- Multiply by a one-digit number by splitting and in a column
- Divide with a remainder and check the answer
- Decide what to do with the remainder in a word problem
23 children are going on a boat trip. Each boat takes 4 children. How many boats are needed? 23 cannot be divided by 4 exactly: something is left over. In this lesson we will learn about remainders and how to multiply bigger numbers by one digit.
Multiplying by splitting
To work out 24 × 3, split 24 into tens and ones: 20 × 3 = 60 and 4 × 3 = 12. Then add the results: 60 + 12 = 72. Multiplying each part separately lets you go beyond the times table.
A box holds 24 markers. How many markers are there in 3 boxes?
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20 × 3 = 60 and 4 × 3 = 12.
60 + 12 = 72.
There are 72 markers in 3 boxes.
A book has 136 pages. How many pages are there in 4 such books?
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Ones: 6 × 4 = 24 → write 4 and carry 2 tens.
Tens: 3 × 4 = 12, 12 + 2 = 14 → write 4 and carry 1 hundred.
Hundreds: 1 × 4 = 4, 4 + 1 = 5.
Answer: 544 pages.
12
136
× 4
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544Division with a remainder
Not every number can be shared equally. If we share 17 sweets among 5 children, each child gets 3 sweets (5 × 3 = 15), and 2 sweets are left over. We write: 17 ÷ 5 = 3 remainder 2.
The part that is left over after dividing. The remainder is always smaller than the divisor.
This is how we check a division with a remainder: 17 = 5 × 3 + 2.
23 children are going on a boat trip. Each boat takes 4 children. How many boats are needed?
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23 − 20 = 3, so 23 ÷ 4 = 5 remainder 3.
5 boats are full, but the other 3 children can't stay on the shore, so they need one more boat.
Answer: 6 boats.
Let's practise
- 1.24 × 3 =
- 2.15 × 4 =
- 3.136 × 4 =
- 4.207 × 3 =
- 5.72 ÷ 3 =
- 6.84 ÷ 4 =
- 7.17 = 5 × 3 +
- 8.29 = 4 × 7 +
- 9.50 = 6 × + 2
Key points
- To multiply a bigger number, split it: 24 × 3 = 20 × 3 + 4 × 3 = 72.
- In column multiplication start with the ones and add the carried digit to the next product.
- Division with a remainder: 17 ÷ 5 = 3 remainder 2; the remainder is always smaller than the divisor.
- Check: divisor × quotient + remainder = dividend.
- In a word problem, the remainder sometimes needs one more item and sometimes is just left over.
Check yourself
10 questions. Every correct answer earns XP.