Rates

4.2  Rates
 
Definition

A special ratio that compares two quantities with different units of measurement.

 
Example

Fatin bought \(2\text{ kg}\) of mangoes at the price of \(\text{RM}10\).

From this situation, the two quantities involved are mass (\(\text{kg}\)) and total amount of money (\(\text{RM}\)).

Thus,

\(\text{Rate}=\dfrac{\text{RM} 10}{2\text{ kg}}.\)

 
Conversion of units of rates:
 
Example

Rajan is riding his bicycle at a speed of \(5\text{ m/s}\).

Convert \(5\text{ m/s}\) to \(\text{km/h}\).

\(\begin{aligned}&\space5\text{ m}/\text{s} \\\\&=\dfrac{5\text{ m}}{1\text{ s}} \\\\&=5\text{ m}\div1\text{ s} \\\\&=\dfrac{5}{1\,000}\text{ km}\div\dfrac{1}{60\times60}\text{ h} \\\\&=\dfrac{5}{1\,000}\times\dfrac{60\times60}{1} \\\\&=18\text{ km/h}. \end{aligned}\)

           

Rates

4.2  Rates
 
Definition

A special ratio that compares two quantities with different units of measurement.

 
Example

Fatin bought \(2\text{ kg}\) of mangoes at the price of \(\text{RM}10\).

From this situation, the two quantities involved are mass (\(\text{kg}\)) and total amount of money (\(\text{RM}\)).

Thus,

\(\text{Rate}=\dfrac{\text{RM} 10}{2\text{ kg}}.\)

 
Conversion of units of rates:
 
Example

Rajan is riding his bicycle at a speed of \(5\text{ m/s}\).

Convert \(5\text{ m/s}\) to \(\text{km/h}\).

\(\begin{aligned}&\space5\text{ m}/\text{s} \\\\&=\dfrac{5\text{ m}}{1\text{ s}} \\\\&=5\text{ m}\div1\text{ s} \\\\&=\dfrac{5}{1\,000}\text{ km}\div\dfrac{1}{60\times60}\text{ h} \\\\&=\dfrac{5}{1\,000}\times\dfrac{60\times60}{1} \\\\&=18\text{ km/h}. \end{aligned}\)