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 $x=1$ .

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How to write ratios in a word problem