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)

\(\times\)	40 (tens)	6 (units)	Total
30 (tens)	\(30 \times 40 = 1,200\)	\(30 \times 6 = 180\)	\(1,200 + 180 = 1,380\)
5 (units)	\(5 \times 40 = 200\)	\(5 \times 6 = 30\)	\(200 + 30 = 230\)
			\(1,380 + 230 = 1,610\)

30 (tens)
40 (tens)	\(30 \times 40 = 1,200\)
6 (units)	\(30 \times 6 = 180\)
Total	\(1,200 + 180 = 1,380\)

5 (units)
40 (tens)	\(5 \times 40 = 200\)
6 (units)	\(5 \times 6 = 30\)
Total	\(200 + 30 = 230\)


40 (tens)
6 (units)
Total	\(1,380 + 230 = 1,610\)

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 \(46 \times 35\).

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First, multiply 6 × 5 and carry the 30 to the tens column
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Then multiply 6 × 3 (= 18) and add the carried 3
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Next, place a zero in the units column since the next step is to multiply 35 × 40
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Then multiply 4 × 5, carry 200 into the hundreds column
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Then multiply 4 × 3 (= 12) and add the carried 2
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Finally, add the results together
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The finished multiplication

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 is less than 10.