Fractions, Decimals & Percentages

What Is a Fraction? Numerators, Denominators and Mixed Numbers

A fraction $\frac{a}{b}$ means $a$ parts of a whole that has been cut into $b$ equal parts. The bottom number is the denominator; the top is the numerator.

Equivalent Fractions and Simplifying to Simplest Form

Equivalent fractions name the same amount with different numbers, like $\frac{1}{2} = \frac{2}{4} = \frac{4}{8}$. Multiplying or dividing the top and bottom by the same number never changes a fraction's value.

Common Denominators: How to Compare, Add and Subtract Fractions

A common denominator is a denominator shared by two or more fractions. Rewriting fractions over a common denominator makes their pieces the same size, so they can be compared, added and subtracted.

Dividing Fractions: Why You Multiply by the Reciprocal

To multiply fractions, multiply the tops and multiply the bottoms. To divide by a fraction, multiply by its reciprocal, the fraction turned upside down: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$.

Decimals Explained: Tenths, Hundredths and Decimal Place Value

A decimal carries place value past the units: the first place after the decimal point is tenths, then hundredths, then thousandths, each a tenth of the place before.

Percentages: Converting Fractions, Decimals and Percents

Percent means per hundred. $35\%$ is $\frac{35}{100}$, or $0.35$. Finding a percentage of an amount means converting the percentage to a decimal and multiplying.

Percentage Increase and Decrease Using Multipliers

A percentage change compares a change with the original amount. Increasing by $p\%$ means multiplying by $1 + \frac{p}{100}$, and decreasing by $p\%$ means multiplying by $1 - \frac{p}{100}$.