Solve (- 71/2 + 1)/(5/6) = (71/3 - 1)/(6/3) | 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

$$\frac{-\frac{71}{2}+1}{\frac{5}{6}}=\frac{\frac{71}{3}-1}{\frac{6}{3}}$$

Verify

$\text{false}$

Solution Steps

Convert $1$ to fraction $\frac{2}{2}$.

$$\frac{-\frac{71}{2}+\frac{2}{2}}{\frac{5}{6}}=\frac{\frac{71}{3}-1}{\frac{6}{3}}$$

Since $-\frac{71}{2}$ and $\frac{2}{2}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{-71+2}{2}}{\frac{5}{6}}=\frac{\frac{71}{3}-1}{\frac{6}{3}}$$

Add $-71$ and $2$ to get $-69$.

$$\frac{-\frac{69}{2}}{\frac{5}{6}}=\frac{\frac{71}{3}-1}{\frac{6}{3}}$$

Divide $-\frac{69}{2}$ by $\frac{5}{6}$ by multiplying $-\frac{69}{2}$ by the reciprocal of $\frac{5}{6}$.

$$-\frac{69}{2}\times \frac{6}{5}=\frac{\frac{71}{3}-1}{\frac{6}{3}}$$

Multiply $-\frac{69}{2}$ times $\frac{6}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-69\times 6}{2\times 5}=\frac{\frac{71}{3}-1}{\frac{6}{3}}$$

Do the multiplications in the fraction $\frac{-69\times 6}{2\times 5}$.

$$\frac{-414}{10}=\frac{\frac{71}{3}-1}{\frac{6}{3}}$$

Reduce the fraction $\frac{-414}{10}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{207}{5}=\frac{\frac{71}{3}-1}{\frac{6}{3}}$$

Convert $1$ to fraction $\frac{3}{3}$.

$$-\frac{207}{5}=\frac{\frac{71}{3}-\frac{3}{3}}{\frac{6}{3}}$$

Since $\frac{71}{3}$ and $\frac{3}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{207}{5}=\frac{\frac{71-3}{3}}{\frac{6}{3}}$$

Subtract $3$ from $71$ to get $68$.

$$-\frac{207}{5}=\frac{\frac{68}{3}}{\frac{6}{3}}$$

Divide $6$ by $3$ to get $2$.

$$-\frac{207}{5}=\frac{\frac{68}{3}}{2}$$

Express $\frac{\frac{68}{3}}{2}$ as a single fraction.

$$-\frac{207}{5}=\frac{68}{3\times 2}$$

Multiply $3$ and $2$ to get $6$.

$$-\frac{207}{5}=\frac{68}{6}$$

Reduce the fraction $\frac{68}{6}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{207}{5}=\frac{34}{3}$$

Least common multiple of $5$ and $3$ is $15$. Convert $-\frac{207}{5}$ and $\frac{34}{3}$ to fractions with denominator $15$.

$$-\frac{621}{15}=\frac{170}{15}$$

Compare $-\frac{621}{15}$ and $\frac{170}{15}$.

$$\text{false}$$