Chapter 1.9, Problem 3LC

To determine

Find the required number.

Answer to Problem 3LC

  $\frac{32}{25}$

  $\text{or}1.28$

Explanation of Solution

Given:

Four − fifths is equal to ten sixteenths of a number

Concept Used:

Convert the phrase 'Four − fifths is equal to ten sixteenths of a number’into equation.

Calculation:

Let the number be $\text{N}$

Ten sixteenths of a number: $\frac{10}{16}\text{N}$

Four − fifths is equal to ten sixteenths of a number: $\frac{4}{5}=\frac{10}{16}\text{N}$

Equation: $\frac{4}{5}=\frac{10}{16}\text{N}$

Solve : Use the cross multiplication method to simplify the equation. $\frac{a}{b}=\frac{c}{d}\Rightarrow a·d=b·c$

  $\begin{array}{l}\frac{4}{5}=\frac{10}{16}\text{N}\\ 5·10\text{N}=4·16\text{[Using cross Multiplication Method] }\\ \text{50N}\text{=}64\\ \frac{50\text{N}}{50}=\frac{64}{50}\text{[}\text{Divide}\text{both}\text{sides}\text{by}50\text{]}\\ \text{N}=\frac{32}{25}=1.28\end{array}$

The required number is $\frac{32}{25}$

  $\text{or}1.28$

Thus, the required number is $\frac{32}{25}$

  $\text{or}1.28$