Question

Write the following ratio in the simplest form
\[186:403\]

Answer 1

Hint: For converting the ratio into the simplest form, we have to find the factors of both the numbers. After finding common factors, divide the common factors to both the numbers. This ratio is converted to the simplest form. E.g. we are given with ratio $a:b$. Let's suppose the values of a and b are 2x and 3x respectively. So, their factors are
$
   a = 2x = 2 \times x \\
   b = 3x = 3 \times x \\
$
Now you can say the common factor of a and b is x. So, divide both the numbers by x we get
$
   \ \dfrac{a}{x}:\dfrac{b}{x} = \dfrac{{2 \times x}}{x}:\dfrac{{3 \times x}}{x} \\
   \ a:b = 2:3 \\
$
Hence $2:3$ is the simplest form of $a:b$.

Complete step-by-step answer:
We are given with a ratio i.e. $186:403$ and we have to write the simplest form of that ratio.
First, we will find the factors of both the numbers in the ratio.
$
   186 = 2 \times 3 \times 31 \\
   403 = 13 \times 31 \\
$
Here you can see 31 is the common factor in 186 and 403. So, divide 31 with both of the numbers to convert it into the simplest form.
$ 186:403 = 2 \times 3 \times 31:13 \times 31$
Divide the numbers in the ratio with 31, we get
$ \dfrac{{2 \times 3 \times 31}}{{31}}:\dfrac{{13 \times 31}}{{31}}$
Cancel 31 from both sides we get
$
   2 \times 3:13 = 6:13 \\
186:403 = 6:13 \\
$
So, the simplest form of \[186:403\] is $6:13$
Answer is 6:13

Note: The ratio is used for comparison between two objects.
Let us suppose we are mixing two things we can compare the quantity and price of the things and find out the end result i.e. quantity and price of the product.
Two ratios are equivalent if the simplest form of that ratio is equal. E.g. \[\dfrac{8}{{12}}\& \dfrac{6}{9}\] are the two ratios and their simplest form being $\dfrac{2}{3}\& \dfrac{2}{3}$ respectively. Therefore, these ratios are equal. Hence, they are equivalent ratios.