Question

How do you simplify $\dfrac{1}{4} + \dfrac{6}{8}$?

Answer 1

We first bring both the fractions into lowest form i.e. we cancel all common factors between
numerator and denominator. Then we take LCM of the terms in denominator and calculate the
value.

• LCM is the least common multiple of two or more numbers. We write each number in the form of
  its prime factors and write the LCM of the numbers as multiplication of prime factors with their
  highest powers.

Complete step-by-step answer:
We have to simplify the value $\dfrac{1}{4} + \dfrac{6}{8}$ … (1)
We write both the fractions in simplest lowest form such that there is no common factor between
numerator and denominator of that fraction.
We look at $\dfrac{1}{4}$and see that there are no common factors between numerator and
denominator, so it is in its lowest form.
Now we look at $\dfrac{6}{8}$and see that there is a common factor i.e. 2 that divides both
numerator and denominator
We can write $\dfrac{6}{8} = \dfrac{{2 \times 3}}{{2 \times 4}}$
Since 2 exists in numerator as well as denominator, we can cancel it out from both numerator and
denominator.
$\Rightarrow \dfrac{6}{8} = \dfrac{3}{4}$ … (2)
Substitute the value from equation (2) in equation (1)
$\Rightarrow \dfrac{1}{4} + \dfrac{6}{8} = \dfrac{1}{4} + \dfrac{3}{4}$
Now we take LCM in right hand side of the equation
Since both the denominators are same i.e. 4 we can say LCM is 4
$\Rightarrow \dfrac{1}{4} + \dfrac{6}{8} = \dfrac{{1 + 3}}{4}$
Add the terms in numerator of fraction in right hand side of the equation
$\Rightarrow \dfrac{1}{4} + \dfrac{6}{8} = \dfrac{4}{4}$
Cancel same factors i.e. 4 from numerator and denominator in right hand side of the equation
$\Rightarrow \dfrac{1}{4} + \dfrac{6}{8} = 1$

$\therefore$The value of $\dfrac{1}{4} + \dfrac{6}{8}$ on simplification is 1.

Note:
Alternate method:
We can directly take LCM of the terms
Since 4 and 8 have Least common multiple 8, then LCM is 8
$\Rightarrow \dfrac{1}{4} + \dfrac{6}{8} = \dfrac{{1 \times 2 + 6}}{8}$
$\Rightarrow \dfrac{1}{4} + \dfrac{6}{8} = \dfrac{{2 + 6}}{8}$
Add the terms in numerator of fraction in right hand side of the equation
$\Rightarrow \dfrac{1}{4} + \dfrac{6}{8} = \dfrac{8}{8}$
Cancel same factors i.e. 8 from numerator and denominator in right hand side of the equation
$\Rightarrow \dfrac{1}{4} + \dfrac{6}{8} = 1$