Question

When is divided by will the quotient be greater than 1 or less than 1? How do you know?

Answer 1

The quotient
`\((a)/(b)\)` will be greater than 1 when
`\(a > b\)` , and it will be less than 1 when
`\(a < b\).`

Step-by-step explanation:

The comparison of the quotient
`\((a)/(b)\)` in relation to 1 is determined by the relative magnitudes of
`\(a\)` and
`\(b\).` When
`\(a\)` is greater than
`\(b\)` , the numerator dominates, resulting in a quotient greater than 1. Conversely, when
`\(a\)` is less than \(b\), the denominator dominates, leading to a quotient less than 1.

To illustrate, consider examples: If
`\(a = 4\) and \(b = 2\),` then
`\((a)/(b) = (4)/(2) = 2 > 1\).` Conversely, if
`\(a = 2\) and \(b = 4\), then \((a)/(b) = (2)/(4) = 0.5 < 1\).`These examples demonstrate the relationship between the values of
`\(a\) and \(b\)` and how it influences the quotient.

Understanding this comparison is crucial in various contexts, such as determining the growth rate, proportions, or ratios. Recognizing when the quotient is greater than or less than 1 provides insights into the relative sizes of the quantities involved. This concept is fundamental in mathematics and has applications in various fields, including finance, science, and engineering.