Topic A: Working with Numbers
Order of operations, negatives, and number lines.
01 — Order of Operations
Doing Steps in the Right Order
When a problem has many steps, always do them in the same order. Remember it as PEMDAS.
- P — Parentheses: do what's inside ( ) first.
- E — Exponents: powers and square roots next.
- MD — Multiply / Divide: left to right, whichever comes first.
- AS — Add / Subtract: left to right, whichever comes first.
- Negatives: a negative times a negative is positive. −3 × −4 = 12.
Example: 3 + 4 × 2 = 3 + 8 = 11 (not 14, because multiply comes before add).
Practice — Doing Steps in the Right Order
Q1 · Multiple Choice
What is 10 − 2 × 3?
Q2 · Short Answer
What is (6 + 2)² ÷ 4?
02 — Number Line & Absolute Value
Negatives & Absolute Value
Numbers get bigger as you move right on a number line.
- Comparing: −8 is less than −2, because −8 is farther left.
- Absolute value |x|: how far a number is from 0. It is never negative.
- Adding a negative: same as subtracting. 5 + (−7) = −2.
- Subtracting a negative: same as adding. 5 − (−7) = 12.
Example: |−9| = 9 and |4| = 4, so |−9| is bigger.
Practice — Negatives & Absolute Value
Q3 · Multiple Choice
Which number is the smallest?
Q4 · Short Answer
What is 4 − (−6)?
Topic B: Fractions, Decimals & Powers
Fraction math, converting, exponents, and roots.
03 — Fractions & Decimals
Fractions, Decimals & Converting
Fractions and decimals are two ways to write the same amount.
- Add/subtract fractions: make the bottoms (denominators) the same first.
- Multiply fractions: top × top, bottom × bottom.
- Divide fractions: flip the second fraction, then multiply.
- Fraction → decimal: divide top by bottom. 3/4 = 3 ÷ 4 = 0.75.
- Decimal → percent: move the decimal two places right. 0.75 = 75%.
Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Practice — Fractions, Decimals & Converting
Q5 · Multiple Choice
What is 2/3 × 3/4?
Q6 · Short Answer
Write 3/5 as a decimal.
04 — Exponents & Roots
Exponents, Roots & Scientific Notation
An exponent tells you how many times to multiply a number by itself.
- Exponent: 2⁴ = 2 × 2 × 2 × 2 = 16.
- Square root √: what number times itself gives this? √49 = 7.
- Anything to the 0 power: equals 1. 5⁰ = 1.
- Scientific notation: a number from 1 to 10 times a power of 10. 4,500 = 4.5 × 10³.
Example: 3² + √16 = 9 + 4 = 13.
Practice — Exponents, Roots & Scientific Notation
Q7 · Short Answer
What is 5³?
Q8 · Multiple Choice
Which is 0.0062 in scientific notation?