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Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
7.1 Ratio Compares Quantities of the Same Kind

Ratios
  • Can be formed, only between things of the same kind.
    Example: length to length, time to time, dollars to dollars, cents to cents and so on.
  • If we relate things of different kinds, as in so many "dollars per hour," that is not called a ratio but a rate.
  • The ratio of like quantities expressed in the same units produces pure or dimensionless numbers.
  • The ratio remains the same regardless of the type of units in which the quantities are expressed.
Example:
John finished his Math home work in 30 minutes and Geography home work in one hour. Would it be right to say that ratio of the time spent on Math to the time spent on Geography is 30:1?
No, because this ratio tells that John spent 30 times more time on Math than on Geography, which is not true. This error occurred because of the comparison of unlike quantities like minutes and hours. Therefore, when you use a ratio to compare two quantities, write both the quantities in the same units.

In the above example, converting the time spent on Geography into minutes we get 60 minutes. Therefore, the ratio of time spent on the two subjects = 30:60 = 1:2. This is correct because the time spent on Geography is actually double the time spent on Math.


Directions: Find the ratio of the first quantity to the second. Also write at least ten examples of your own.

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Date:___________________

Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
7.1 Ratio Compares Quantities of the Same Kind

Q 1: 6 days, 3 weeks
6:21
21:6
6:3

Q 2: 1 dollar, 150 cents
1:150
150:100
100:150

Q 3: 1 dollar, 6 quarter
1:6
6:4
4:6

Q 4: 1 dollar, 100 dime
1:10
1:100
10:1

Q 5: I nickel, 1 dime
1:1
10:5
5:10

Q 6: 1 feet, 15 inches
12:15
1:15
15:12

Q 7: 1 lb, 180 oz
180:16
16:180
1:180

Q 8: 1 meter, 20 decimeter
1:20
2:1
1:2

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Question 10: This question is available to subscribers only!


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