Equality & Inequality
Equality in mathematics means two expressions have identical value, represented by the equals sign (=). An equation like 5 + 3 = 8 shows that the sum on the left equals the number on the right. Understanding equality forms the foundation for solving equations and comparing mathematical expressions throughout primary and secondary mathematics.
Why it matters
Equality concepts appear throughout daily life, from splitting a £12 restaurant bill equally among 3 friends (£4 each) to checking if a 150g chocolate bar costs the same per gram as a 300g bar at twice the price. In Year 1, pupils learn to read and interpret the equals sign as part of the UK National Curriculum. This foundation supports fraction equivalence in Year 4, algebraic equations at GCSE level, and advanced problem-solving in A-level mathematics. Shopping comparisons rely on equality principles — determining whether 2 bottles of juice at £1.50 each equals the same value as a 4-pack costing £3.00. Understanding equality also underpins budgeting skills, where income must equal or exceed expenses for financial balance.
How to solve equality & inequality
Equality & Equations
- The equals sign means both sides have the same value.
- A balanced equation stays balanced if you do the same to both sides.
- Use + , − , × , ÷ on both sides to keep equality.
- Check by substituting your answer back in.
Example: 7 + ? = 12 → ? = 12 − 7 = 5. Check: 7 + 5 = 12. ✓
Worked examples
Which is correct? 1 + 2 = 3 or 1 + 2 = 2?
Answer: 3
- Look at each side separately → 1 + 2 = ? — Before we can compare, we need to figure out what 1 + 2 actually equals. Think of it like counting: start at 1 and count up 2 more.
- Add up the left side: 1 + 2 → 3 — If you have 1 apples and get 2 more, you have 3 apples total. So 1 + 2 = 3.
- Look at the other side: 3 → 3 — The other side of the equals sign shows 3. We just need to compare this with our answer.
- Compare — are they the same? → 3 — 3 is the same as 3. The equals sign works like a balance scale — both sides weigh the same!
Fill in the blank: 3 + __ = 6
Answer: 3
- What operation do we see? → 3 + __ = 6 — We see addition. Something is being added to 3 to make 6. Think of it like a jar: you have 3 marbles and need 6 total.
- Use the opposite operation to find the blank → __ = 6 - 3 — Addition and subtraction are opposites. If adding gives us 6, then subtracting takes us back. We subtract 3 from 6.
- Calculate → 3 — 6 - 3 = 3. The missing number is 3.
- Check by plugging back in → 3 + 3 = 6 ✓ — Let's verify: 3 + 3 = 6. It works! Always check your answer by putting it back into the original problem.
Does 2 + 10 equal 8 + 4?
Answer: true
- Work out the left side first → 2 + 10 = 12 — Add the numbers on the left: 2 + 10 = 12. Think of combining two groups of objects.
- Work out the right side → 8 + 4 = 12 — Now the right side: 8 + 4 = 12.
- Compare — are the two sides equal? → true — Left side = 12, right side = 12. They match! Like a balance scale with equal weights on both sides.
Common mistakes
- Writing 4 + 3 = 7 + 2 = 9 in a chain, when 4 + 3 = 7 but 7 ≠ 9, so the statement contains both true and false parts.
- Assuming 5 + □ = 8 means □ = 5 + 8 = 13, when the correct answer is □ = 8 - 5 = 3.
- Believing 6 = 3 + 3 is incorrect because the equals sign faces the 'wrong way', when equality works in both directions.