Long multiplication

I can multiply a number by a 2-digit number using long multiplication.

For grown-ups: this lesson in words

Years 5 and 6 · Maths

Here are 12 rows of 6 cupcakes. That is 6 × 12.
Split the 12 rows into 10 rows and 2 rows.
6 × 10 = 60 and 6 × 2 = 12
60 + 12 = 72, so 6 × 12 = 72
Picture: An array of 12 rows of 6 cupcakes. A gap splits it after 10 rows, into 10 rows of 6 cupcakes and 2 rows of 6 cupcakes.
Long multiplication does the same. Let's work out 32 × 21.
Start with the ones digit of 21, which is 1. 2 × 1 = 2
3 × 1 = 3. The first row is 32 × 1 = 32
Picture: 32 times 21 worked out as a long multiplication: the answer is 672.
Now the tens digit of 21. It is 2 tens, which is 20. First, write a 0 in the ones place.
That 0 is a placeholder. It keeps the next digits in the tens and hundreds places.
2 × 2 = 4 and 3 × 2 = 6. The second row is 32 × 20 = 640
Picture: 32 times 21 worked out as a long multiplication: the answer is 672.
Now add the two rows, 32 and 640, ones under ones.
32 + 640 = 672, so 32 × 21 = 672
Two rows, then add them. That is long multiplication.
Picture: 32 times 21 worked out as a long multiplication: the answer is 672.
A good habit: estimate first. Here are 32 and 21 on a number line. Round each one to the nearest ten.
32 is about 30.
21 is about 20.
30 × 20 = 600
Picture: A number line from 10 to 40, labelled every 10. A dot at the 1st tick after 20 labelled "21" and a dot at the 2nd tick after 30 labelled "32". The frog makes 2 hops: the 2nd tick after 30 to 30 (about 30) and the 1st tick after 20 to 20 (about 20).

partial product:: The answer to one row, before the rows are added.
placeholder:: The 0 written first in the tens row, so every digit stays in its place.
estimate:: A rough answer, found by rounding the numbers first.

This is the first part of the lesson. Grown-ups can unlock every lesson in the grown-ups area.