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