Question

Express each of the following ratios in the simplest form:
186: 403

Answer 1

Hint: We know that a ratio is a number used to compare two quantities of the same unit and it is made by dividing one quantity by the other quantity of the same unit. A ratio can be expressed as a fraction but it is important that one read the ratio correctly.

Complete step-by-step answer:
A ratio can be read carefully that is when we have a ratio is of the form a:b it is read as the ratio of a to b and it can be denoted in the fraction as $ \dfrac{a}{b} $ whereas the ratio b:a is read as the ratio of b to a and it can be denoted in fraction similarly by $ \dfrac{b}{a} $ .
Since we have been asked to express the ratio in the simplest form by simplest form we mean that the final ratio must not have anything in common and there should be no common factor in both the numerator and denominator in the fraction. So that it cannot be further reduced.
The given ratio 186: 403 can be written in the fraction as:
 $
  \Rightarrow 186:403 \\
  \Rightarrow \dfrac{{186}}{{403}} \;
 $
Now it can be divided by its H.C.F or highest common factor to reduce the ratio to its simplest form and we know that the Highest common factor for 186 and 403 is 31,
 $
  \therefore 31 \times 6 = 186 \\
  \therefore 31 \times 13 = 403 \;
 $
Therefore multiplying the fraction by 31 at both the numerator and denominator we get,
 $
  \Rightarrow \dfrac{{186}}{{403}} \times \dfrac{{31}}{{31}} \\
  \Rightarrow \dfrac{6}{{13}} \;
 $
This simplest form can be similarly converted into a ratio by the above method. Therefore the simplest ratio of 186: 403 is
6:13.
So, the correct answer is “6:13”.

Note: Now this ratio, the ratio 6 to 13 cannot be further reduced as they have no common factor anymore. Also ratios can be compared only between like terms one cannot compare kg to g. This can be done by converting one of the terms to get all the like terms to compare.