Integers, Fractions and Decimals: Year 7 Study Guide
Year 7 consolidates number skills and extends them to negative numbers and indices.
Integers are the whole numbers and their negatives. Adding a negative number moves left on the number line, and subtracting a negative is the same as adding: 5 − (−3) = 8. Multiplying or dividing two numbers with the same sign gives a positive; with different signs it gives a negative.
Index notation shows repeated multiplication: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. A square number is n², a cube number is n³, and √ and ∛ undo them. Students also work with prime factorisation, the highest common factor and the lowest common multiple, and use BODMAS (brackets, orders, division and multiplication, addition and subtraction).
Sign rules
| Calculation | Rule | Answer |
|---|---|---|
| (−5) + (−3) | same signs: add, keep sign | −8 |
| (−5) + 8 | different signs: subtract | 3 |
| 4 − (−6) | subtract = add the opposite | 10 |
| (−7) × (−2) | same signs: positive | 14 |
| (−18) ÷ 3 | different signs: negative | −6 |
Fractions and decimals
Add and subtract fractions using a common denominator: 3/4 − 2/5 = 15/20 − 8/20 = 7/20. Multiply straight across: 2/3 × 9/10 = 18/30 = 3/5. Divide by multiplying by the reciprocal: 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8. Convert a fraction to a decimal by dividing: 7/20 = 0.35. Some decimals repeat: 1/3 = 0.333…
LCM of denominators.
Equivalent fractions.
Add, subtract, multiply or divide.
Use the HCF.
Indices and order of operations
BODMAS tells us 3 + 2 × 4² = 3 + 2 × 16 = 35. Brackets change it: (3 + 2) × 4² = 80. Multiply powers of the same base by adding the indices (a³ × a² = a⁵). A prime factor tree for 72 gives 2 × 2 × 2 × 3 × 3 = 2³ × 3². Use this to find the HCF and LCM of larger numbers.
Worked examples and common mistakes
Example: The temperature at 6 am is −3 °C and rises 11 °C: −3 + 11 = 8 °C. Common mistakes: treating −3² as 9 (it is −9 without brackets), forgetting the BODMAS order and adding denominators. Check with a calculator, then explain your reasoning.
Check your understanding: model answers
1. −24 + 10 = −14. 2. 10/12 − 3/12 = 7/12. 3. 144 = 2⁴ × 3².
✨ Key Takeaways
- Same signs multiply to a positive.
- Subtracting a negative adds.
- BODMAS sets the order.
- Indices show repeated multiplication.
💬 Questions for Discussion & Reflection
- Work out (−4) × 6 + 10.
- Work out 5/6 − 1/4.
- Write 144 as a product of prime factors.
Print graph paper for number lines →