Solve Find using distributivity . (i ) \{7/5 * (- 3/12)\} + \{7/5 * 5/12\}

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Question

$$\{ \frac { 7 } { 5 } \times ( \frac { - 3 } { 12 } ) \} + \{ \frac { 7 } { 5 } \times \frac { 5 } { 12 } \}$$

Evaluate

$\frac{7}{30}\approx 0.233333333$

Solution Steps

Reduce the fraction $\frac{-3}{12}$ to lowest terms by extracting and canceling out $3$.

$$\frac{7}{5}\left(-\frac{1}{4}\right)+\frac{7}{5}\times \frac{5}{12}$$

Multiply $\frac{7}{5}$ times $-\frac{1}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-1\right)}{5\times 4}+\frac{7}{5}\times \frac{5}{12}$$

Do the multiplications in the fraction $\frac{7\left(-1\right)}{5\times 4}$.

$$\frac{-7}{20}+\frac{7}{5}\times \frac{5}{12}$$

Fraction $\frac{-7}{20}$ can be rewritten as $-\frac{7}{20}$ by extracting the negative sign.

$$-\frac{7}{20}+\frac{7}{5}\times \frac{5}{12}$$

Multiply $\frac{7}{5}$ times $\frac{5}{12}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{7}{20}+\frac{7\times 5}{5\times 12}$$

Cancel out $5$ in both numerator and denominator.

$$-\frac{7}{20}+\frac{7}{12}$$

Least common multiple of $20$ and $12$ is $60$. Convert $-\frac{7}{20}$ and $\frac{7}{12}$ to fractions with denominator $60$.

$$-\frac{21}{60}+\frac{35}{60}$$

Since $-\frac{21}{60}$ and $\frac{35}{60}$ have the same denominator, add them by adding their numerators.

$$\frac{-21+35}{60}$$

Add $-21$ and $35$ to get $14$.

$$\frac{14}{60}$$

Reduce the fraction $\frac{14}{60}$ to lowest terms by extracting and canceling out $2$.

$$\frac{7}{30}$$

Show Solution

Factor

$\frac{7}{2 \cdot 3 \cdot 5} = 0.23333333333333334$