frac{5}{9}$ is $\frac{2}{9}+\frac{3}{9}$:
$\frac{2}{9}+\frac{3}{9}=\frac{2+3}{9}=\frac{5}{9}$
Another way we can decompose $\frac{5}{9}$ is $\frac{1}{9}+\frac{2}{9}+\frac{2}{9}$:
$\frac{1}{9}+\frac{2}{9}+\frac{2}{9}=\frac{1+2+2}{9}=\frac{5}{9}$

### Example 2: Number line

How can we decompose $\frac{6}{4}$?
One way we can decompose $\frac{6}{4}$ is $\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}$:
$\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{1+1+1+1+1+1}{4}=\frac{6}{4}$
Another way we can decompose $\frac{6}{4}$ is $\frac{3}{4}+\frac{3}{4}$:
$\frac{3}{4}+\frac{3}{4}=\frac{3+3}{4}=\frac{6}{4}$

## Practice

Problem 1
Which of these sums equal $\frac{14}{10}$ ?

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

## Want to join the conversation?

• how to you decompose a mixed number or a negative fraction
• If you are asking how to convert a mixed number to an improper fraction,you just have to multiply the whole number and the denominator and then add the numerator. The answer you get will be the numerator and the denominator stays the same
• what are negative fractions?
• Fractions that are represented on the LEFT SIDE from 0 on a Number Line.
• how do you decompose a mixed number?
• Its that easy! Think of 19/5 and your to lazy to do 19/5 so 5/5+5/5+5/5+4/5=19/5 you see how we added 3 wholes? and there is 4/5 left over so its 3 4/5, hope this was helpful! Thanks for 25 likes! New goal is 50+.
• How do you add negative fractoins
• It may be tricky. Use -0.04 + 0.03. Its like saying 0.04 - 0.03 but it's completely different. -0.04 + 0.03 = 0.01, this is true since it helps reduce the sum to make it closer to 0, which is actually greater than all of these numbers. Hope it helped, I guess.
• how do you add two decimals with different denomenators
• Let's pretend the 2 decimals are 0.5+ 0.25. So 1 is the whole right? So you divide 100/25=4.But 25x1=25. So that's equal to 1/4. Then you try to find the 0.5 which is easy 100-50=50. and that's only half of it so its 1/2. You then try to find a common denominator which is obviously 4 so 1/2x2/2=2/4. You then add 2/4+1/4 and boom. The answers 3/4. Decimal form: 0.75
• how do you decompose an fractions
• Basically, just turn the numerator into a sum of smaller numbers.
Example: 7∕9 = (3 + 4)∕9 = 3∕9 + 4∕9

This is useful when turning an improper fraction into a mixed number.
Example:
13∕5
= (5 + 5 + 3)∕5
= 5∕5 + 5∕5 + 3∕5
= 1 + 1 + 3∕5
= 2 ³∕₅
• how do you decompose a negative fraction?
• Step 1: Factor the bottom: 5x−4 x2−x−2 = 5x−4 (x−2) (x+1)
Step 2: Write one partial fraction for each of those factors: 5x−4 (x−2) (x+1) = A1 x−2 + A2 x+1
Step 3: Multiply through by the bottom so we no longer have fractions: 5x−4 = A 1 (x+1) + A 2 (x−2)
Step 4: Now find the constants A 1 and A 2:

This is how to decompose the negative fraction. Hope it helped!
(1 vote)
• how do you divied fractions?
• You might want to check out the video “Understanding division of fractions”.
• And how can you decompose a fraction with no danominator
• if there is no denominator, then it is not a fraction. but you can make any number a fraction, since every whole number implicitly have a denominator of 1. For example:

the number 5, you can make it a fraction like this 5/1, the value will still be the same since you still have 5 wholes.
• When you add or subtraction can you use your fangers doing it.