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Mixed Numbers as Improper Fractions

2 and 3/4 = [(4 x 2)+3]/4=11/4

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Mixed Numbers as Improper Fractions

License: CC BY-NC 3.0

Casey ordered eight pizzas for the drama club to enjoy. Each pizza had ten slices. At the end of the pizza party, there were two whole pizzas and two slices left. How many slices weren’t eaten? How can you express this as an improper fraction of pizza slices?

In this concept, you will learn how to rewrite mixed numbers as an improper fraction.

Writing Mixed Numbers as Improper Fractions

A mixed number is a number that has both wholes and parts in it. Here is a mixed number.

514

There are five whole items and one-fourth of a whole. The opposite of a mixed number is an improper fraction.

An improper fraction is a fraction that has a larger numerator than the denominator. Here is an improper fraction.

125

The denominator tells you how many parts the whole has been divided into. This whole has been divided into 5 parts. The numerator tells you the number of parts. In this case, there are twelve parts. There are more parts than there are in 1 whole.

To write a mixed number as an improper fraction, write the mixed number as a fraction in terms of parts instead of in terms of wholes and parts. Remember that a whole number can also be written as a fraction. The numerator is equal to the denominator.

1=55

Change 213 to an improper fraction.

First, multiply the whole number by the denominator to convert the whole to a fraction and add the numerator. This will give you the new numerator.

2×3+1=7

Then, put the sum over the denominator. The denominator is 3.

213=73

The mixed number 213 is also written as 73.

Change the following mixed numbers to improper fractions.

Examples

Example 1

Earlier, you were given a problem about Casey and the pizzas

Convert 2 pizzas and 2 slices to an improper fraction to find the number of uneaten slices of pizza.

Two whole pizzas and two slices =2210

First, multiply the whole number by the denominator and add the numerator.

2×10+2=22

Then, put the sum over the denominator. The denominator is 10.

2210=2210

There were a total of 22 slices of pizza left uneaten.

Example 2

Express 478 as an improper fraction.

First, multiply the whole number by the denominator and add the numerator.

4×8+7=39

Then, put the sum over the denominator. The denominator is 8.

478=398

The mixed number 478 is expressed as 398.

Example 3

313

First, multiply the whole number by the denominator and add the numerator.

3×3+1=10

Then, put the sum over the denominator. The denominator is 3.

313=103

The mixed number 313 is expressed as 103.

Example 4

523

First, multiply the whole number by the denominator and add the numerator.

3×5+2=17

Then, put the sum over the denominator. The denominator is 3.

313=103

The mixed number 523 is expressed as 173.

Example 5

618

First, multiply the whole number by the denominator and add the numerator.

6×8+1=49

Then, put the sum over the denominator. The denominator is 3.

618=498

The mixed number 618 is expressed as 498.

Review

Write each mixed number as an improper fraction.

  1. 212
  2. 314
  3. 513
  4. 423
  5. 614
  6. 625
  7. 713
  8. 825
  9. 745
  10. 827
  11. 834
  12. 956
  13. 658
  14. 923
  15. 512
  16. 1614

Review (Answers)

To see the Review answers, open this PDF file and look for section 5.14.

Resources

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Vocabulary

Equivalent

Equivalent means equal in value or meaning.

improper fraction

An improper fraction is a fraction in which the absolute value of the numerator is greater than the absolute value of the denominator.

Mixed Number

A mixed number is a number made up of a whole number and a fraction, such as 4\frac{3}{5}.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0

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