Equivalent ratio table

Equivalent ratio table

The ratio of two quantities can be classified into groups of equivalent ratios and tabulated in the equivalent ratio table. With equivalent ratio table, one can find the missing numbers in some given ratios by using the following steps:

1. Inspect the table and identify a column which is complete, that is, it does not have an unknown. Compute the ratio of the two numbers in the column and use that ratio as a fixed reference for calculating the unknown by comparison.
2. Form a simple equation by comparing the ratio with the missing value to the fixed reference ratio.
3. Solve the simple equation to get the missing value in the table.

Example 1

Fill in the following equivalent ratio table by finding the unknown represented by the letters.

P	16	20	36	R
5	A	25	Q	60

Solution

Follow the steps below:

1. Check the table to identify a column which is complete. In the given table, the third column is complete.
2. Write and simplify the ratio of the numbers in the third column by dividing each number by the G.C.F, which is 5.

Thus, 20/5 : 25/5 = 4 : 5.

3. In order to find the value of 'p', compare the first column ratio to the ratio of the third column as follows: p : 5 = 4 : 5, which is the same as p/5 = 4/5. Thus, 5p = 4 × 5. Divide by 5 both sides: 5p/5 = 4 × 5/5 p = 20/5 = 4.

Therefore, p = 4.

4. In order to find the value of 'a', compare the second column ratio to that of the third column as follows: 16 : a = 4 : 5, which is the same as 16/a = 4/5. Thus, 4a = 16 × 5. Divide by 4 both sides: 4a/4 = 16 × 5/4 a = 80/4 = 20.

Therefore, a = 20.

5. In order to find the value of 'q', compare the fourth column ratio to the third column ratio as follows: 36 : q = 4 : 5, which is the same as 36/q = 4/5. Thus, 4q = 36 × 5. Divide by 4 both sides: 4q/4 = 36 × 5/4 q = 180/4 = 45.

Therefore, q = 45.

6. In order to find the value of 'r', compare the fifth column ratio to the third column ratio as follows: r : 60 = 4 : 5. This is the same as r/60 = 4/5. Thus, 5r = 4 × 60. Divide by 5 both sides: 5r/5 = 4 × 60/5 r = 240/5 = 48.

Therefore, r = 48.

Therefore, the missing numbers are bolded in the following table:

4	16	20	36	48
5	20	25	45	60

Example 2

Find the values of the variables in the following equivalent ratio table:

3	b	21	d	45	162	240
a	28	c	63	e	378	f

Solution

Follow the steps below:

1. Check the table to identify the column which is complete. In the given table, the sixth column is complete.
2. Simplify the ratio of numbers in the sixth column by dividing each number by the G.C.F, which is 54.

162/54 : 378/54 = 3 : 7.

3. In order to find the value of 'a', compare the ratio of the first column to that of the sixth column as follows: 3 : a = 3 : 7, which is the same as 3/a = 3/7. So, 3a = 3 × 7. Divide by 3 both sides: 3a/3 = 3 × 7/3 a = 21/3 = 7.

Therefore, a = 7.

4. In order to find the value of 'b', compare the second column ratio to the sixth column ratio as follows: 3 : 7 = b : 28, which is the same as 3/7 = b/28. So, 7b = 3 × 28. Divide by 7 both sides: 7b/7 = 3 × 28/7 b = 84/7 = 12.

Therefore, b = 12.

5. In order to find the value of 'c', compare the third column ratio to the sixth column ratio as follows: 3 : 7 = 21 : c, which is the same as 3/7 = 21/c. So, 3c = 7 × 21. Divide by 3 both sides: 3c/3 = 7 × 21/3 c = 147/3 = 49.

Therefore, c = 49.

6. In order to find the value of 'd', compare the fourth column ratio to the sixth column ratio as follows: 3 : 7 = d : 63, which is the same as 3/7 = d/63. So, 7d = 3 × 63. Divide both sides by 7: 7d/7 = 3 × 63/7 d = 189/7 = 27.

Therefore, d = 27.

7. In order to find the value of 'e', compare the fifth column ratio to the sixth column ratio as follows: 3 : 7 = 45 : e, which is the same as 3/7 = 45/e. So, 3e = 7 × 45. Divide both sides by 3: 3e/3 = 7 × 45/3 e = 315/3 = 105.

Therefore, e = 105.

8. In order to find the value of 'f', compare the seventh column ratio to the sixth column ratio as follows: 3 : 7 = 240 : f, which is the same as 3/7 = 240/f. So, 3f = 7 × 240. Divide both sides by 3: 3f/3 = 7 × 240/3 f = 1680/3 = 560.

Therefore, a = 7, b = 12, c = 49, d = 27, e = 105, f = 560.