Question

If you can buy $\dfrac{1}{4}$ pizza for 5 dollars, how much can you purchase for 8 dollars?

Answer 1

Hint: In the above problem, it is given that $\dfrac{1}{4}$ of the total pizza costs 5 dollars and are asked to find the amount of pizza for 8 dollars. So, the amount of pizza for 1 dollar is equal to the multiplication of $\dfrac{1}{4}$ by $\dfrac{1}{5}$ then the amount of pizza for 8 dollars is equal to multiplication of $\dfrac{1}{4}$ by $\dfrac{1}{5}$ and by 8.

Complete step-by-step answer:
It is given that the amount of pizza we can buy for 5 dollars is $\dfrac{1}{4}$. And we are asked to find the amount of pizza we can purchase for 8 dollars.
To solve this problem, we are going to use a unitary method. The amount of pizza for 5 dollars is $\dfrac{1}{4}$ and the amount of pizza for 1 dollar is equal to the multiplication of $\dfrac{1}{4}$ by $\dfrac{1}{5}$ and mathematical expression for this conversion is as follows:
$=\dfrac{1}{4}\times \dfrac{1}{5}=\dfrac{1}{20}$
From the above, we got the amount of pizza for 1 dollar is $\dfrac{1}{20}$ of total pizza. Now, the amount of pizza we can purchase for 8 dollars is equal to multiplication of $\dfrac{1}{20}$ by 8 and we get,
$=\dfrac{1}{20}\times 8$
As you can see that the numerator and denominator of the above expression will be divided by 4 sp dividing numerator and denominator of the above expression by 4 we get,
$\Rightarrow \dfrac{2}{5}$
From the above, the amount of pizza which can be purchased for 8 dollars is equal to $\dfrac{2}{5}$ of pizza.

Note: We can check the above amount of pizza which we have calculated for 8 dollars by using the unitary method.
It is given that we can buy $\dfrac{1}{4}$ pizza for 5 dollars then a full pizza can be purchased for 5 dollars multiplied by 4 and the answer is:
$20\text{ }dollars$
Now, the cost of $\dfrac{2}{5}$ of full pizza is equal to $\dfrac{2}{5}$ multiplied by 20 dollars and we get,
$\Rightarrow \dfrac{2}{5}\times 20$
In the above expression, numerator and denominator is divided by 5 and we get,
$\Rightarrow \dfrac{2}{1}\times 4=8\text{ }dollars$
As you can see that we are getting the same 8 dollars which is given in the above problem for $\dfrac{2}{5}$ of pizza so the amount of pizza for 8 dollars which we have found above is correct.