## How to write ratios in a word problem

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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 market of \(40\) vendors, \(23\) of them sell apples, and the rest \(17\) sell bananas. So, the ratio of the vendors selling apples to those selling bananas would be \(23 \ : \ 17\). Moreover, in mathematical terms, this is read as “\(23\) is to \(17\).”

### Types of Ratios

Now, there are \(2\) types of ratios. They are called “part-to-part” and “part-to-whole.” So, when we say that in a group of \(17\) teachers, \(9\) teach math and \(8\) teach physics, then the part-to-part ratio is \(9 \ : \ 8\). Basically, a **part-to-part** ratio denotes the clear distinction between two entities.

Now, if we say that out of \(10\) books in a library, \(7\) are of computer science. So, here part-to-whole ratio is \(7 \ : \ 10\). This means that out of \(10\) books in the library, every \(7\) are of computer science. So, basically, a **part-to-whole** ratio denotes the ratio between the whole group to a specific entity.

### Calculation of Ratios

To understand the exact process of calculating ratios, let’s take up the following problem.**Question**: Suppose, \(24\) tigers and \(17\) lions make up for an entire zoo. So, what is the ratio of tigers and lions in that zoo?

- Firstly, identify the
**unique entities**. In this case, \(24\) tigers and \(17\) lions are unique entities. - Next, write these in a
**fraction**form. So, we write it as \(\frac{24}{17}\) - 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 tigers and lions in the zoo is \(24 \ : \ 17\).

### Simplifying Ratios

Check the entities in the given problem for writing ratios. Then **divide **both sides of the ratio to simplify it further. Suppose there are \(14\) apples and \(7\) oranges. So, the ratio of apples to oranges would be \(\frac{14}{7} \ = \ 14 \ : \ 7 \ = \ 2 \ : \ 1\).

### Ratio and Rates Word Problems

Now suppose, a problem like this is given, where \(x \ : \ 4 \ = \ 4 \ : \ 16\) and we are required to find \(x\).

So, we can write, \(\frac{x}{4} \ = \ \frac{4}{16}\) and by cross multiplication and simplifying the fractions, we can get \(x=1\).