Multiplication

CBC Grade 5 Mathematics — Multiplication

Lesson Objectives

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

• Multiply a 3-digit number by a 2-digit number
• Estimate a product by rounding both numbers to the nearest ten
• Create number patterns involving multiplication, staying under 1,000
• Appreciate the use of multiplication in everyday situations

Multiplication

Multiplying is a fast way of adding the same number many times. Instead of adding 342 six times, we multiply.

a) Setting it out

Write the bigger number on top and the 2-digit number underneath.

Line up the columns from the right.

Draw a line underneath.

b) Multiplying by the ones

Start with the ones digit of the bottom number.

Multiply it by every digit on top, working from the right.

An answer past 9 carries into the next column, just as it does when adding.

c) Multiplying by the tens

Now use the tens digit.

Before you start this line, write a zero in the ones place. That zero is there because you are multiplying by tens, not ones.

Missing that zero is the commonest mistake in this topic. It makes the answer far too small.

d) Adding the two lines

Add your two lines together to get the final answer.

Keep the columns straight while adding. Most remaining errors come from digits sliding out of line.

e) Estimating first

Round both numbers to the nearest ten, then multiply.

The estimate is 10 200 and the answer is 8 892. They are in the same range, so the answer looks sensible.

Suppose your answer were 889 or 88 920. The estimate would show at once that something was wrong.

Estimate before you calculate. Then you already know roughly what to expect.

f) Number patterns

Some patterns multiply instead of adding.

In 2, 6, 18, 54 each number is 3 times the one before.

To find the rule, ask what you multiply by each time.

Keep the numbers under 1 000 at this level. In this pattern the next one is 162.

g) Useful checks

Multiplying by an even number always gives an even answer.

Multiplying by 5 always ends in 0 or 5.

Multiplying by 10 adds a zero to the end.

h) Where this is used

Working out the cost of many items. Counting rows of seats. Finding a total from a daily amount. Working out area.

:::checkpoint Check yourself

1. Work out 253 × 34.
2. Why do you write a zero before multiplying by the tens?
3. Estimate 487 × 22 by rounding to the nearest ten.
4. Give the next number in 3, 12, 48. :::

Definitions

• Product — the result of multiplying two numbers.
• Factor — a number being multiplied.
• Estimate — an approximate answer, found by rounding before calculating.

Must Remember

1. Make sure the tens and ones parts genuinely add back up to the original number.
2. Multiply by the tens part fully, including the extra zero.
3. Round both numbers the same way before estimating.
4. Check a pattern by confirming each term follows the same rule as the one before it.

Conclusion

Split the 2-digit number into tens and ones, multiply the 3-digit number by each part, then add the results — the same method every time.