Solve યોગ્ય ગુણધર્મનો ઉપયોગ ક \{5/3 - 3/10\} + \{5/3 + 12/10\} C

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Question

$$\{ \frac { 5 } { 3 } + \frac { - 3 } { 10 } \} + \{ \frac { 5 } { 3 } + \frac { 12 } { 10 } \}$$

Evaluate

$\frac{127}{30}\approx 4.233333333$

Solution Steps

Fraction $\frac{-3}{10}$ can be rewritten as $-\frac{3}{10}$ by extracting the negative sign.

$$\frac{5}{3}-\frac{3}{10}+\frac{5}{3}+\frac{12}{10}$$

Least common multiple of $3$ and $10$ is $30$. Convert $\frac{5}{3}$ and $\frac{3}{10}$ to fractions with denominator $30$.

$$\frac{50}{30}-\frac{9}{30}+\frac{5}{3}+\frac{12}{10}$$

Since $\frac{50}{30}$ and $\frac{9}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{50-9}{30}+\frac{5}{3}+\frac{12}{10}$$

Subtract $9$ from $50$ to get $41$.

$$\frac{41}{30}+\frac{5}{3}+\frac{12}{10}$$

Least common multiple of $30$ and $3$ is $30$. Convert $\frac{41}{30}$ and $\frac{5}{3}$ to fractions with denominator $30$.

$$\frac{41}{30}+\frac{50}{30}+\frac{12}{10}$$

Since $\frac{41}{30}$ and $\frac{50}{30}$ have the same denominator, add them by adding their numerators.

$$\frac{41+50}{30}+\frac{12}{10}$$

Add $41$ and $50$ to get $91$.

$$\frac{91}{30}+\frac{12}{10}$$

Reduce the fraction $\frac{12}{10}$ to lowest terms by extracting and canceling out $2$.

$$\frac{91}{30}+\frac{6}{5}$$

Least common multiple of $30$ and $5$ is $30$. Convert $\frac{91}{30}$ and $\frac{6}{5}$ to fractions with denominator $30$.

$$\frac{91}{30}+\frac{36}{30}$$

Since $\frac{91}{30}$ and $\frac{36}{30}$ have the same denominator, add them by adding their numerators.

$$\frac{91+36}{30}$$

Add $91$ and $36$ to get $127$.

$$\frac{127}{30}$$

Show Solution

Factor

$\frac{127}{2 \cdot 3 \cdot 5} = 4\frac{7}{30} = 4.233333333333333$