Question

Compute and express the result as a mixed fraction?
1. $ 2 + \dfrac{3}{4} $
2. $ \dfrac{7}{9} + \dfrac{1}{3} $

Answer 1

Hint: First of convert the given expressions in the form of the mixed fractions. Mixed number can be defined as the combination of a whole number and the fraction. Fraction can be defined as the number expressed in the form of the numerator and the denominator. Then simplify the expression for the resultant required value.

Complete step-by-step answer:
Given expression: 1) $ 2 + \dfrac{3}{4} $
Find the LCM (least common multiple) for the above expression. LCM can be defined as the least or the smallest number with which the given numbers are exactly divisible. It is also called the least common divisor.
 $ = 2\left( {\dfrac{4}{4}} \right) + \dfrac{3}{4} $
Simplify the above expression –
 $ = \dfrac{8}{4} + \dfrac{3}{4} $
When denominators are same, then the numerators are added –
 $ = \dfrac{{11}}{4} $
Convert the above expression in the form of the mixed fraction
 $ = 2\dfrac{3}{4} $
Hence, the required solution is $ 2 + \dfrac{3}{4} = 2\dfrac{3}{4} $

2) Given expression: $ \dfrac{7}{9} + \dfrac{1}{3} $
Find the LCM (least common multiple) for the above expression
 $ = \dfrac{7}{9} + \dfrac{1}{3}\left( {\dfrac{3}{3}} \right) $
Simplify the above expression –
 $ = \dfrac{7}{9} + \dfrac{3}{9} $
When denominators are same, then the numerators are added –
 $ = \dfrac{{10}}{9} $
Convert the above expression in the form of the mixed fraction
 $ = 1\dfrac{1}{9} $
Hence, the required solution is $ \dfrac{7}{9} + \dfrac{1}{3} = 1\dfrac{1}{9} $

Note: Always remember the terminology that - LCM is the highest number compared to HCF for two given numbers. Also, LCM comprises the value of the HCF for the two given values. HCF (Highest common factor is also defined as the greatest common factor. LCM (Least common multiple) is also called as the least common divisor.