Question

Express the following as ratio in simplest form.
2 dozen to 1 score.

Answer 1

Hint:
Here, we will use the conversion of weight to solve the given question. First we will convert the dozen and score into numbers. Then we will divide the 2 dozen (in number) with the 1 score (in numbers) to get the simplest form. We will then write the fraction in the ratio form.

Complete step by step solution:
We have to calculate the ratio of 2 dozen to 1 score. For that we need to know the value of one dozen and one score.
We know that the value of one dozen is 12 and the value of one score is 20.
Now to calculate the value of 2 dozen, we will multiply the value of one dozen by 2.
Therefore,
2 dozen\[ = 24\] .
Now we will divide the values of 2 dozen and 1 score.
\[\Rightarrow \dfrac{{2{\text{ dozen}}}}{{1{\text{ score}}}}{\text{ = }}\dfrac{{24}}{{20}}\]
Simplifying the fraction, we get
 \[\Rightarrow \dfrac{{2{\text{ dozen}}}}{{1{\text{ score}}}}{\text{ = }}\dfrac{6}{5}\]

Now we cannot further simplify the ratio, therefore the required ratio of \[2{\text{ dozen : }}1{\text{ score}}\] is \[6:5\].

Note:
Here are some properties of ratio are:-
1) If two ratios are equal then their inverses are also equal.
2) For four numbers, let’s take a, b, c, d. if \[a:b = c:d\] then \[a:c = b:d\]i.e. if the second term and third term interchange their places, then also the four terms are still in proportion.
3) If two ratios are equal then the ratio of their sum of numerator and denominator to the denominator are also equal.
4) If two ratios are equal then the ratio of the difference of numerator and denominator to the denominator are also equal.