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Level 1 · Topic 1

Number & Calculation

Multiples, factors, percentages, ratio, proportion and order of operations

Multiples, factors and primes

Multiples of a number are its times table results. Multiples of 6: 6, 12, 18, 24…

Factors of a number are whole numbers that divide into it exactly. Factors of 12: 1, 2, 3, 4, 6, 12.

Prime numbers have exactly two factors — 1 and themselves: 2, 3, 5, 7, 11, 13, 17, 19…

LCM
Lowest Common Multiple
HCF
Highest Common Factor
Prime
Only factors: 1 & itself
Square
n × n (e.g. 4² = 16)
💡 Is 1 prime? No — 1 has only one factor (itself), and primes need exactly two. The smallest prime is 2.

Percentages — increase and decrease

At Level 1 you need to calculate percentage increases and decreases, not just find a percentage of an amount.

Percentage increase: Original + (% × Original)
Percentage decrease: Original − (% × Original)
Percentage change: (Change ÷ Original) × 100
💡 Multiplier method: A 20% increase = multiply by 1.20. A 15% decrease = multiply by 0.85. Faster for calculator questions.

Ratio and proportion

A ratio compares two or more quantities. The ratio 3:2 means for every 3 of one thing, there are 2 of another.

To divide in a ratio: add the parts, divide the total by the sum, then multiply each part.

3:2
3 parts to 2 parts (5 total)
Simplify
Divide both by HCF
Unitary
Find 1 part first
💡 Unitary method: "3 items cost £7.50. Find 1 item first: £7.50 ÷ 3 = £2.50. Then × however many you need."

Order of operations (BODMAS)

When a calculation has multiple operations, you must follow the correct order:

B — Brackets first
O — Orders (powers and roots)
D — Division
M — Multiplication
A — Addition
S — Subtraction

So 3 + 4 × 2 = 11 (not 14) because multiplication comes before addition.

💡 Remember: Division and multiplication have equal priority — work left to right. Same for addition and subtraction.
1Finding the HCF and LCM
▼
Find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of 12 and 18.
  1. 1Factors of 12: 1, 2, 3, 4, 6, 12
  2. 2Factors of 18: 1, 2, 3, 6, 9, 18
  3. 3Common factors: 1, 2, 3, 6. Highest is 6. So HCF = 6.
  4. 4Multiples of 12: 12, 24, 36… Multiples of 18: 18, 36… First match is 36. So LCM = 36.
✅ HCF = 6  |  LCM = 36
2Percentage increase
▼
A TV costs £320. The price increases by 15%. What is the new price?
  1. 1Find 15% of £320: 10% = £32, 5% = £16, so 15% = £48
  2. 2Add to original: £320 + £48 = £368
  3. 3Multiplier method check: £320 × 1.15 = £368 ✓
✅ New price = £368
3Percentage decrease
▼
A jacket costs £85. It is reduced by 20% in a sale. What is the sale price?
  1. 1Find 20% of £85: 10% = £8.50, 20% = £17
  2. 2Subtract: £85 − £17 = £68
  3. 3Multiplier: £85 × 0.80 = £68 ✓
✅ Sale price = £68
4Dividing in a ratio
▼
Two friends share £240 in the ratio 3:5. How much does each person get?
  1. 1Total parts: 3 + 5 = 8 parts
  2. 2Value of 1 part: £240 ÷ 8 = £30
  3. 3Person 1: 3 × £30 = £90
  4. 4Person 2: 5 × £30 = £150
  5. 5Check: £90 + £150 = £240 ✓
✅ Person 1 gets £90, Person 2 gets £150.
5Unitary method (proportion)
▼
5 pens cost £3.75. How much would 8 pens cost?
  1. 1Find the cost of 1 pen: £3.75 ÷ 5 = £0.75
  2. 2Multiply by 8: £0.75 × 8 = £6.00
✅ 8 pens cost £6.00.
6Order of operations (BODMAS)
▼
Calculate: 5 + 3 × (8 − 2) ÷ 2
  1. 1Brackets first: (8 − 2) = 6 → expression becomes 5 + 3 × 6 ÷ 2
  2. 2Multiply & divide left to right: 3 × 6 = 18, then 18 ÷ 2 = 9 → expression becomes 5 + 9
  3. 3Addition: 5 + 9 = 14
✅ Answer = 14
Question 1
Which of the following is a prime number?
Question 2
A salary of £24,000 increases by 5%. What is the new salary?
Question 3
Share £350 in the ratio 2:5. What is the larger share?
Question 4
Calculate: 4 + 2² × 3
Question 5
4 litres of paint costs £18.80. How much would 7 litres cost?
Question 6
A price of £56 is reduced by 35%. What is the new price?
Question 7
Find the HCF of 24 and 36.
Question 8
Concrete mix uses cement and sand in the ratio 1:4. How much sand is needed for 15 kg of cement?
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