Question

Express the following ratios in the simplest form. (a) 36 m to 16 m (b) 65 books to 91 books.

Answer 1

Hint: We know that a fraction is said to be written in a simplest form if the numerator and denominator will not have a common factor except 1. So, we have to simplify the numerator and denominator as small as possible. Based on this definition, the simplest form can be found.

Complete step by step solution:
We know that a fraction is said to be written in the simplest form if the numerator and denominator will not have a common factor except 1.
From the question, it is clear that we should find the simplest form of a given question.
In this question
(a), it is clear that we have to find the simplest form of ratio of 36 m to 16 m.
To find the simplest form, we should find the ratio of 36 m to 16 m. Let us assume this ratio is equal to R.
\[\Rightarrow R=\dfrac{36m}{16m}\]
Now let us remove m from numerator and denominator from the ratio R.
\[\Rightarrow R=\dfrac{36}{16}\]
We know that 4 is the common factor of 36 and 16.
So, let us divide the numerator by 4 and the denominator by 4.
We know that if we divide 36 with 4 then the value of the numerator will be equal to 9.
So, the numerator will become 9.
We know that if we divide 16 with 4 then the denominator by 4.
So, the denominator will become 4.
So, the ratio can be evaluated as follows:
\[\Rightarrow R=\dfrac{9}{4}\]
We know that except 1 there is no other factor between 9 and 4.
So, the simplest form of the ratio of 36 m to 16 m is equal to \[\dfrac{9}{4}\].
In this question
(b), it is clear that we have to find the simplest form of ratio of 65 to 91.
To find the simplest form, we should find the ratio of 65 to 91. Let us assume this ratio is equal to R.
\[\Rightarrow R=\dfrac{65}{91}\]
We know that 13 is the common factor of 65 and 91.
So, let us divide the numerator by 13 and the denominator by 13.
We know that if we divide 65 with 13 then the value of the numerator will be equal to 5.
So, the numerator will become 5.
We know that if we divide 91 with 13 then the denominator by 7.
So, the denominator will become 7.
So, the ratio can be evaluated as follows:
\[\Rightarrow R=\dfrac{5}{7}\]
We know that except 1 there is no other factor between 5 and 7.
So, the simplest form of the ratio of 65 books to 91 books is equal to \[\dfrac{5}{7}\].

Note: Students should be careful in not having calculation mistakes while solving this problem. If a small mistake is done, then the final answer may get interrupted. Here they asked simplest form students should not reduce answers into decimals for example in case 1 \[\Rightarrow \dfrac{9}{4}\] \[\Rightarrow 2.25\] is wrong. Students should also avoid misconceptions as well. A small misconception will also lead to interruption of the final answer.