Question

Fill in the boxes: (a). \[\left( {} \right) - \dfrac{5}{8} = \dfrac{1}{4}\] , (b). \[\left( {} \right) - \dfrac{1}{5} = \dfrac{1}{2}\] , (c). \[\left( {} \right) - \dfrac{1}{2} = \dfrac{1}{6}\] .

Answer 1

Hint: First assume the empty box as \[x\] in the given equation for our convenience. We have to add or subtract the same quantity on both sides of the given equation so that we get \[x\] separately on the LHS of the given equation. Then simplifying the RHS of the equation to get the value of \[x\] means (the value to fill in the box).

Complete step-by-step answer:
(a).
Given \[\left( {} \right) - \dfrac{5}{8} = \dfrac{1}{4}\]
Let \[x\] be the value of the given empty box, then the above equation become
 \[x - \dfrac{5}{8} = \dfrac{1}{4}\] ---(1)
Adding \[\dfrac{5}{8}\] in both sides of the equation (1), we get
 \[x - \dfrac{5}{8} + \dfrac{5}{8} = \dfrac{1}{4} + \dfrac{5}{8} \Rightarrow x = \dfrac{7}{8}\]
Hence \[\dfrac{7}{8}\] is fill in the box of the equation \[\left( {} \right) - \dfrac{5}{8} = \dfrac{1}{4}\] .
(b).
Given \[\left( {} \right) - \dfrac{1}{5} = \dfrac{1}{2}\]
Let \[x\] be the value of the given empty box, then the above equation become
 \[x - \dfrac{1}{5} = \dfrac{1}{2}\] ---(2)
Adding \[\dfrac{1}{5}\] in both sides of the equation (2), we get
 \[x - \dfrac{1}{5} + \dfrac{1}{5} = \dfrac{1}{2} + \dfrac{1}{5} \Rightarrow x = \dfrac{7}{{10}}\]
Hence \[\dfrac{7}{{10}}\] is fill in the box of the equation \[\left( {} \right) - \dfrac{1}{5} = \dfrac{1}{2}\] .

(c).
Given \[\left( {} \right) - \dfrac{1}{2} = \dfrac{1}{6}\]
Let \[x\] be the value of the given empty box, then the above equation become
 \[x - \dfrac{1}{2} = \dfrac{1}{6}\] ---(3)
Adding \[\dfrac{1}{2}\] in both sides of the equation (3), we get
 \[x - \dfrac{1}{2} + \dfrac{1}{2} = \dfrac{1}{6} + \dfrac{1}{2} \Rightarrow x = \dfrac{4}{6} = \dfrac{2}{3}\]
Hence \[\dfrac{2}{3}\] is fill in the box of the equation \[\left( {} \right) - \dfrac{1}{2} = \dfrac{1}{6}\] .

Note: Note that sign of the value which is add or subtract form the given equation is important many times students assign wrong signs and they get wrong answers. Also note that any problem asking to fill the value in the box by finding a method we have to assume any variable so that we can easily get an answer without any missed convenience.