Answer:
Refer explanation below.
Step-by-step explanation:
For two integers a and b, denoted LCM(a,b), the LCM is the smallest integer that is divisible by both a and b.
Distributive property: \(a(b+c)=ab+ac\)
We are given two expression,
\(\frac{1}{2}+\frac{1}{4}\) and \(\frac{1}{2}+\frac{1}{3}\)
We have to show how we solve them differently.
Considering the first expression,
\(\frac{1}{2}+\frac{1}{4}\)
Here we can apply the inverse of distributive property,
taking \(\frac{1}{2}\) common from the fraction, We get
\(\Rightarrow \frac{1}{2}(1+\frac{1}{2})\)
\(\Rightarrow \frac{1}{2}(\frac{2+1}{2})\)
\(\Rightarrow \frac{1}{2}(\frac{3}{2})\)
\(\Rightarrow \frac{3}{4}\)
Now consider the second expression,
\(\frac{1}{2}+\frac{1}{3}\)
Take least common factor of denominator that is 2 and 3.
LCM(2,3) = 6 , we get,
\(\frac{3+2}{6}=\frac{5}{6}\)
Thus, We can solve the two fraction differently.
