Q23. - Algebra 1

Question

The simplified form of $\frac{7}{10}-\frac{2}{15}$.

Step-by-Step Solution

Answer

The simplified form of $\frac{7}{10}-\frac{2}{15}$ is $\frac{17}{30}$.

Step 1.

The statement “$\frac{7}{10}-\frac{2}{15}$.”

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 “$\frac{7}{10}-\frac{2}{15}$.”

 

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 10 and 15 is 30.

 

So, multiply $\frac{7}{10}$ by 3 and $\frac{2}{15}$ by 2 in both numerator and denominator,

 

Thus, the given expression can be simplified as,

$\frac{7}{10}-\frac{2}{15}=\frac{7\times 3}{10\times 3}-\frac{2\times 2}{15\times 2}$

$\frac{7}{10}-\frac{2}{15}=\frac{21}{30}-\frac{4}{30}$

$\frac{7}{10}-\frac{2}{15}=\frac{21-4}{30}$

$\frac{7}{10}-\frac{2}{15}=\frac{17}{30}$

Step 4. Recheck.

Since, $\frac{17}{30}$ cannot be simplified further,

 

Hence, the simplified form of $\frac{7}{10}-\frac{2}{15}$ is $\frac{17}{30}$.