Q39. - Algebra 1

Question

The simplified form of $-\frac{1}{12}-\left(-\frac{3}{4}\right)$.

Step-by-Step Solution

Answer

The simplified form of $-\frac{1}{12}-\left(-\frac{3}{4}\right)$ is $\frac{2}{3}$.

Step 1. Given

The statement “$-\frac{1}{12}-\left(-\frac{3}{4}\right)$.”

Step 2. Concept.

When two fractions with different denominators are subtracted then the two unlike fractions, are converted into like fractions by multiplying the denominators with a common factor of their lowest common multiple (LCM).

Step 3. Calculation.

Consider the provided statement “$-\frac{1}{12}-\left(-\frac{3}{4}\right)$.”

 

Recall that when two fractions with different denominators are subtracted then the two unlike fractions, are converted into like fractions by multiplying the denominators with a common factor of their lowest common multiple (LCM).

 

LCM of 12 and 4 is 12.

 

So, multiply $\frac{3}{4}$ by 3 in both numerator and denominator,

 

Thus, the given expression can be simplified as,

$-\frac{1}{12}-\left(-\frac{3}{4}\right)=-\frac{1}{12}+\frac{3}{4}$

$-\frac{1}{12}-\left(-\frac{3}{4}\right)=-\frac{1}{12}+\frac{3\times 3}{4\times 3}$

$-\frac{1}{12}-\left(-\frac{3}{4}\right)=-\frac{1}{12}+\frac{9}{12}$

$-\frac{1}{12}-\left(-\frac{3}{4}\right)=\frac{8}{12}$

Step 4. Recheck.

Now, 8 can be written as the product of 4 and 2.

 

12 can be written as the product of 4 and 3.

 

So, $\frac{8}{12}$ can be simplified as,

$\frac{8}{12}=\frac{4\times 2}{4\times 3}$

 

Striking off the common terms, we get,

$\frac{8}{12}=\frac{2}{3}$

Hence, the simplified form of $-\frac{1}{12}-\left(-\frac{3}{4}\right)$ is $\frac{2}{3}$.