\(\frac{\mathrm{b+c} }{\mathrm{a} } = \frac{\mathrm{b} }{\mathrm{a} } + \frac{\mathrm{c} }{\mathrm{a} } \) defines which of the following?
Distributive property for division.
Commutative property for division.
Distributive property for multiplication.
Commutative property for multiplication.
Detailed Explanation
The distributive property for division helps in solving expressions like \(\frac{\mathrm{b+c} }{\mathrm{a} }\) . It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \(\frac{\mathrm{b+c} }{\mathrm{a} } = \frac{\mathrm{b} }{\mathrm{a} } + \frac{\mathrm{c} }{\mathrm{a} }\) . For example, \(\frac{\mathrm{ a^3+6 a^2 } }{\mathrm{ a^2 } } = \frac{\mathrm{ a^3 } }{\mathrm{ a^2 } } + \frac{\mathrm{6 a^2 } }{\mathrm{ a^2 } } = a+6\).
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