When two numbers are multiplied, doubling one number and halving the other can be used to: • write a multiplication sum differently:
24 × 5 = 12 × 10 = 6 × 20 = 3 × 40 (first number is halved; second number is doubled)
• find the answer easily, especially when 5 and 2 are factors of the two numbers involved: 24 × 5 = 12 × 10 = 120 (it makes multiplication easier).
Use multiplication to do division
Four-fact families for multiplication and division enable us to: • use multiplication to check division: If 21 ÷ 3 = 7 then 7 × 3 = 21 or 3 × 7 = 21
• use division to check multiplication: If 8 × 9 = 72 then 72 ÷ 8 = 9 and 72 ÷ 9 = 8
Since multiplication and division are inverse operations, multiplication undoes division and division undoes multiplication.
Multiply by 10, 100 and 1 000 Learners should know that: • multiplying by 10 changes units into tens:
tens into hundreds: hundreds into thousands:
• multiplying by 100 changes units into hundreds: tens into thousands:
• multiplying by 1 000 changes units into thousands:
10 × 4 = 40 10 × 40 = 400 10 × 400 = 4 000
which means that a nought is inserted at the end of the whole number.
100 × 4 = 400 100 × 40 = 4 000
which means that two noughts are inserted at the end of the whole number. 1 000 × 4 = 4 000 which means that three noughts are inserted at the end of the whole number.
Multiply by multiples of 10, 100 and 1 000 Learners should know that: • multiplying by 20 means multiplying by 2 and by 10 • multiplying by 300 means multiplying by 3 and by 100 • multiplying by 5 000 means multiplying by 5 and by 1 000.
Section 3: Teaching and learning Mathematics
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