Mastering Fractions

Understand the basics of fractions, including simplifying, converting between mixed numbers and improper fractions, and finding common denominators.

Key Ideas

A fraction represents a part of a whole.
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor.
To add or subtract fractions, you must find a common denominator first.
Multiplying fractions: multiply numerators together and denominators together.
Dividing fractions: Keep, Change, Flip (multiply by the reciprocal).

Example 1

Calculate 2/3 + 1/4.

Explanation

Find a common denominator for 3 and 4. The lowest common multiple is 12.

Convert 2/3 to twelfths: (2 × 4) / (3 × 4) = 8/12.

Convert 1/4 to twelfths: (1 × 3) / (4 × 3) = 3/12.

Add the numerators: 8/12 + 3/12 = 11/12.

Example 2

Simplify 18/24.

Explanation

Find the factors of 18: 1, 2, 3, 6, 9, 18.

Find the factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.

The greatest common factor is 6.

Divide numerator and denominator by 6: 18 ÷ 6 = 3, and 24 ÷ 6 = 4.

The simplified fraction is 3/4.

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Common Mistakes

Exam Tip

"When dealing with mixed numbers in calculations, it's often safer to convert them to improper fractions first."