How can we use the concept:
Things to remember about ratios:
- In a ratio the first item in a sentence comes first in the ratio.
- The first number is called the antecedent and the second number is called the consequent.
- The antecedent and the consequent can not be rearranged.
To calculate ratios you can use colons, fractions, decimals, percentages, or placing the word “to” between the values that are being compared. For example if there are 14 girls to 20 boys in a classroom, you could express the ratio in the following ways:
- 14:20 This can be reduced to 7:10
- 14/20 or reduced as 7/10
- 0.7 as a decimal
- 14 to 20 or reduces as 7 to 10
*Make sure to reduce your ratios to the smallest whole numbers possible.*
Sample Math Problems
Question
If a gym has 28 male members and 36 female members, what is the ratio of male to females at the gym? (Give your answer in the lowest form)
Solution
First, you would write out the ratio using a colon. Make sure to put the number of males first, since it came first in the sentence. 28:36
Then, you could reduce 28 and 36 by 4.
So, 28:36 reduces to 7:9
Question
A store has 67 juice options. If 42 of the juices are vegetable juice, and the rest are fruit juice, what is the ratio of fruit juice to the total number of juices? (Give your answer in the lowest form)
Solution
First, you would need to find how many juices are fruit by subtracting 43 from 69. 27 juices are fruit.
Then, you would write out your ratio of fruit juices to total juices. 27 : 69
Finally, you need to reduce. 27 and 69 can both be divided by 3. Which would be 9 : 23
Question
Jack drew 6 hearts and 21 circles. What is the ratio of hearts to circles in the lowest form?
Solution
First, you would want to write out the ratio. Make sure your answer goes with the question. We are looking for hearts to circles. 6 : 21
Then, you would reduce your ratio if possible. 6 and 21 can both be divided by 3. So, 6 : 21 reduces to 2 : 7
Question
Rey has nickels, dimes, and quarters in the ratio of 6 : 2 : 1. If 26 of Rey's coins are dimes, how many nickels and quarters does Rey have?
Solution
First, you know that the number of dimes is 26. So for the ratio you would want to think multiplication 6 : 2 : 1. Since the dimes are in the middle you could think 2 times something must equal 26 (the number of dimes). 2 x 13 =26. So for each part of the ratio you would multiply by 13.
Next, multiply each part of the ratio by 13 to get the equivalent ratio.
6 x 13 = 78
2 x 13 = 26
1 x 13 = 13.
So, the ratio would become 78 : 26 : 13
The answer would be that Rey has 78 nickels and 13 quarters.
