Solve (((1)/(2)-(2)/(3))+((5)/(3)-(10)/(3)))-(5)/(9) | 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

$$(( \frac{ 1 }{ 2 } - \frac{ 2 }{ 3 } )+( \frac{ 5 }{ 3 } - \frac{ 10 }{ 3 } ))- \frac{ 5 }{ 9 }$$

Evaluate

$-\frac{43}{18}\approx -2.388888889$

Solution Steps

Least common multiple of $2$ and $3$ is $6$. Convert $\frac{1}{2}$ and $\frac{2}{3}$ to fractions with denominator $6$.

$$\frac{3}{6}-\frac{4}{6}+\frac{5}{3}-\frac{10}{3}-\frac{5}{9}$$

Since $\frac{3}{6}$ and $\frac{4}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-4}{6}+\frac{5}{3}-\frac{10}{3}-\frac{5}{9}$$

Subtract $4$ from $3$ to get $-1$.

$$-\frac{1}{6}+\frac{5}{3}-\frac{10}{3}-\frac{5}{9}$$

Least common multiple of $6$ and $3$ is $6$. Convert $-\frac{1}{6}$ and $\frac{5}{3}$ to fractions with denominator $6$.

$$-\frac{1}{6}+\frac{10}{6}-\frac{10}{3}-\frac{5}{9}$$

Since $-\frac{1}{6}$ and $\frac{10}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{-1+10}{6}-\frac{10}{3}-\frac{5}{9}$$

Add $-1$ and $10$ to get $9$.

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

Reduce the fraction $\frac{9}{6}$ to lowest terms by extracting and canceling out $3$.

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

Least common multiple of $2$ and $3$ is $6$. Convert $\frac{3}{2}$ and $\frac{10}{3}$ to fractions with denominator $6$.

$$\frac{9}{6}-\frac{20}{6}-\frac{5}{9}$$

Since $\frac{9}{6}$ and $\frac{20}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-20}{6}-\frac{5}{9}$$

Subtract $20$ from $9$ to get $-11$.

$$-\frac{11}{6}-\frac{5}{9}$$

Least common multiple of $6$ and $9$ is $18$. Convert $-\frac{11}{6}$ and $\frac{5}{9}$ to fractions with denominator $18$.

$$-\frac{33}{18}-\frac{10}{18}$$

Since $-\frac{33}{18}$ and $\frac{10}{18}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-33-10}{18}$$

Subtract $10$ from $-33$ to get $-43$.

$$-\frac{43}{18}$$

Factor

$-\frac{43}{18} = -2\frac{7}{18} = -2.388888888888889$