How to Find Proportional Ratios

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What are proportional ratios?

In mathematics, a 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.’
So, let’s look at an example. Suppose, in a computer shop having \(25\) computers, \(13\) of them are desktops and the rest are laptops. So, the ratio of desktops to laptops would be \(13 \ : \ 12\). Moreover, in mathematical terms, this is read as “\(13\) is to \(12\).”
So, now we move on to what exactly is a proportional ratio. It is a ratio between \(4\) numbers, such that the simplified ratio between the first two is exactly equal to the simplified ratio between the other \(2\) numbers. For example, \(3, \ 6, \ 9\) and \(18\) are in a proportion as \(3 \ : \ 6\) is equal to \(9 \ : \ 18\) as when we simplify both, we get \(1 \ : \ 2\) as a result.

How to Calculate Ratios?

To understand the exact process of calculating ratios, let’s take up the following problem.
Question: 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 \(22 \ : \ 19\).

Proportional Ratios

Another interesting type of ratios is the 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. Now, let’s consider the following problem.
Q: Suppose two ratios \(1 \ : \ 3\) and \(x \ : \ 9\) is proportional. Then solve for \(x\)?
A: We know that proportional ratios are identical. So, \(\frac{1}{3} \ = \ \frac{x}{9}\) , which solves as \(x=3\).

Free printable Worksheets

Exercises for Proportional Ratios

1) \(28 : 49 = x : 7 \)\( \ \Rightarrow \ \)

2) \(16 : 20 = x : 5 \)\( \ \Rightarrow \ \)

3) \(30 : 78 = x : 13 \)\( \ \Rightarrow \ \)

4) \(12 : 16 = x : 4 \)\( \ \Rightarrow \ \)

5) \(69 : 99 = 23 : x \)\( \ \Rightarrow \ \)

6) \(10 : 35 = x : 7 \)\( \ \Rightarrow \ \)

7) \(18 : 69 = 6 : x \)\( \ \Rightarrow \ \)

8) \(24 : 40 = 3 : x \)\( \ \Rightarrow \ \)

9) \(65 : 80 = 13 : x \)\( \ \Rightarrow \ \)

10) \(21 : 27 = 7 : x \)\( \ \Rightarrow \ \)

Answers

1) \(28 : 49 = x : 7 \)\( \ \Rightarrow \ \color{red}{49x = 28 \times 7} \)\( \ \Rightarrow \ \color{red}{ x \ = 4} \)

2) \(16 : 20 = x : 5 \)\( \ \Rightarrow \ \color{red}{20x = 16 \times 5} \)\( \ \Rightarrow \ \color{red}{ x \ = 4} \)

3) \(30 : 78 = x : 13 \)\( \ \Rightarrow \ \color{red}{78x = 30 \times 13} \)\( \ \Rightarrow \ \color{red}{ x \ = 5} \)

4) \(12 : 16 = x : 4 \)\( \ \Rightarrow \ \color{red}{16x = 12 \times 4} \)\( \ \Rightarrow \ \color{red}{ x \ = 3} \)

5) \(69 : 99 = 23 : x \)\( \ \Rightarrow \ \color{red}{69x = 99 \times 23} \)\( \ \Rightarrow \ \color{red}{x \ = 33} \)

6) \(10 : 35 = x : 7 \)\( \ \Rightarrow \ \color{red}{35x = 10 \times 7} \)\( \ \Rightarrow \ \color{red}{ x \ = 2} \)

7) \(18 : 69 = 6 : x \)\( \ \Rightarrow \ \color{red}{18x = 69 \times 6} \)\( \ \Rightarrow \ \color{red}{x \ = 23} \)

8) \(24 : 40 = 3 : x \)\( \ \Rightarrow \ \color{red}{24x = 40 \times 3} \)\( \ \Rightarrow \ \color{red}{x \ = 5} \)

9) \(65 : 80 = 13 : x \)\( \ \Rightarrow \ \color{red}{65x = 80 \times 13} \)\( \ \Rightarrow \ \color{red}{x \ = 16} \)

10) \(21 : 27 = 7 : x \)\( \ \Rightarrow \ \color{red}{21x = 27 \times 7} \)\( \ \Rightarrow \ \color{red}{x \ = 9} \)

How to Find Proportional Ratios