Question

Translate the phrase "a number decreased by the quotient of three and four." (A)\(n-\frac{3}{4}\) (B) \(=\frac{3}{4}-n\) (C) \(\frac{n-3}{4}\) (D) \(\frac{3}{4-n}\)

Short answer

The correct translation of the phrase 'a number decreased by the quotient of three and four' is (A) \(n-\frac{3}{4}\).

Step-by-step solution

Understanding the Mathematical Terms

First, let's understand the mathematical terms. 'A number' can be represented by a variable, for example, \(n\). 'Decreased by' means subtraction in mathematics. 'The quotient of three and four' is a division operation and can be represented as \(\frac{3}{4}\).

Translate 'Decreased by' Operation to Mathematical Symbolism

'Decreased by' is a subtraction operation. So 'a number decreased by the quotient of three and four' means we are subtracting \(\frac{3}{4}\) from our number \(n\).

Formulating the Expression

Combining these understandings, 'a number decreased by the quotient of three and four' translates into the mathematical expression \(n - \frac{3}{4}\). This means we are first taking a number of decrease and then subtracting three-fourths from it.