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Dividing decimals

Dividing decimals

The same result
6 cakes for 2 children, or 60 cakes for 20 children – each gets 3.

The result of a division (the quotient) stays the same when both numbers are multiplied by the same number: 6÷2=60÷20=600÷200=3\displaystyle {6\div2}={60\div20}={600\div200}={3}.

Dividing by a decimal

52.3÷0.4\displaystyle 52.3\div0.4 – multiply both by 10, and the divisor (the number you divide by) is a whole number: 52.3÷0.4=523÷4=130.75\displaystyle {52.3\div0.4}={523\div4}={130.75}.

How much to multiply by: 10, 100 or 1000

Multiply by 10, 100 or 1000 – as much as it takes for the divisor to become whole: 1.44÷0.12=144÷12\displaystyle {1.44\div0.12}={144\div12} (times 100). The number being divided may stay a decimal: 1.44÷1.2=14.4÷12\displaystyle {1.44\div1.2}={14.4\div12}.

Long divisions on a calculator

For long divisions you may use a calculator – but first estimate, and check that the result makes sense.

Exercise 1

Write a division with the same result and a whole divisor, and solve it.

a

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

    b

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

      c

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

        d

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

          e

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

            Exercise 2

            3÷0.5\displaystyle 3\div0.5 is bigger than 3.
            Why does dividing by a number less than 1 give a bigger result?