Solving Ratio and Proportion Problems Part 1

One of the key concepts tested in the Civil Service Exam is ratio and proportion. In this series, we are going to discuss how to solve problems involving ratio and proportion. We first begin below by explaining the meaning and concept of ratio and how to represent it.

Suppose we are cooking, and for every 4 teaspoons of vinegar, we put 3 teaspoons of soy sauce, then we can say the ratio of the volume of vinegar to the volume of soy sauce is “four is to three” and represent it as 4:3. We can also use the fraction 4/3 to represent the ratio above. Now, we discuss more examples about ratio.

Example 1

In a class, there are 24 girls and 18 boys. What is the ratio of (1) the number of girls to the number of boys and (2) the number of boys to the number of girls?

Answer

The number of girls is 24 and the number of boys is 18, so the ratio of the number of girls to the number of boys is 24:18 or 24/18. In contrast, the ratio of the number of boys to the number of girls is 18:24 or 18/24.

Example 2

In a box of colored balls, there are 5 red balls and 8 blue balls. What is the ratio of the number of blue balls to the total number of balls?

Answer

The number of blue balls is 8 and the total number of balls is 5 + 8 = 13. Therefore the ratio of the number of blue balls to the total number of balls is 8:13 or 8/13.

Example 3

Gemma put 2 teaspoons of sugar for every cup of coffee. Represent the ratio of the number of teaspoons of sugar if there are 6 cups of coffee.

Answer

For every cup of coffee, we need 2 teaspoons. Therefore, for 6 cups of coffee, we need 6 times 2 = 12 teaspoons. So, the ratio of the number of teaspoons and 6 cups of coffee is 12:6.

In the three examples above, we have learned how to represent ratio. The ratio A: B means how many times of B is A. For example, the ratio 4:3 means A is 4/3 times of B.

In the next post, we are going to discuss about proportion or equal ratio.

Practice Exercises on Subtraction of Integers

To answer the exercises below, it is assumed that you have already finished reading addition of integers and subtraction of integers.

In subtraction of integers, we have learned two rules:

(1) a – b = a + (-b)
(2) a – (-b) = a + b

We will use these rules in answering the exersises below.

Exercises

1. 2 – 5
2. 18 – ( – 2)
3. 16 – 7
4. -17 – 3
5. -9 – (-3)
6. 0 – (-11)
7. -18 – (-25)
8. -10 – 9
9. 12 – (-9)
10. -6 – 3

Solutions/Answers

1. 2 – 5

Solution 1: 5 is greater than 2. If you subtract two numbers, if the subtrahend is larger than the minuend, the answer will be negative. So, the answer is -3.

Solution 2: From rule 1, a – b = a + (-b), so 2 + 5 = 2 + (-5) = -3
Answer:

2. 18 – ( – 2)

Solution: From rule 2, a – (-b) = a + b, so 18 + 2 = 20.

Answer: 20

3. 16 – 7

Answer: 9

4. -17 – 3

Solution: From rule 1, -17 – 3 = -17 + (- 3) = -20. Recall that in adding two negative numbers, we just add the numbers and then the answer will be negative.

Answer: -20

5. -9 – (-3)

Solution: From rule 2, -9 – (-3) = -9 + 3 = -6.

6. 0 – (-11)

Solution: From rule 2, 0 – (-11) = 0 + 11 = 11.

7. -18 – (-25)

Solution: From rule 2, a –(-b) = a + b. So, -18 + 25 = 7.

8. -10 – 9

Solution: From rule 1, a – b = a + (-b), so -10 + (- 9) = – 19.

9. 12 – (-9)

Solution: From rule 2, a –(-b) = a + b, so 12 + 9 = 21.

10.- 6 – 3

Solution: From rule 1, a – b = a + (-b) = -6 + -3 = -9.

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