Ratio: The relative size of two quantities expressed as the quotient of one divided by the other; the ratio of a to b is written as a: b or a/b.
Proportion: A proportion is an equation where two ratios are set equal to each other.
Let us look at some examples of using ratios and proportions to solve problems.
Examples 1:
In a classroom, the ratio of boys to girls is 4 to 7 or 4:7. If there are 35 girls in the class, then how many total students are there in the class?
Solution 1:
The first step is to find the number of boys in the class. In order to determine this value we set up a proportion using the ratio of boys to girls:
4 boys/7 girls = x boys/35 girls
We can now cross-multiply to solve the equation for x, which is the number of boys in the class:
4/7 = x/35
(4)(35) = 7x
140 = 7x
X = 140/7
X = 20
Therefore, we have found that there are 20 boys in the class.
Now we know that the total number of students in the class is equal to the number of girls plus the number of boys. So we can do the following operation to solve for the final answer:
35 girls + 20 boys = 55 students
Therefore, we have found that there are a total of 55 students in the class.
Example 2:
The legend on a map says .5 inches represents 14 miles. How many inches are needed to represent 105 miles?
Solution 2:
The proportion we need to set up in order to solve this problem is as follows:
0.5 inches/14 miles = x inches/105 miles
Now we will cross-multiply in order to solve for x, which is the number of inches needed to represent 105 miles.
0.5/14 = x/105
(0.5)(105) = 14x
52.5 = 14x
X = 52.5/14
X = 3.75
Therefore, we have found that 3.75 inches on the map represent 105 miles
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This article was written for you by Mia, one of our tutors at Test Prep Academy.