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Proper, Improper and Mixed Numbers is taught in the note for Fractions. Read it below and look for the section on this topic.

Fractions

9 min read

What a fraction means

A fraction shows parts of a whole. In the bottom number, the denominator, says how many equal parts the whole is cut into. The top number, the numerator, says how many of those parts we take.

Three ways to see three-quartersThe fraction three quarters shown as three of four equal parts of a bar, three of four equal sectors of a circle, and six of eight counters in a set.bar: 3 of 4 partscircle: 3 of 4 sectorsset: 6 of 8 counters3/4 of a whole
Try itShade a fraction

Change the numerator and the denominator. The bar is cut into equal parts and some are shaded.

Equivalent fractions

Cutting every part into two keeps the shaded amount the same.
Multiply or divide the top and bottom by the same number and the value does not change.

Comparing and adding fractions

To compare or add fractions you need the same denominator. Change each fraction to an equivalent one with a common denominator, then compare the numerators.

Worked exampleWhich is bigger: 3/4 or 5/8?

Compare and .

  1. The smallest common denominator of 4 and 8 is 8.
  2. Change the first fraction.
  3. Compare the numerators: 6 is greater than 5.

Answer: is bigger than .

Worked exampleAdding with different denominators

Work out .

  1. Common denominator: 12.
  2. Change both fractions.
  3. Add the numerators and keep the denominator.

Answer: .

Multiply tops and bottoms. To divide, flip the second fraction and multiply.
Check yourself Which fraction is equivalent to 2/3?
Check yourself What is 2/5 + 1/5?

Key terms

Numerator
The top number: how many parts are taken.
Denominator
The bottom number: how many equal parts make the whole.
Equivalent fractions
Different fractions with the same value.
Mixed number
A whole number and a fraction together.

Summary

  • A fraction is parts of a whole: numerator over denominator.
  • Equivalent fractions come from multiplying or dividing top and bottom by the same number.
  • Use a common denominator to compare and to add or subtract.
  • To divide by a fraction, multiply by its flip.
Comparison of Fractions