Rational Numbers
Class 8 · Mathematics
4 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Closure of Number Sets
Part of: Properties of rational numbers
A set of numbers is 'closed' under an operation if doing that operation on any two of them always gives an answer inside the same set. Whole numbers are closed under addition: 3 + 4 is 7. But 3 - 4 is -1, which is not a whole number.
Why it matters. Closure tells us when an answer is safe to expect. Without it, children assume that every subtraction or division works inside the numbers they know, and get confused when negatives and fractions appear.
Try it in two minutes
- Write the numbers 3 and 8 on two cards. Ask your child to add, subtract, multiply and divide them in this order.
- After each answer ask: is this a whole number? An integer? A fraction?
- Then swap to 8 and 3 and see which operations still stay inside the whole numbers.
Try at home. Ask your child for one pair of whole numbers whose difference is not a whole number.
Order and Grouping of Rational Numbers
Part of: Properties of rational numbers
Commutative means the order of the two numbers does not matter: 2/3 + 1/2 is the same as 1/2 + 2/3. Associative means the grouping of three numbers does not matter: (a + b) + c is a + (b + c). Both hold for addition and multiplication of rational numbers, but not for subtraction or division.
Why it matters. These properties let children reorder and regroup to make mental calculations easier, for example pairing fractions that add to a whole number. Knowing where they fail avoids careless mistakes in subtraction and division.
Try it in two minutes
- Take three numbers, say 2, 5 and 9. Ask your child to add them in two different orders and in two different groupings.
- Now do the same with subtraction. Ask: did the answers match this time?
- Try 8 ÷ 4 and 4 ÷ 8 to show that division also depends on the order.
Try at home. Ask your child to add 7/10 + 3/8 + 3/10 the quickest way and say which pair to add first.
Zero and One: The Identities
Part of: Special numbers and distributivity
Zero and one are special. Adding 0 to a number leaves it unchanged: 5/8 + 0 is 5/8. Multiplying a number by 1 also leaves it unchanged: 5/8 × 1 is 5/8. So 0 is called the additive identity and 1 the multiplicative identity.
Why it matters. Knowing the identities stops common mix-ups such as thinking that multiplying by 0 keeps a number the same. They are also the base of many shortcuts in algebra later.
Try it in two minutes
- Ask your child: what do I add to 7 to get 7 again? Then: what do I multiply 7 by to get 7 again?
- Repeat with a fraction like 3/5.
- Ask what happens when you multiply 3/5 by 0 and compare it with multiplying by 1.
Try at home. Ask your child to write three expressions that all have the value 2/5, using + 0 and × 1.
Distributivity of Multiplication
Part of: Special numbers and distributivity
Distributivity says that multiplying a number by a sum is the same as multiplying it by each part and adding: 3 × (4 + 5) is 3 × 4 + 3 × 5. It works for rational numbers and for subtraction too, so a(b - c) = ab - ac.
Why it matters. Distributivity is the base of expanding and simplifying in algebra. It also makes mental maths easier, such as 7 × 98 as 7 × 100 - 7 × 2.
Try it in two minutes
- Ask your child to find 6 × 13 two ways: directly, and as 6 × 10 + 6 × 3.
- Try 6 × 19 as 6 × 20 - 6 × 1.
- Then repeat with a fraction, for example 1/2 × (6 + 10).
Try at home. Ask your child to work out 25 × 18 using 25 × 20 - 25 × 2.
What your child will practise
- Closure of Number Sets: Number Sort (Sort It Out)
- Closure of Number Sets: Ocean Quick Fire (Quick Fire)
- Distributivity of Multiplication: Jungle Quick Fire (Quick Fire)
- Order and Grouping of Rational Numbers: Mission Control Quest (Collect the Answer)
- Zero and One: The Identities: Jungle Puzzle (Clue Puzzle)
- Quiz: Closure of Number Sets (8 questions)
- Quiz: Distributivity of Multiplication (8 questions)
- Quiz: Order and Grouping of Rational Numbers (8 questions)
- Quiz: Zero and One: The Identities (8 questions)