Fractions, decimals, percentages and operations
Fractions, decimals, percentages
- fraction = numerator over denominator; percentage = "out of 100" ($37\% = 0.37$).
- Convert: fraction → decimal by dividing ($\tfrac38 = 0.375$); decimal → % by ×100.
- Multiply fractions: tops × tops, bottoms × bottoms ($\tfrac23\times\tfrac45 = \tfrac{8}{15}$). Divide: × the reciprocal.
Practice
Write 3/8 as a decimal.
3 ÷ 8 = 0.375.
Practice
What is 2/3 × 4/5?
Multiply tops and bottoms: (2×4)/(3×5) = 8/15.
Order of operations & ordering
- Order: brackets, indices, ×÷ (left→right), +− (left→right). e.g. $-6\times-3 + 7\times2 = 18 + 14 = 32$.
- Negatives: $5 - (-3) = 8$; same signs multiply to +, different to −.
- To order a mixed list, convert all to decimals first.
Practice
Using the order of operations, work out −6 × −3 + 7 × 2.
Multiply first: −6×−3 = 18 and 7×2 = 14; then 18 + 14 = 32.
You've got it
Key idea
- $\tfrac38 = 0.375$; percentage = "out of 100"
- order of operations: brackets → indices → ×÷ → +−
- compare a mixed list by converting everything to decimals