How to Create a Proportion

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In mathematics, the ratio is defined as the comparison between two numbers. This is generally done to find out how big or small a number or a quantity is with respect to another. So, what method do we use to find these ratios? Well, we use the division method. In a ratio, two numbers are divided. The dividend part is known as the ‘antecedent’, whereas the divisor is known as the ‘consequent.’
Also, for creating a proportion, we need to have four numbers such that upon simplification, both fractional parts appear to be same. For example, \(3:9\) and \(6:18\) are in proportion. When we simplify these, we get \(1:3\) for both these individual ratios.

Understanding Calculation of Ratios

To understand the exact process of calculating ratios, let’s take up the following problems.
Question 1: Suppose, \(22\) elephants and \(19\) hippos make up for an entire zoo. So, what is the ratio of elephants and hippos in that zoo?

Firstly, identify the unique entities. In this case, \(22\) elephants and \(19\) hippos are unique entities.
Next, write these in a fraction form. So, we write it as \(\frac{22}{19}\)
Now, we need to check if this fraction can be further simplified or not. Here, it can’t be simplified further.
So, the ratio of elephants and hippos in the zoo is \(22:19\).

Question 2: Suppose, \(19\) biology books and \(15\) physics books make up for an entire library. So, what is the ratio of biology and physics books in that library?

Firstly, identify the unique entities. In this case, \(19\) biology books and \(15\) physics books are unique entities.
Next, write these in a fraction form. So, we write it as \(\frac{19}{15}\)
Now, we need to check if this fraction can be further simplified or not. Here, it can’t be simplified further.
So, the ratio of biology books and physics books in the library is \(19:15\).

Proportional Ratios

Another interesting type of ratios are proportional ratios. If two distinct ratios can be simplified into the same fraction, then they are said to be proportional ratios. Suppose we have two ratios as \(1:2\) and \(2:4\). Now, we can clearly see that the second ratio can be reduced to \(1:2\), and thus both of them are proportional.

How to Create a Proportion?

So, suppose we are given \(4\) numbers like \(1 \ , \ 2 \ , \ 4,\) and \(8\) and are asked to create a proportion. So, we have learnt that a proportion always has equivalent ratios. Hence, we will create a proportion which is \(\frac{1}{2}=\frac{4}{8}\).

Free printable Worksheets

Exercises for Create a Proportion

1)\(30, 5, 2, 75 \)\( \ \Rightarrow \ \)

2) \(18, 5, 2, 45 \)\( \ \Rightarrow \ \)

3) \(3, 26, 1, 78 \)\( \ \Rightarrow \ \)

4) \(20, 12, 5, 48 \)\( \ \Rightarrow \ \)

5) \(17, 3, 1, 51 \)\( \ \Rightarrow \ \)

6) \(16, 5, 1, 80 \)\( \ \Rightarrow \ \)

7) \(66, 27, 22, 81 \)\( \ \Rightarrow \ \)

8) \(29, 2, 1, 58 \)\( \ \Rightarrow \ \)

9) \(12, 2, 1, 24 \)\( \ \Rightarrow \ \)

10) \(4, 7, 1, 28 \)\( \ \Rightarrow \ \)

Answers

1) \(30, 5, 2, 75 \)\( \ \Rightarrow \ \color{red}{30 : 75 = 2 : 5} \)

2) \(18, 5, 2, 45 \)\( \ \Rightarrow \ \color{red}{18 : 45 = 2 : 5} \)

3) \(3, 26, 1, 78 \)\( \ \Rightarrow \ \color{red}{3 : 78 = 1 : 26} \)

4) \(20, 12, 5, 48 \)\( \ \Rightarrow \ \color{red}{20 : 48 = 5 : 12} \)

5) \(17, 3, 1, 51 \)\( \ \Rightarrow \ \color{red}{17 : 51 = 1 : 3} \)

6) \(16, 5, 1, 80 \)\( \ \Rightarrow \ \color{red}{16 : 80 = 1 : 5} \)

7) \(66, 27, 22, 81 \)\( \ \Rightarrow \ \color{red}{66 : 81 = 22 : 27} \)

8) \(29, 2, 1, 58 \)\( \ \Rightarrow \ \color{red}{29 : 58 = 1 : 2} \)

9) \(12, 2, 1, 24 \)\( \ \Rightarrow \ \color{red}{12 : 24 = 1 : 2} \)

10) \(4, 7, 1, 28 \)\( \ \Rightarrow \ \color{red}{4 : 28 = 1 : 7} \)

How to Create a Proportion