Solve of rational numbers is - 2/7 + 9/16 + 5/7 - 1/16 + 1/2 - 5 | 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

$$\frac { - 2 } { 7 } + \frac { 9 } { 16 } + \frac { 5 } { 7 } - \frac { 1 } { 16 } + \frac { 1 } { 2 } - 5$$

Evaluate

$-\frac{25}{7}\approx -3.571428571$

Solution Steps

Fraction $\frac{-2}{7}$ can be rewritten as $-\frac{2}{7}$ by extracting the negative sign.

$$-\frac{2}{7}+\frac{9}{16}+\frac{5}{7}-\frac{1}{16}+\frac{1}{2}-5$$

Least common multiple of $7$ and $16$ is $112$. Convert $-\frac{2}{7}$ and $\frac{9}{16}$ to fractions with denominator $112$.

$$-\frac{32}{112}+\frac{63}{112}+\frac{5}{7}-\frac{1}{16}+\frac{1}{2}-5$$

Since $-\frac{32}{112}$ and $\frac{63}{112}$ have the same denominator, add them by adding their numerators.

$$\frac{-32+63}{112}+\frac{5}{7}-\frac{1}{16}+\frac{1}{2}-5$$

Add $-32$ and $63$ to get $31$.

$$\frac{31}{112}+\frac{5}{7}-\frac{1}{16}+\frac{1}{2}-5$$

Least common multiple of $112$ and $7$ is $112$. Convert $\frac{31}{112}$ and $\frac{5}{7}$ to fractions with denominator $112$.

$$\frac{31}{112}+\frac{80}{112}-\frac{1}{16}+\frac{1}{2}-5$$

Since $\frac{31}{112}$ and $\frac{80}{112}$ have the same denominator, add them by adding their numerators.

$$\frac{31+80}{112}-\frac{1}{16}+\frac{1}{2}-5$$

Add $31$ and $80$ to get $111$.

$$\frac{111}{112}-\frac{1}{16}+\frac{1}{2}-5$$

Least common multiple of $112$ and $16$ is $112$. Convert $\frac{111}{112}$ and $\frac{1}{16}$ to fractions with denominator $112$.

$$\frac{111}{112}-\frac{7}{112}+\frac{1}{2}-5$$

Since $\frac{111}{112}$ and $\frac{7}{112}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{111-7}{112}+\frac{1}{2}-5$$

Subtract $7$ from $111$ to get $104$.

$$\frac{104}{112}+\frac{1}{2}-5$$

Reduce the fraction $\frac{104}{112}$ to lowest terms by extracting and canceling out $8$.

$$\frac{13}{14}+\frac{1}{2}-5$$

Least common multiple of $14$ and $2$ is $14$. Convert $\frac{13}{14}$ and $\frac{1}{2}$ to fractions with denominator $14$.

$$\frac{13}{14}+\frac{7}{14}-5$$

Since $\frac{13}{14}$ and $\frac{7}{14}$ have the same denominator, add them by adding their numerators.

$$\frac{13+7}{14}-5$$

Add $13$ and $7$ to get $20$.

$$\frac{20}{14}-5$$

Reduce the fraction $\frac{20}{14}$ to lowest terms by extracting and canceling out $2$.

$$\frac{10}{7}-5$$

Convert $5$ to fraction $\frac{35}{7}$.

$$\frac{10}{7}-\frac{35}{7}$$

Since $\frac{10}{7}$ and $\frac{35}{7}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-35}{7}$$

Subtract $35$ from $10$ to get $-25$.

$$-\frac{25}{7}$$

Factor

$-\frac{25}{7} = -3\frac{4}{7} = -3.5714285714285716$