Page 46 - Arithmetic

Rate
A ratio compares two quantities with the same unit, while a rate compares two quantities with different units. Just like ratio, a rate is written in the form of a fraction 𝑎
𝑏
For example,
A teacher charges $100 for one hour of personal tutoring, or a car can travel 180 miles for 20 gallons of gas.
As the units are different, it becomes critical to write the units when talking about rate. The two different quantities are usually split by one of the following words: per, on, for, in, from.
The rate of change problems involve calculating the quantity per unit of measurement.
For example, meters per second
Unit Rate
A unit rate is a rate with denominator as one. For example, 70 miles per hour
Here, a person can travel 70 miles in one hour.
Worked Example 19
Henry can travel 540 miles in 9 hours in his car. What is the speed of the car expressed as a unit rate?
Solution:
Speed of car = 540 𝑚𝑖𝑙𝑒𝑠 9 h𝑜𝑢𝑟𝑠
Divide the numerator and denominator by 9 to get the unit rate in the denominator Speed of car in unit rate = 540 ÷ 9 = 60 miles per hour.
99
Therefore, Henry can travel 60 miles per hour.
Pipe and Cisterns
REMEMBER:
If a pipe can fill a tank in ‘x’ hours and another pipe can empty the tank in ‘y’ hours such that y>x, then
11
when both the pipes are opened simultaneously, the part of the tank filled in one hour = -
𝑥𝑦
If a pipe can fill a tank in ‘x’ hours and another pipe can empty the tank in ‘y’ hours such that x>y, then
11
when both the pipes are opened simultaneously, the part of the tank filled in one hour = -
𝑦𝑥
Page 45 of 55
Arithmetic Concept