Multiply and divide three-digit numbers
Distribute place-value parts, exchange when needed and check a division with multiplication.
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Multiply each place-value part
Find 236 × 4. Think of 236 as 200, 30 and 6.
Add the partial products: 800 + 120 + 24 = 944.
A written column method keeps the same parts: 24 ones give four ones and two tens; twelve tens plus those two tens give fourteen tens; eight hundreds plus the exchanged hundred give nine hundreds. The answer is still 944.
Estimate 240 × 4 = 960. A result near 960 is sensible.
Divide from the greatest place
Find 726÷3. Share seven hundreds between three groups: each gets two hundreds, and one hundred remains. Exchange it for ten tens. With the original two tens, share twelve tens: each gets four tens. Share the six ones: each gets two ones.
Each group has 242. Check 242 × 3 = 726.
For 815÷4, two hundreds per group use 800 and leave 15. There are no full tens to share to each group. Write zero in the tens place. Fifteen ones give three per group with three left: 203 remainder 3.
Check 203 × 4 + 3 = 815. Writing 23 would lose two hundred-sized groups.
You can record the sharing in place-value steps. Each amount in a row is a count of that row’s units.
| Place | Available | In each group | Left at this place |
|---|---|---|---|
| Hundreds | 8 | 2 | 0 |
| Tens | 1 | 0 | 1 |
| Ones | 15 | 3 | 3 |
The one ten left in the second row becomes ten ones. Add the original five ones to get 15 ones in the last row. The digits for each group are 2, 0 and 3: 203, with three ones left. Keep the zero row as part of the working.
Check your understanding 1 Keep all partial products
Find 147 × 6.
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600 + 240 + 42 = 882. A column calculation gives the same total after exchanging ones and tens.
Check your understanding 2 A zero in the quotient
Find 918÷3. Explain why the tens digit of your answer matters.
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Share nine hundreds to get three hundreds per group. One ten is too small to give each group a whole ten, so write zero tens and exchange the ten for ten ones. Eighteen ones give six ones per group. The answer is 306; 306 × 3 = 918.
Choose the operation before the method
Seven identical bags contain 126 marbles each. Find the total. Then imagine 126 marbles shared among seven bags and find how many belong in each. Write a sentence for each answer.
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Seven bags of 126 contain 126 × 7 = 882 marbles altogether. Sharing 126 equally between seven bags gives 126÷7 = 18 marbles per bag. The same two numbers play different roles.
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