Chapter 6.5, Problem 38HP

To determine

To give: two examples that are given proportional.

Explanation of Solution

Given information:

The given proportion

  $\frac{6\text{hits}}{8\text{at}\text{bats}}$ .

Calculation:

The two ratios are said to be in proportion if they are equal.

Consider the below ratios.

  $\frac{3\text{hits}}{4\text{at}\text{bats}}\text{and}\frac{12\text{hits}}{16\text{at}\text{bats}}.$

Compare the ratios $\frac{3\text{hits}}{4\text{at}\text{bats}}\text{and}\frac{12\text{hits}}{16\text{at}\text{bats}}\text{with}\frac{6\text{hits}}{8\text{at}\text{bats}}$

Divide the numerator and denominator by 2.

  $\frac{6\text{hits}}{8\text{at}\text{bats}}=\frac{3\text{hits}}{4\text{at}\text{bats}}$

Divide the numerator and denominator by 4.

  $\frac{12\text{hits}}{16\text{at}\text{bats}}=\frac{3\text{hits}}{4\text{at}\text{bats}}$

Since the three ratios $\frac{3\text{hits}}{4\text{at}\text{bats}}\text{and}\frac{12\text{hits}}{16\text{at}\text{bats}}\text{with}\frac{6\text{hits}}{8\text{at}\text{bats}}$ are equal.

Therefore, the ratios $\frac{3\text{hits}}{4\text{at}\text{bats}}\text{and}\frac{12\text{hits}}{16\text{at}\text{bats}}$ are proportional to $\frac{6\text{hits}}{8\text{at}\text{bats}}$ .

Hence, the required examples are

  $\frac{3\text{hits}}{4\text{at}\text{bats}}\text{and}\frac{12\text{hits}}{16\text{at}\text{bats}}$ .