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1995-01-03
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êêèDIVIDING FRACTIONS, ELEMENTARY LEVEL
è In this section we will be looking at dividing positive fractions.
When you divide two positive fractions, the answer is always positive.
The procedure is to change the operation to multiplication, invert the
second fraction, then treat the problem as a multiplication problem.
The positive fractions are described in the list below.
êêêëPositive Fractions
#êêê╚è╔è╩è╦è╠è═è╬ï...
êêê1è1è1è1è1è1è1
#êêê╚è╔è╩è╦è╠è═è╬ï...
êêê2è2è2è2è2è2è2
#êêê╚è╔è╩è╦è╠è═è╬ï...
êêê3è3è3è3è3è3è3
êêê.
êêê.
êêê.
Example 1)èDivide the fractions, 16/5 by 12/15.ïIt is very important
that the fraction that is doing the dividing is written as the second
fraction.ïSince 12/15 is doing the dividing, it must be the second
fraction.ïYou may have noticed a pattern at this point.ïIf you recall,
it is also important in subtracting fractions which fraction comes
second.ïIn the addition and multiplication operations, however, it
does not matter which fraction is first or second. The answer in ç
two cases will work out to be the same number.
è First, you should change the operation to multiplication and invert
the second fraction.
êêêë16è12ê16è15
#êêêë── ÷ ──è=è── ∙ ──
êêêë 5è15ê 5è12
Next, you should treat the problem as a multiplication problem.ïMulti-
ply the two numerators and the two denominators.
êêêè16è15êï16∙15
#êêêè── ∙ ──è =è ─────
êêêè 5è12êè5∙12
Then, express each number in prime factored form.
êêêë 16∙15êï2∙2∙2∙2∙3∙5
#êêêë ─────è =è ───────────
êêêê5∙12êè 5∙2∙2∙3
Next, you should cancel out any like factors on the top and bottom.
êêê2∙2∙2∙2∙3∙5êï2∙2
#êêê───────────è =è ───
êêêï5∙2∙2∙3êë1
Finally, you should multiply any remaining factors.
êêêêï2∙2
#êêêêï───è=è4
êêêêè1
Thus, the quotient of 16/5 and 12/15 is 4.