Fractions

6 minQuiz at the end

Parts of a Fraction

A fraction represents a part of a whole.

Numerator → the top number (how many parts we have) Denominator → the bottom number (how many equal parts the whole is divided into)

In ¾: numerator = 3, denominator = 4 → we have 3 out of 4 equal parts.

Equivalent fractions look different but represent the same value.

½ = 2/4 = 3/6 = 4/8

To create an equivalent fraction, multiply or divide both the numerator and denominator by the same number.

2/3 × (2/2) = 4/6 ← equivalent to 2/3

Divide both numerator and denominator by their Greatest Common Factor (GCF).

8/12 → GCF of 8 and 12 is 4 → 8÷4 / 12÷4 = 2/3

Same denominator: add or subtract the numerators, keep the denominator.

3/7 + 2/7 = 5/7

Different denominators: find the Lowest Common Denominator (LCD) first.

½ + ¼ → LCD = 4 → 2/4 + 1/4 = 3/4

⅔ − ½ → LCD = 6 → 4/6 − 3/6 = 1/6

Multiply numerators together, then denominators together. Simplify if possible.

¾ × ⅔ = (3×2)/(4×3) = 6/12 = ½

Keep, Change, Flip: keep the first fraction, change ÷ to ×, flip the second fraction (reciprocal).

¾ ÷ ½ = ¾ × 2/1 = 6/4 = 3/2 = 1½

A mixed number has a whole number and a fraction: 2¾ An improper fraction has a numerator larger than the denominator: 11/4

Convert mixed → improper: multiply whole number by denominator, add numerator.

2¾ = (2×4 + 3)/4 = 11/4

Convert improper → mixed: divide numerator by denominator.

11/4 = 2 remainder 3 = 2¾

To compare fractions, give them the same denominator, then compare numerators.

Which is bigger: 3/5 or 5/8? LCD = 40 → 24/40 vs 25/40 → 5/8 is bigger