Question

Billy ate \[1\dfrac{1}{4}\] pizzas and John ate \[1\dfrac{2}{3}\]. How much more pizza did John eat than billy?

Answer 1

Hint: To find the comparison between two substances or things we will subtract the two variables and check whether the difference is positive or not. If positive then the first variable is greater than the other or if the difference came out to be negative we can say that the second variable is greater than the first.

Complete step by step solution:
Let us assume Billy as the first variable and John as the second variable.
Now as we need to find who has eaten more amount of pizza we will subtract one variable from another.
From the question we can say that the first variable i.e. billy has a value of \[1\dfrac{1}{4}\](number of pizza billy ate)
And the second variable i.e. john has a value of \[1\dfrac{2}{3}\](number of pizza john ate)
Now to find which person has eaten more we will just subtract one person from another i.e.
First variable (billy) – Second variable (john)
Let us assume the answer to the above equation be a, so we get
a= First variable (billy) – Second variable (john)……………. (1)
From this the final value is greater than zero (0) i.e. a > 0; we can say that the first variable is more than second variable and if final value is less than zero (0) i.e. a < 0; we can say that the second variable is more than first variable.
Now to make our calculation easier we are going to change the mixed fraction into improper fraction and we get,
First variable (billy) = \[1\dfrac{1}{4}\]
\[\Rightarrow 1\dfrac{1}{4}=\dfrac{5}{4}\]
Second variable (john) = \[1\dfrac{2}{3}\]
\[\Rightarrow 1\dfrac{2}{3}=\dfrac{5}{3}\]
So finally we can say that
First variable (billy) = \[\dfrac{5}{4}\]
Second variable (john) = \[\dfrac{5}{3}\]
Now to find who ate more we will be using equation (1)
\[a=\dfrac{5}{4}-\dfrac{5}{3}\]
Now we will take the LCM to make our calculation easier and we get the LCM as 12 and then we will multiply both LHS and RHS by 12 and we get,
\[\begin{align}
  & \Rightarrow (12)a=12(\dfrac{5}{4}-\dfrac{5}{3}) \\
 & \Rightarrow 12a=\dfrac{(12)(5)}{4}-\dfrac{(12)(5)}{3} \\
 & \Rightarrow 12a=(3)(5)-(4)(5) \\
 & \Rightarrow 12a=15-20 \\
 & \Rightarrow 12a=-5 \\
 & \Rightarrow a=\dfrac{-5}{12} \\
\end{align}\]
Now as we can see that a<0; second variable (john) is more than first variable (billy).
So we can finally say that John ate more pizza than billy.

Note:
The mistakes that are generally made is what to assume and when, actually it doesn’t matter what you assume, just remember to take a variable when comparing and make cases for that variable just like we did in this question.