Chapter 3.3, Problem 52HP

To determine

To find: Two rational numbers greater than $\frac{1}{3}$ and the product is less than $\frac{1}{3}$ .

Answer to Problem 52HP

Two rational numbers greater than $\frac{1}{3}$ and the product is less than $\frac{1}{3}$ are $\frac{2}{5}$ and $\frac{2}{7}$ .

Explanation of Solution

Given:

Two rational numbers must be greater than $\frac{1}{3}$ .

Calculation:

Two rational numbers that are greater than $\frac{1}{3}$ are $\frac{2}{5}$ , $\frac{3}{5}$ , $\frac{2}{7}$ , $\frac{3}{7}$ etc.

Multiply any two rational number which are greater than $\frac{1}{3}$ such that the product must be less than $\frac{1}{3}$ .

  $\frac{2}{7}\times \frac{2}{5}=\frac{4}{35}$

Convert the fraction $\frac{4}{35}$ into decimal.

  $\frac{4}{35}\approx 0.1142$

Convert the fraction $\frac{1}{3}$ into decimal.

  $\frac{1}{3}\approx 0.333$

As, 0.1142 is less than the number 0.333, therefore, the two rational numbers are $\frac{2}{5}$ and $\frac{2}{7}$ .

Thus, the two rational numbers greater than $\frac{1}{3}$ and the product is less than $\frac{1}{3}$ are $\frac{2}{5}$ and $\frac{2}{7}$ .