Fractions and Decimals

Understanding fractions and decimals—and how to convert between them—is essential for the ParaPro Mathematics section.

Understanding Fractions

A fraction represents a part of a whole.

Types of Fractions:

• Proper: Numerator < Denominator (¾)
• Improper: Numerator ≥ Denominator (5/4)
• Mixed Number: Whole number + fraction (1¼)

Converting Between Mixed Numbers and Improper Fractions

Mixed → Improper: Multiply whole by denominator, add numerator

$2\frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{11}{4}$

Improper → Mixed: Divide numerator by denominator

$\frac{11}{4} = 11 ÷ 4 = 2 \text{ remainder } 3 = 2\frac{3}{4}$

Adding and Subtracting Fractions

Same Denominator: Add/subtract numerators, keep denominator

$\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$

Different Denominators: Find common denominator first

$\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$

Multiplying Fractions

Multiply numerators, multiply denominators:

$\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$

Dividing Fractions

Multiply by the reciprocal (flip the second fraction):

$\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$

Converting Fractions to Decimals

Divide the numerator by the denominator:

$\frac{3}{4} = 3 ÷ 4 = 0.75$

Common Fraction-Decimal Equivalents

Converting Decimals to Fractions

1. Write the decimal as a fraction over a power of 10
2. Simplify

Example: 0.75 = 75/100 = ¾

Classroom Application

Help students with fractions and decimals by:

• Using fraction circles and bars for visual understanding
• Showing equivalence with real-world examples (pizza, money)
• Creating fraction-decimal conversion charts
• Practicing with manipulatives before abstract problems
• Using number lines to compare fractions