Question

What should be subtracted from $ 10 $ to get $ 4\dfrac{1}{4} $ ?

Answer 1

Hint:
Here we can let the number to be subtracted from $ 10 $ be any variable and then form an equation. Now we just need to solve the equation formed to get the value of the required variable which is the term to be subtracted.

Complete step by step solution:
Here we are told to find the number that must be subtracted from $ 10 $ to get $ 4\dfrac{1}{4} $
First we need to know how the simplification of the form $ a\dfrac{b}{c} $ is done. Here we must know that this form of the fraction $ (a\dfrac{b}{c}) $ is known as the mixed fraction. For simplifying it into the form where we have only the numerator and denominator, we need to follow the procedure:
1) After simplifying the denominator will be $ c $
2) The numerator will be $ ac + b $ which means that $ a $ is multiplied with $ c $ and $ b $ is added to the product $ ac $
So we can write $ a\dfrac{b}{c} $ as $ \dfrac{{ac + b}}{c} $
Similarly we can write $ 4\dfrac{1}{4} $ as $ \dfrac{{(4 \times 4) + 1}}{4} $ $ = \dfrac{{17}}{4} $
We are given to find the number that must be subtracted from $ 10 $ to get $ 4\dfrac{1}{4} $
Let the number to be subtracted be $ x $
Now we are given that subtraction of $ x $ from $ 10 $ gives $ 4\dfrac{1}{4} $
So we can write this statement in the equation form in which we need to subtract $ x $ from $ 10 $ and equate it to $ 4\dfrac{1}{4} $ $ = \dfrac{{17}}{4} $
So we can write
 $ 10 - x = \dfrac{{17}}{4} $
Now simplifying further we get:
 $ 10 - \dfrac{{17}}{4} = x $
Now we need to take the LCM of the denominators which are $ 1,4 $
LCM of $ 1,4 $ is the least number that is divisible by both $ 1{\text{ and }}4 $ which is $ 4 $
Hence taking LCM we get
 $ 10 - \dfrac{{17}}{4} = x $
 $ \dfrac{{40 - 17}}{4} = x $
 $ \dfrac{{23}}{4} = x $
So we get the value of $ x $ as $ \dfrac{{23}}{4} $
Now we can again convert this into the mixed fraction by writing it as $ \dfrac{{23}}{4} = \dfrac{{4(5) + 3}}{4} = 5\dfrac{3}{4} $

So we need to subtract $ 5\dfrac{3}{4} $ from $ 10 $ to get $ 4\dfrac{1}{4} $ .

Note:
Here in these types of problems we can also visualise the term $ 4\dfrac{1}{4} $ as $ 4 + \dfrac{1}{4} $ which means that the fraction $ \dfrac{1}{4} $ is added to the number $ 4 $ . Student must make the calculations correctly.