Year 5AC9M5N06

Long Multiplication

Solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies; check the reasonableness of answers.

Read this first

Break a big multiply into small ones you already know. Then add them up.

Multiplying makes a rectangle. 4 rows of 6 is 24 squares. Big numbers work the same way, just split into parts.

Words you need

Product: The answer when you multiply.
Partial product: One part of the answer, before you add them all up.
Place holder: The 0 you write when you multiply by the tens.

Worked example

e.g. Work out

23 \times 14

Split 14 into 10 and 4. Now you have two easy multiplies.
First multiply by the 4. $23 \times 4 = 92$ .
Now multiply by the 10. Write a 0 first to hold the ones column, then $23 \times 1 = 23$ . That gives 230.
Add the two parts. $92 + 230 = 322$ .
So $23 \times 14 = 322$ .

The 0 is the part people forget. You are multiplying by 10, not by 1, so the answer must shift one column left.

Practice

The pictures fade as you go. By the last few you are on your own.

1What is

6 \times 7

? Count the array.with a picture

Answer42. Six rows of seven.

2Work out

32 \times 12

.with a hint

Need a hint?

Split 12 into 10 and 2. Do $32 \times 2$ , then $32 \times 10$ , then add.

Answer384.

32 \times 2 = 64

and

32 \times 10 = 320

. Then

64 + 320 = 384

3Work out

45 \times 13

.with a hint

Need a hint?

Do $45 \times 3$ first, then $45 \times 10$ . Remember the 0.

Answer585.

45 \times 3 = 135

and

45 \times 10 = 450

. Then

135 + 450 = 585

24 \times 15

on your own

Answer360

36 \times 21

on your own

Answer756

52 \times 18

on your own

Answer936

7A box holds 24 pencils. How many pencils in 16 boxes?on your own

Answer384 pencils.

24 \times 16 = 384

Think about it

Why do you write a 0 when you multiply by the tens digit?

One good answerBecause you are multiplying by 10, not by 1. The 0 shifts the answer one column left, which makes it ten times bigger.

23 \times 14

the same as

14 \times 23

One good answerYes. Multiplying either way round gives the same answer. Turn the array on its side and the number of squares does not change.

How could you check

32 \times 12 = 384

without doing it again?

One good answerEstimate.

32

is about

30

and

12

is about

10

, so the answer should be near

300

. 384 is close, so it looks right. If you had got 3840 you would know something went wrong.

Common mistakes

Forgetting the 0 when multiplying by the tens.

Without it you multiply by 1 instead of 10, and the answer comes out far too small.

Adding the two parts in the wrong columns.

Line the digits up by column before you add. Ones under ones, tens under tens.

Not checking whether the answer is sensible.

Round both numbers and estimate first. It takes seconds and catches big mistakes.