Division of monomials means product of their quotient of numerical coefficients and quotient of their literal coefficients.
Since, the product of 3m and 5n = 3m × 5n = 15mn; it follows that
(i) \(\frac{15mn}{3m} = \frac{3 \times 5 \times m \times n}{3 \times m}\) = 5n
or, 15mn ÷ 3m = 5n
i.e. when 15mn is divided by 3m, the quotient is 5n.
(ii) \(\frac{15mn}{5n} = \frac{3 \times 5 \times m \times n}{5 \times n}\) = 3m
or, 15mn ÷ 5n = 3m
i.e. when 15mn is divided by 5n, the quotient is 3m.
1. Divide 35mxy
by 5my
35mxy ÷ 5my
= \(\frac{35mxy}{5my}\)
Now, we need to write each term in the expanded form and then cancel the terms which are common to both numerator and denominator.
= \(\frac{\not{5} \times 7 \times \not{m} \times x \times \not{y}}{\not{5} \times \not{m} \times \not{y}}\)
= 7x
= \(\frac{14a^{7}}{2a^{5}}\)
Now, we need to write each term in the expanded form and then cancel the terms which are common to both numerator and denominator.
= \(\frac{\not{2} \times 7 \times \not{a} \times \not{a} \times \not{a} \times \not{a} \times \not{a} \times a \times a}{\not{2} \times \not{a} \times \not{a} \times \not{a} \times \not{a} \times \not{a}}\)
= 7 × a × a= \(\frac{14a^{7}}{2a^{5}}\)
= \(\frac{14}{2} \times \frac{a^{7}}{a^{5}}\)
Now we will write the each numerical part \((\frac{14}{2})\) in the expanded form and then cancel the terms which are common to both numerator and denominator and in case of literal part subtract the smaller power of a literal from bigger power of the same literal.
= \(\frac{\not{2} \times 7}{\not{2}} \times a^{7  5}\)
= 7 × ^{2}= \(\frac{81p^{3}q^{6}}{27p^{6}q^{3}}\)
= \(\frac{81}{27} \times \frac{p^{3}q^{6}}{p^{6}q^{3}}\)
Now we will write the each numerical part (\frac{81}{27}) in the expanded form and then cancel the terms which are common to both numerator and denominator and in case of literal part subtract the smaller power of a literal from bigger power of the same literal.
= \(\frac{\not{3} \times \not{3} \times \not{3} \times 3}{\not{3} \times \not{3} \times \not{3}} \times \frac{q^{6  3}}{p^{6  3}}\)
= \(3 \times \frac{q^{3}}{p^{3}}\)
= \(\frac{3q^{3}}{p^{3}}\)
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Multiplication of Two Monomials
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