Solve (-0.125+(2)/(3))-(5(1)/(9)-1(7)/(8)) | 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

$$(-0.125+ \frac{ 2 }{ 3 } )-(5 \frac{ 1 }{ 9 } -1 \frac{ 7 }{ 8 } )$$

Evaluate

$-\frac{97}{36}\approx -2.694444444$

Solution Steps

Convert decimal number $-0.125$ to fraction $-\frac{125}{1000}$. Reduce the fraction $-\frac{125}{1000}$ to lowest terms by extracting and canceling out $125$.

$$-\frac{1}{8}+\frac{2}{3}-\left(\frac{5\times 9+1}{9}-\frac{1\times 8+7}{8}\right)$$

Least common multiple of $8$ and $3$ is $24$. Convert $-\frac{1}{8}$ and $\frac{2}{3}$ to fractions with denominator $24$.

$$-\frac{3}{24}+\frac{16}{24}-\left(\frac{5\times 9+1}{9}-\frac{1\times 8+7}{8}\right)$$

Since $-\frac{3}{24}$ and $\frac{16}{24}$ have the same denominator, add them by adding their numerators.

$$\frac{-3+16}{24}-\left(\frac{5\times 9+1}{9}-\frac{1\times 8+7}{8}\right)$$

Add $-3$ and $16$ to get $13$.

$$\frac{13}{24}-\left(\frac{5\times 9+1}{9}-\frac{1\times 8+7}{8}\right)$$

Multiply $5$ and $9$ to get $45$.

$$\frac{13}{24}-\left(\frac{45+1}{9}-\frac{1\times 8+7}{8}\right)$$

Add $45$ and $1$ to get $46$.

$$\frac{13}{24}-\left(\frac{46}{9}-\frac{1\times 8+7}{8}\right)$$

Multiply $1$ and $8$ to get $8$.

$$\frac{13}{24}-\left(\frac{46}{9}-\frac{8+7}{8}\right)$$

Add $8$ and $7$ to get $15$.

$$\frac{13}{24}-\left(\frac{46}{9}-\frac{15}{8}\right)$$

Least common multiple of $9$ and $8$ is $72$. Convert $\frac{46}{9}$ and $\frac{15}{8}$ to fractions with denominator $72$.

$$\frac{13}{24}-\left(\frac{368}{72}-\frac{135}{72}\right)$$

Since $\frac{368}{72}$ and $\frac{135}{72}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{24}-\frac{368-135}{72}$$

Subtract $135$ from $368$ to get $233$.

$$\frac{13}{24}-\frac{233}{72}$$

Least common multiple of $24$ and $72$ is $72$. Convert $\frac{13}{24}$ and $\frac{233}{72}$ to fractions with denominator $72$.

$$\frac{39}{72}-\frac{233}{72}$$

Since $\frac{39}{72}$ and $\frac{233}{72}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{39-233}{72}$$

Subtract $233$ from $39$ to get $-194$.

$$\frac{-194}{72}$$

Reduce the fraction $\frac{-194}{72}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{97}{36}$$

Factor

$-\frac{97}{36} = -2\frac{25}{36} = -2.6944444444444446$