Question

A farmer producer $1\dfrac{3}{5}$ times as much peanuts this season as he did last season, find the ratio of last season production to this season.

Answer 1

Hint: First we have to convert the data into improper fraction because it gives a mixed fraction. Then applying the formula we get the required answer.

Formula used: Formula of ratio and proportion that is $a:b = \dfrac{a}{b}$

Complete step-by-step answer:
Let’s assume that the farmer produced $x$ peanuts in the last season.
So, from the given data we can write that the farmer produced $1\dfrac{3}{5}{x_{}}$ in this season.
Here we convert the above mixed fraction into improper fraction, $ = \dfrac{8}{5}x$
We have assumed that the production in the last season is $x$ and the production in this season is $\dfrac{8}{5}x$
We can write that the ratio of last season peanut production and this season peanut product
Now we can write it as $x:\dfrac{8}{5}x$
Here a =x and b = $\dfrac{8}{5}x$
Now we have to applying the formula of ratio and proportion that is $a:b = \dfrac{a}{b}$
$ \Rightarrow \dfrac{x}{{\dfrac{8}{5}x}}$
By taking reciprocal we get,
$ = \dfrac{{5x}}{{8x}}$
Cancel the terms we get,
$ = \dfrac{5}{8}$
Thus the ratio of last season peanut to the present season peanut production $ = 5:8$

Note: It is a simple question of ratio proportion which can be solved by assuming one as $x$.
The formula which is used for finding ratio is $a:b = \dfrac{a}{b}$
The basic properties of ratio include that it will always take place between two similar quantities, the units must be identical always and there must be significant order of terms.
The concept of ratio and proportion are two identical concepts and it is the basis for understanding different concepts in maths as well as in science.
We apply the concept of ratio and proportion in our everyday life like in business while handling money or other concepts. Both of these concepts are integral parts of mathematics. You can also find a lot of examples in reality such as velocity rate, price of a commodity, where we generally apply the ratio proportion principle. It is possible to compare two ratios if the ratios are equal to fractions.