Division

CBC Grade 5 Mathematics — Division

Lesson Objectives

By the end of this topic, a learner should be able to:

• Divide a 3-digit number by a 2-digit number
• Explain how multiplication and division are inverse operations
• Estimate a quotient by rounding to the nearest ten
• Perform combined operations using all four operations
• Appreciate the use of division in everyday situations

Division

Dividing shares a number into equal parts. It also tells you how many times one number fits into another.

a) The words

The number being divided is the dividend.

The number you divide by is the divisor.

The answer is the quotient.

Anything left over is the remainder.

b) Division undoes multiplication

Multiplication and division are inverse operations. Each undoes the other.

Because 6 × 7 = 42, we know 42 ÷ 7 = 6. We also know 42 ÷ 6 = 7.

This is useful. If you know your times tables, you already know a great many divisions.

It also gives you a way to check. Multiply your answer by the divisor and you should get back the dividend.

c) Estimating first

Round both numbers to the nearest ten, then divide.

For 768 ÷ 24, round to 770 ÷ 20, which is about 38.

Now you know the answer should be around 38, not 4 or 400.

d) Dividing step by step

Work from the left of the dividend.

See how many times the divisor fits. Write that digit above the line.

Multiply, subtract, then bring down the next digit. Repeat until there are no digits left.

e) Remainders

Not every division is exact.

For 50 ÷ 8, the answer is 6 with 2 left over. We write it as 6 remainder 2.

The remainder must always be smaller than the divisor. A remainder of 9 when dividing by 8 means another 8 would still fit.

Check it like this: divisor × quotient + remainder should give the dividend. Here 8 × 6 + 2 = 50.

f) Combined operations

Some problems use all four operations together.

Do brackets first. Then multiply and divide, working left to right. Then add and subtract, also left to right.

Take 20 + 60 ÷ 6 × 2. Divide to get 10. Multiply to get 20. Then add to get 40.

g) Where this is used

Sharing sweets equally. Working out the price of one item from the price of many. Splitting a class into groups. Finding how many packets fill a box.

:::checkpoint Check yourself

1. Work out 855 ÷ 15.
2. Check your answer by multiplying.
3. What is the largest possible remainder when dividing by 9?
4. Work out 30 + 40 ÷ 4 − 5. :::

Definitions

• Dividend — the number being divided.
• Divisor — the number dividing into the dividend.
• Quotient — the result of a division.
• Remainder — what's left over when a number doesn't divide evenly.

Must Remember

1. Check a division by multiplying the quotient by the divisor.
2. A remainder is a valid answer, not a mistake.
3. Round both dividend and divisor the same way before estimating.
4. In combined operations, work through brackets first, then in order.

Conclusion

Division and multiplication are two sides of the same fact — checking by multiplying back is the most useful habit here.