Multiplying and dividing whole numbers

Grid method for multiplying numbers

The grid method is a visual way of multiplying two numbers. Each digit in the number is divided into its place value column. For example, calculate 46 \times 35:

  • 46 = 40 (four tens) plus 6 (6 units)
  • 35 = 30 (three tens) plus 5 (5 units)
\times40 (tens)6 (units)Total
30 (tens) 30 \times 40 = 1,200 30 \times 6 = 180 1,200 + 180 = 1,380
5 (units) 5 \times 40 = 200 5 \times 6 = 30 200 + 30 = 230
1,380 + 230 = 1,610

Therefore, 46 \times 35 = 1,610.

Column method for multiplying numbers

Numbers can be multiplied together using the column method which involves writing one number underneath the other.

Example

Calculate 46 \times 35.

Units column, 5 x 6

First, multiply 6 × 5 and carry the 30 to the tens column

Therefore, 46 \times 35 = 1,610.

Short division

Small numbers can be divided using knowledge of times tables. Larger numbers can be divided using short division. Short division is a written method that uses mental arithmetic to divide a number in stages. It is ideal when the divisor is less than 10.

Question

Using short division, divide 895 by 5.

895 \div 5 means 'how many times will 5 divide into 895?'. The 5 is called the divisor.

Example of short division (895 / 5)

Divide each digit by 5. Start with the hundreds:

8 \div 5 = 1

Calculate the remainder:

5 \times 1 = 5, 8 - 5 = 3

So the remainder is 3. Carry three hundred into the tens column:

39 \div 5 = 7

Calculate the remainder:

5 \times 7 = 35, 39 - 35 = 4

So the remainder is 4. Carry four tens into the units column:

45 \div 5 = 9

Therefore, 895 \div 5 = 179. The solution of the division is called the quotient.

Sometimes, a digit in a particular place value column may not be divisible by the divisor.

Question

What is 129 \div 3?

Example of short division (129 / 3)

1 \div 3 is not possible, so carry one hundred into the tens column.

12 \div 3 = 4, with no remainder.

9 \div 3 = 3

129 \div 3 = 43