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Word Problems: Ratios
In order to solve problems involving ratios, you should be able to:
  • work with fractions
  • simplify fractions
A ratio is a way of expressing a relationship between two numbers that can be expressed in the following three common ways:
as a fraction
with a colon (:)
using the word “to
Suppose we are told that there are three nurses for every ten patients at a hospital. The three ways this ratio of nurses to patients can be written are:
  • as a fraction:
  • with a colon: 3:10
  • with “to”: 3 to 10
Notice that in each case, the number of nurses is written first (or in the numerator of the fraction). This is because the problem stated that we were to express the ratio of nurses to patients. Typically the first thing mentioned in a ratio problem is what is listed first.
If the problem had asked us to express the number of patients to nurses, each of our ratios would be written in the opposite order:
  • as a fraction:
  • with a colon: 10:3
  • with “to”: 10 to 3
When working with ratios, it is extremely important to pay attention to order. Read each problem carefully to find out what is being asked.

Let's Practice

Question #1
At the Technology Convention there were 17 males for every 12 females. Express each of the following relationships as a ratio in fraction form:
a. the number of males to females attending the Technology Convention.
b. the number of males to the total number of people present at the Technology Convention.

Question #2
Out of every 100 students at a two-year college, 52 are taking a math class. Express each of the following relationships as a ratio in fraction form:
a. the number of students taking a math class to the total number of students.
b. the number of students not taking a math class to the number of students taking a math class.

Try These
Question #1
AudioCameron went to a restaurant where there were 80 seats for non-smokers and 10 seats for smokers. Express the ratio of the number of seats for smokers to the total number of seats.

Question #2
AudioA waiter at a local restaurant notes that during the day his customers ordered 3 diet drinks for every 2 non-diet drinks. Express the ratio of diet drinks to non-diet drinks as a fraction.

Being able to write correct ratios is important when comparing two quantities. It is also an important and essential skill in solving proportions where more than one ratio is involved. Make sure that you completely understand ratios before going on to work with proportions.

S Taylor

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