Q38. - Algebra 1

Question

The simplified form of $-\frac{4}{5}+\left(-\frac{1}{3}\right)$.

Step-by-Step Solution

Answer

The simplified form of $-\frac{4}{5}+\left(-\frac{1}{3}\right)$ is $-\frac{17}{15}$.

Step 1.

The statement “$-\frac{4}{5}+\left(-\frac{1}{3}\right)$.”

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 “$-\frac{4}{5}+\left(-\frac{1}{3}\right)$.”

 

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 5 and 3 is 15.

 

So, multiply $\frac{4}{5}$ by 3 and $\frac{1}{3}$ by 5 in both numerator and denominator,

 

Thus, the given expression can be simplified as,

$-\frac{4}{5}+\left(-\frac{1}{3}\right)=-\frac{4\times 3}{5\times 3}+\left(-\frac{1\times 5}{3\times 5}\right)$

$-\frac{4}{5}+\left(-\frac{1}{3}\right)=-\frac{12}{15}+\left(-\frac{5}{15}\right)$

$-\frac{4}{5}+\left(-\frac{1}{3}\right)=-\frac{12}{15}-\frac{5}{15}$

$-\frac{4}{5}+\left(-\frac{1}{3}\right)=-\frac{17}{15}$

Step 4. Recheck.

Since, $-\frac{17}{15}$ cannot be simplified further,

 

Hence, the simplified form of $-\frac{4}{5}+\left(-\frac{1}{3}\right)$ is $-\frac{17}{15}$.