Fractions, Decimals, and Percentages

Fraction operations

• Add and subtract: use a common denominator. 2/3 + 1/4 = 8/12 + 3/12 = 11/12.
• Multiply: multiply tops and bottoms. 2/3 × 9/10 = 18/30 = 3/5.
• Divide: multiply by the reciprocal. 3/4 ÷ 1/2 = 3/4 × 2 = 3/2.
• Mixed numbers: change to improper fractions first. 2 1/2 = 5/2.

Converting

Fraction	Decimal	Percentage
1/2	0.5	50%
1/4	0.25	25%
1/5	0.2	20%
1/8	0.125	12.5%
1/3	0.333...	33.3%

• Decimal to percentage: multiply by 100.
• Fraction to decimal: divide the top by the bottom.

Recurring decimals to fractions (Extended)

Example. x = 0.272727...

100x = 27.2727...

100x − x = 27, so 99x = 27 and x = 3/11.

Multiply by 10, 100 or 1000 depending on how many digits repeat.

Ordering

Convert everything to decimals to compare: 3/5 = 0.6, 0.62, 61% = 0.61. Order: 3/5, 61%, 0.62.

Percentage of an amount

15% of 80 = 0.15 × 80 = 12.

Quick summary

• Common denominators to add; multiply across; flip and multiply to divide.
• Move between fractions, decimals and percentages fluently.
• Recurring decimals: multiply, subtract, solve.