Topic 3 of 9
Step 6: Long division and equivalent fractions
Multiplying by one- and two-digit numbers
Step 6 · Long division and equivalent fractions topics
Read multiplication as "times as many", multiply a number of up to four digits by a one-digit number, and multiply two two-digit numbers with an area model.
Times as many
Multiplication can compare sizes. If a tree is 4 times as tall as a 3 meter bush, the tree is 4 × 3 = 12 meters tall.
Multiplying by a one-digit number
Split the bigger number by place value, multiply each part, and add. Multiplying column by column with carrying does the same work.
Example: Splitting by place
What is 4 × 326?
- 326 = 300 + 20 + 6.
- 4 × 300 = 1,200, 4 × 20 = 80, 4 × 6 = 24.
- 1,200 + 80 + 24 = 1,304.
Answer1,304
Example: In columns
What is 7 × 2,418?
- 7 × 8 = 56: write 6, carry 5.
- 7 × 1 = 7, plus 5 is 12: write 2, carry 1.
- 7 × 4 = 28, plus 1 is 29: write 9, carry 2.
- 7 × 2 = 14, plus 2 is 16.
Answer16,926
Multiplying two two-digit numbers
An area model splits both numbers into tens and ones. Each part of the rectangle is a small multiplication, and the total area is the answer.
| × | 20 | 3 |
|---|---|---|
| 10 | 200 | 30 |
| 4 | 80 | 12 |
Example: Using an area model
What is 23 × 14?
- Split: 23 = 20 + 3 and 14 = 10 + 4.
- 20 × 10 = 200, 3 × 10 = 30, 20 × 4 = 80, 3 × 4 = 12.
- 200 + 30 + 80 + 12 = 322.
Answer322
In columns the same work is two rows: 23 × 4 = 92, then 23 × 10 = 230. The zero is there because the 1 in 14 is really 10. 92 + 230 = 322.
Try it yourself
Work each one on paper first, then open the answer to check.
A dog weighs 5 times as much as a 6 kg cat. How heavy is the dog?
Show answer
30 kg.
What is 3 × 742?
Show answer
2,226.
What is 6 × 1,305?
Show answer
7,830.
What is 34 × 12?
Show answer
408. 34 × 10 = 340 and 34 × 2 = 68.
What is 47 × 25?
Show answer
1,175.