Converting Between Improper Fractions and Mixed Numbers
Objective
Know how to convert an improper fraction to a mixed number, and how to convert a mixed number to an improper fraction.
Example
Convert the following fraction to an improper fraction
1
4
5
Answer:
9
5
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Explanation
Mixed numbers and improper fractions are the same thing, just written differently. So why do we have two ways of writing the same thing?
Mixed numbers look nice. With small denominators, they are the easiest way to imagine what a number looks like.
Improper fractions are hard to imagine, but they are easier to make calculations with.
What does this mean for us? We often want to convert all of our mixed numbers to improper fractions before we make any calculations. Then after we have found our answer, we convert it back to a mixed number, so that it will look nice.
Here I'm going to show the shortcuts. If you don't understand why it works, you'll probably forget it soon, so you may want to want an explanation here and here. (This is true for most things you learn. If you don't understand why it works, you're bound to forget it.)
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Mixed to Improper
To convert a mixed number to an improper fraction, the formula is:
Denominator x Whole Number + Numerator
1
4
5
5 x 1 + 4 = 9
This number will be your new numerator. The denominator stays the same
9
5
Answer:
9
5
Improper to Mixed
To convert a mixed number to an improper fraction, the formula is:
Numerator ÷ Denominator
9
5
9 ÷ 5 = 1 remainder 4
Your quotient is your whole number, your remainder is your new numerator. Your denominator stays the same
1
4
5
Answer:
1
4
5
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Examples
Example 1
Convert the following fraction to an improper fraction?
7
2
3
3 x 7 + 2 = 23
23
3
Answer:
23
3
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Example 2
Convert the following fraction to a mixed number or integer.
24
9
24 ÷ 9 = 2 remainder 6
2
6
9
Answer:
2
6
9
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Example 3
Convert the following fraction to a mixed number or integer.
24
8
24 ÷ 8 = 3 remainder 0
3
0
8
If your numerator is zero, get rid of the fraction part.
3
Answer: 3
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Practice your skills
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Ready?