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.2Write the following statement in mathematical form: 3 less than the quotient of a and b.a) (a-3)/bb) a/(b-3)c) a/b - 3d) none of the above

Question

Write the following statement in mathematical form: 3 less than the quotient of a and b.

a) (a3)b \frac{(a-3)}{b}
b) a(b3) \frac{a}{(b-3)}
c) ab3 \frac{a}{b} - 3
d) none of the above

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Solution

Break Down the Problem

  1. We need to express the statement "3 less than the quotient of a a and b b " in mathematical form.

Relevant Concepts

  1. The quotient of a a and b b is represented as ab \frac{a}{b} . To express "3 less than" this quotient, we would subtract 3 from the quotient.

Analysis and Detail

  1. The mathematical expression for "3 less than the quotient of a a and b b " can be written as: ab3 \frac{a}{b} - 3

Verify and Summarize

  1. Comparing our expression ab3 \frac{a}{b} - 3 with the given options:
    • a) a3b \frac{a - 3}{b} (This represents "the quotient of a3 a - 3 and b b " which is incorrect)
    • b) ab3 \frac{a}{b-3} (This represents "the quotient of a a and b3 b-3 " which is incorrect)
    • c) ab3 \frac{a}{b} - 3 (This matches our expression)
    • d) none of the above (This is incorrect since we have a matching option)

Final Answer

The correct mathematical form is option c: ab3 \frac{a}{b} - 3

This problem has been solved

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