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1995-01-03
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êê MULTIPLYING FRACTIONS, ELEMENTARY LEVEL
è In this section we will be looking at multiplying positive frac-
tions.ïWhen you multiply two positive fractions, the answer is always
positive.ïThe procedure is to multiply the two numerators and the
two denominators, express the resulting numerator and denominator in
prime factored form, cancel any like factors that occur on the top and
bottom, and finally multiply any remaining factors.ïThe positive frac-
tions and zero are described in the following list.
êêêë Positive Fractions
#êêêï╚è╔è╩è╦è╠è═è╬ ...
êêêï1è1è1è1è1è1è1
#êêêï╚è╔è╩è╦è╠è═è╬ ...
êêêï2è2è2è2è2è2è2
#êêêï╚è╔è╩è╦è╠è═è╬ ...
êêêï3è3è3è3è3è3è3
êêêè .
êêêè .
êêêè .
Example 1)èMultiply the fractions 4/15 and 5/6.
è First, you should multiply the two numerators and the two denomi-
nators.
êêêë 4è5ê 4∙5
#êêêë── ∙ ─è=è────
êêêë15è6ê15∙6
Next, you should express each number in prime factored form.
êêêë4∙5êè 2∙2∙5
#êêêè ────è =è ───────
êêêè 15.6êï3∙5∙2∙3
Then, cancel out any like factors that occur on the top and bottom.
êêêë 2∙2∙5êè 2
#êêêè ───────è =è ───
êêêè 3∙5∙2∙3êï3∙3
Finally, you should multiply any remaining factors.
êêêêè2êï2
#êêêê ───è =è ─
êêêê 3∙3êï9
Thus, the product of 4/15 and 5/6 is 2/9.