Powers of ten and operation order

The value of each digit changes

In 246 × 100 = 24 600, every original digit has one hundred times its former value. The 2 changes from 200 to 20,000. The zeros hold the now-empty tens and ones places.

For 36 000÷1000 = 36, each digit has one thousandth its former value. First decide whether the answer should grow or shrink; that catches a reversed operation.

A multiple such as 300 can be split: 24 × 300 = 24 × 3 × 100 = 7200. Similarly 7200÷300 = 7200÷100÷3 = 72÷3 = 24. These steps do not need a calculator. Check division by multiplying the answer and divisor.

A written expression has an agreed meaning

Work inside brackets first. Then do multiplication and division from left to right. Finally do addition and subtraction from left to right.

For 18-12÷3 + 2 × 4, first find 12÷3 = 4 and 2 × 4 = 8. Now 18-4 + 8 = 14 + 8 = 22.

Compare (18-12)÷3 + 2 × 4 = 6÷3 + 8 = 10. Brackets changed the grouping, so the answer changed. “Addition before subtraction” is not the rule: 20-8 + 3 = 15, not 9.

Check your understanding 1 Explain before calculating

Find 48÷6 × 2 and 48÷(6 × 2). Why do the answers differ?

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Without brackets, work left to right: 8 × 2 = 16. With brackets, the divisor is the whole product 12, so 48÷12 = 4.

Choose an expression for a story

Four packs each contain 30 cards. Eighteen cards are given away. The cards left are 4 × 30-18 = 102. The expression 4 × (30-18) would give away 18 from every pack, a different story.

Cards left from five packs of 20 after giving away 16 cards

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