## 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 \(x=3\).

### 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) **\(21 : 27 = 7 : x \)\( \ \Rightarrow \ \)