Multiply by one or two digits

Keep the value of the multiplier

For 326 × 24, the 24 means 20 and 4, not 2 and 4.

326 × 4 = 1304, 326 × 20 = 6520, 326 × 24 = 1304 + 6520 = 7824.

The second partial product is ten times 326 × 2. In a column layout, begin it in the tens place, or write its zero ones explicitly. Forgetting that place would add only 652 and give a much smaller answer.

The parts can be split the other way as well:

These are alternative organisations of the same product, not separate amounts to add together.

A four-digit number times one digit

For 2407 × 3, multiply the parts:

A column calculation must keep the zero tens. The 21 ones provide two tens and one one. Their two tens are part of the result even though the original number had no tens.

Check your understanding 1 Use the tens in the multiplier

Find 148 × 32.

Product

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4736. The partial products are 148 × 30 = 4440 and 148 × 2 = 296.

Estimate before accepting a result

For 398 × 21, 400 × 20 = 8000 gives a scale check. The exact answer is 398 × 20 + 398 = 8358. An answer around 800 would lose a factor of ten.

Check your understanding 2 Explain a missing place

A learner finds 215 × 13 by calculating 215 × 3 = 645 and 215 × 1 = 215, then adding them. What does that actually calculate, and how should it be repaired?

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It calculates four groups of 215, because the second partial product used one group rather than ten. The correct second part is 215 × 10 = 2150. Add 2150 + 645 = 2795.

For a story, give the product’s unit. If 24 packets each contain 326 seeds, the answer is 7824 seeds, not packets.