Multiplication and division. Calculation techniques

Multiplication can be thought of as repeated addition of the same addend:

6\times 5

means five sixes. It helps to split a factor and use the distributive property:

7\times 12=7\times(10+2)=70+14=84

. Numbers ending in zero are often multiplied “by place”: multiply the significant digits, then attach the zeros. Division undoes multiplication: if

a\times b=c

, then

c\div b=a

(for suitable

a,b,c

). In long division, work from left to right: partial dividend, digit of the quotient, multiply and subtract, bring down the next digit.

Multiplication is repeated addition of the same number

Splitting a factor:

a\times(b+c)=a\times b+a\times c

Check division with multiplication: quotient

\times

divisor

\approx

dividend

Long division uses the same steps for two- and three-digit dividends

Multiplication as repeated addition

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