Solve (3)/(5)+(-(1)/(2))-(2)/(3)\div(8)/(9)=

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Question

$$\frac{ 3 }{ 5 } +(- \frac{ 1 }{ 2 } )- \frac{ 2 }{ 3 } \div \frac{ 8 }{ 9 } =$$

Evaluate

$-\frac{13}{20}=-0.65$

Solution Steps

Least common multiple of $5$ and $2$ is $10$. Convert $\frac{3}{5}$ and $\frac{1}{2}$ to fractions with denominator $10$.

$$\frac{6}{10}-\frac{5}{10}-\frac{\frac{2}{3}}{\frac{8}{9}}$$

Since $\frac{6}{10}$ and $\frac{5}{10}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-5}{10}-\frac{\frac{2}{3}}{\frac{8}{9}}$$

Subtract $5$ from $6$ to get $1$.

$$\frac{1}{10}-\frac{\frac{2}{3}}{\frac{8}{9}}$$

Divide $\frac{2}{3}$ by $\frac{8}{9}$ by multiplying $\frac{2}{3}$ by the reciprocal of $\frac{8}{9}$.

$$\frac{1}{10}-\frac{2}{3}\times \frac{9}{8}$$

Multiply $\frac{2}{3}$ times $\frac{9}{8}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{10}-\frac{2\times 9}{3\times 8}$$

Do the multiplications in the fraction $\frac{2\times 9}{3\times 8}$.

$$\frac{1}{10}-\frac{18}{24}$$

Reduce the fraction $\frac{18}{24}$ to lowest terms by extracting and canceling out $6$.

$$\frac{1}{10}-\frac{3}{4}$$

Least common multiple of $10$ and $4$ is $20$. Convert $\frac{1}{10}$ and $\frac{3}{4}$ to fractions with denominator $20$.

$$\frac{2}{20}-\frac{15}{20}$$

Since $\frac{2}{20}$ and $\frac{15}{20}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-15}{20}$$

Subtract $15$ from $2$ to get $-13$.

$$-\frac{13}{20}$$

Show Solution

Factor

$-\frac{13}{20} = -0.65$