Understanding Fractions

A fraction represents a part of a whole.

Parts of a Fraction

$\frac{3}{4}$

• Numerator (top): How many parts we have (3)
• Denominator (bottom): How many equal parts make a whole (4)

Read as "three-fourths" or "three out of four"

Visualizing Fractions

Think of a pizza cut into 4 equal slices. If you eat 3 slices:

• You ate $\frac{3}{4}$ of the pizza
• $\frac{1}{4}$ remains

Types of Fractions

Proper Fractions

Numerator < Denominator $\frac{2}{5}, \frac{3}{4}, \frac{7}{8}$ Value is less than 1.

Improper Fractions

Numerator ≥ Denominator $\frac{5}{3}, \frac{7}{4}, \frac{9}{9}$ Value is 1 or greater.

Mixed Numbers

A whole number and a fraction together $2\frac{3}{4}$ "Two and three-fourths"

Converting Between Forms

Improper to Mixed

Divide numerator by denominator: $\frac{11}{4} = 11 \div 4 = 2 \text{ R } 3 = 2\frac{3}{4}$

Mixed to Improper

Multiply whole by denominator, add numerator: $2\frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{11}{4}$

Equivalent Fractions

Fractions that represent the same value: $\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8}$

Multiply or divide both parts by the same number.