4A Percents, Fractions & Decimals Study Guide

Key Vocabulary

Percent — a ratio that compares a number to 100. "Per cent" means "per hundred." (porcentaje)

Fraction — a part of a whole written as one number over another (numerator/denominator). (fracción)

Decimal — a number written using a decimal point to show tenths, hundredths, etc. (decimal)

Equivalent — having the same value, even if written differently. (equivalente)

Convert — to change from one form to another (e.g., fraction to decimal). (convertir)

Percents, fractions, and decimals are three ways to write the same value. Use this triangle to remember how to convert between them:

        PERCENT
        /      \
  ×100 /        \ ÷100
      /          \
 DECIMAL ———— FRACTION
     divide numerator
     by denominator

Example: 3/4 → 0.75 → 75%
3 ÷ 4 = 0.75 | 0.75 × 100 = 75%

1/4 → 1 ÷ 4 = 0.25

0.25 × 100 = 25%

40% → 40/100 → 2/5

75% ÷ 100 = 0.75

% = (part ÷ whole) × 100

Fraction → Decimal: divide top by bottom
Decimal → Percent: multiply by 100

50% = 0.50 = 1/2 — NOT 50! The percent sign means "out of 100."
Decimal point moves 2 places: To go from percent to decimal, move the point 2 places LEFT. To go from decimal to percent, move it 2 places RIGHT.
Always simplify fractions: 50/100 should be written as 1/2.
Percents can be greater than 100%: 150% = 1.5 = 3/2. This means MORE than the whole.

1. Convert 3/4 to a percent.

2. Convert 0.35 to a percent.

3. Convert 60% to a fraction in simplest form.

4. Convert 125% to a decimal.