Math
Five core skills with worked examples, then a practice quiz.
1. Fractions
Adding and subtracting
Fractions need a common denominator (the same bottom number) before you add or subtract. Change the fractions, then work with the tops only.
Common denominator is 6: 3/6 + 2/6 = 5/6
Multiplying
Multiply the tops, multiply the bottoms, then simplify.
Dividing
Keep the first fraction, flip the second (use its reciprocal), and multiply.
2. Percents
"Percent" means "out of 100." To find a percent of a number, change the percent to a decimal and multiply.
25% = 0.25, and 0.25 × 80 = 20
Percent change
percent change = (new − old) ÷ old × 100
(60 − 50) ÷ 50 = 0.2, so it is a 20% increase.
3. Order of operations
Work in this order, left to right within each step:
- Parentheses
- Exponents
- Multiplication and Division (left to right)
- Addition and Subtraction (left to right)
Multiply first: 3 + 8 = 11
With parentheses: (3 + 4) × 2 = 7 × 2 = 14
4. Area and perimeter
| Shape | Area | Perimeter / circumference |
|---|---|---|
| Rectangle | length × width | 2 × (length + width) |
| Triangle | 1/2 × base × height | add the three sides |
| Circle | π × r² | 2 × π × r |
Area = 5 × 3 = 15 square units. Perimeter = 2 × (5 + 3) = 16 units.
Area is measured in square units, and perimeter in plain units. That is a common thing to mix up.
5. Solving equations
Whatever you do to one side of an equation, do to the other side. Undo operations in reverse order: first add or subtract, then multiply or divide.
Subtract 5 from both sides: 2x = 12
Divide both sides by 2: x = 6
Check: 2(6) + 5 = 17 ✓
Practice quiz
Tap an answer. You will see right away whether it is correct and why.