Solve - 1/2 * (- 4/7) + 3/14 * 1/2 + 7/2 * (- 1/2) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{-1}{2}\times\frac{-4}{7}+\frac{3}{14}\times\frac{1}{2}+\frac{7}{2}\times-\frac{1}{2}$$

Evaluate

$-\frac{19}{14}\approx -1.357142857$

Solution Steps

Fraction $\frac{-1}{2}$ can be rewritten as $-\frac{1}{2}$ by extracting the negative sign.

$$-\frac{1}{2}\times \frac{-4}{7}+\frac{3}{14}\times \frac{1}{2}+\frac{7}{2}\left(-\frac{1}{2}\right)$$

Fraction $\frac{-4}{7}$ can be rewritten as $-\frac{4}{7}$ by extracting the negative sign.

$$-\frac{1}{2}\left(-\frac{4}{7}\right)+\frac{3}{14}\times \frac{1}{2}+\frac{7}{2}\left(-\frac{1}{2}\right)$$

Multiply $-\frac{1}{2}$ times $-\frac{4}{7}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(-4\right)}{2\times 7}+\frac{3}{14}\times \frac{1}{2}+\frac{7}{2}\left(-\frac{1}{2}\right)$$

Do the multiplications in the fraction $\frac{-\left(-4\right)}{2\times 7}$.

$$\frac{4}{14}+\frac{3}{14}\times \frac{1}{2}+\frac{7}{2}\left(-\frac{1}{2}\right)$$

Reduce the fraction $\frac{4}{14}$ to lowest terms by extracting and canceling out $2$.

$$\frac{2}{7}+\frac{3}{14}\times \frac{1}{2}+\frac{7}{2}\left(-\frac{1}{2}\right)$$

Multiply $\frac{3}{14}$ times $\frac{1}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{7}+\frac{3\times 1}{14\times 2}+\frac{7}{2}\left(-\frac{1}{2}\right)$$

Do the multiplications in the fraction $\frac{3\times 1}{14\times 2}$.

$$\frac{2}{7}+\frac{3}{28}+\frac{7}{2}\left(-\frac{1}{2}\right)$$

Least common multiple of $7$ and $28$ is $28$. Convert $\frac{2}{7}$ and $\frac{3}{28}$ to fractions with denominator $28$.

$$\frac{8}{28}+\frac{3}{28}+\frac{7}{2}\left(-\frac{1}{2}\right)$$

Since $\frac{8}{28}$ and $\frac{3}{28}$ have the same denominator, add them by adding their numerators.

$$\frac{8+3}{28}+\frac{7}{2}\left(-\frac{1}{2}\right)$$

Add $8$ and $3$ to get $11$.

$$\frac{11}{28}+\frac{7}{2}\left(-\frac{1}{2}\right)$$

Multiply $\frac{7}{2}$ times $-\frac{1}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{11}{28}+\frac{7\left(-1\right)}{2\times 2}$$

Do the multiplications in the fraction $\frac{7\left(-1\right)}{2\times 2}$.

$$\frac{11}{28}+\frac{-7}{4}$$

Fraction $\frac{-7}{4}$ can be rewritten as $-\frac{7}{4}$ by extracting the negative sign.

$$\frac{11}{28}-\frac{7}{4}$$

Least common multiple of $28$ and $4$ is $28$. Convert $\frac{11}{28}$ and $\frac{7}{4}$ to fractions with denominator $28$.

$$\frac{11}{28}-\frac{49}{28}$$

Since $\frac{11}{28}$ and $\frac{49}{28}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-49}{28}$$

Subtract $49$ from $11$ to get $-38$.

$$\frac{-38}{28}$$

Reduce the fraction $\frac{-38}{28}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{19}{14}$$

Factor

$-\frac{19}{14} = -1\frac{5}{14} = -1.3571428571428572$