Basic Mathematics for College Students

1.4 Multiplying Whole Numbers 43

Solution
Each step of this multiplication is explained separately. Your solution need only
look like the laststep.

Vertical form

We begin by multiplying 436 by 3.

We continue by multiplying 436 by 2 tens, or 20. If we think of 20 as , then we
simply multiply 436 by 2 and attach one zero to the result.

1

1

1

1

The product is 10,028.

Draw another line beneath the two completed rows. Add

column by column, working right to left. This sum gives the

product of 435 and 23.

4

1

3

1

6

 2 3

1 3 0 8

8 7 2 0

1 0, 0 2 8

Multiply 4 by 2. The product is 8. There is no carried digit to

add. Write the 8 in the thousands column.

4

1

3

1

6

 2 3

1 3 0 8

8 7 2 0

Multiply 3 by 2. The product is 6. Add 6 to the carried 1 to get

7. Write the 7 in the hundreds column. There is no carry.

4

1

3

1

6

 2 3

1 3 0 8

7 2 0

Write the 0 that is to be attached to the result of 20 436 in

the ones column (shown in blue). Then multiply 6 by 2. The

product is 12. Write 2 in the tens column and carry 1.

4

1

3

1

6

 2 3

1 3 0 8

2 0

2  10

Multiply 4 by 3. The product is 12. Add the 12 to the carried 1 to

get 13. Write 13.

4

1

3

1

6

 2 3

1 3 0 8

Multiply 3 by 3. The product is 9. To the 9, add the carried 1 to

get 10. Write the 0 in the tens column and carry the 1 to the

hundreds column.

4

1

3

1

6

 2 3

0 8

Multiply 6 by 3. The product is 18. Write 8 in the ones column

and carry 1 to the tens column.

4 3

1

6

 2 3

8

Vertical form multiplication is often

easier if the number with the larger

amount of digits is written on top.

4 3 6

 2 3

Hundreds column

Tens column

Ones column