At the end of this lesson, students should be able to:
A RATIO is a comparison of two numbers or quantities that indicates how many times the first number contains the second. The quantities being compared are called the terms of the ratio and they are quantities of a comparable kind, such as objects, persons, lengths, etc.
For example, if a bowl of fruit contains eight oranges and six lemons, then the ratio of oranges to lemons is eight to six. Note that, in the expression “the ratio of oranges to lemons”,” oranges” comes first. This order is very important and must be respected. Whichever quantity comes first; its number must come first. If the expression had been “the ratio of lemons to oranges“, then it would have been “six to eight“.
A ratio is usually written in one of these three ways.
The ratio of 15 men to 20 women can be express as
There are 16 ducks and 9 geese in a certain park. Express the ratio of ducks to geese in all three formats.
If the numerator and denominator of the reduced form have no common factors, the ratio is said to be in its lowest terms. Since there are an infinite number of fractions that are equivalent to a given ratio such as 3 out of 4, when comparing ratios, it is convenient to write the fractions in reduced or simplified form.
Let’s return to the 15 men and 20 women in our original group. Ratio of men to women is 15:20. This means that you can also express the ratio of men to women as 3/4, 3:4, or “3 to 4”
This points out something important about ratios; the numbers used in the ratio might not be the absolute measured values. The ratio “15 to 20” refers to the absolute number of men and women respectively in the group of thirty-five people. The simplified or reduced ratio “3 to 4” implies that, for every three men, there are four women. The simplified ratio also indicates that, in any representative set of seven people (3 + 4 = 7) from this group, three will be men.
In other words, the men comprise 3/4 of the people in the group. These relationships and reasoning are what you use to solve many word problems.
Method 1: Using Multiplication
Method 2: Using Divisors
The fraction will be in the lowest or simplest form if the numerator and denominator of the fraction have no common factors, which is to say that they are RELATIVELY PRIME.
Equivalent ratios are just like equivalent fractions. If two ratios have the same value, then they are equivalent even though they may look very different.
When working with ratio involving different units, always convert them to the same units. A ratio can be simplified only when the units of the quantities are the same.
Express 25 minutes: 1 hour as a ratio in its simplest form.
The units must be the same so change 1 hour to 60 minutes
25 minutes: 1 hour
=25 minutes: 60minutes Cancel the units
= 25:60 Divide both sides by 5
So 25 minutes: 1 hour simplifies to 5:12