Solve 6 = (2/3 - 5/2 + 1)/(4/5 - 2/3 + 3/2) | 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

$$6=\frac{\frac{2}{3}-\frac{5}{2}+1}{\frac{4}{5}-\frac{2}{3}+\frac{3}{2}}$$

Verify

$\text{false}$

Solution Steps

Least common multiple of $3$ and $2$ is $6$. Convert $\frac{2}{3}$ and $\frac{5}{2}$ to fractions with denominator $6$.

$$6=\frac{\frac{4}{6}-\frac{15}{6}+1}{\frac{4}{5}-\frac{2}{3}+\frac{3}{2}}$$

Since $\frac{4}{6}$ and $\frac{15}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$6=\frac{\frac{4-15}{6}+1}{\frac{4}{5}-\frac{2}{3}+\frac{3}{2}}$$

Subtract $15$ from $4$ to get $-11$.

$$6=\frac{-\frac{11}{6}+1}{\frac{4}{5}-\frac{2}{3}+\frac{3}{2}}$$

Convert $1$ to fraction $\frac{6}{6}$.

$$6=\frac{-\frac{11}{6}+\frac{6}{6}}{\frac{4}{5}-\frac{2}{3}+\frac{3}{2}}$$

Since $-\frac{11}{6}$ and $\frac{6}{6}$ have the same denominator, add them by adding their numerators.

$$6=\frac{\frac{-11+6}{6}}{\frac{4}{5}-\frac{2}{3}+\frac{3}{2}}$$

Add $-11$ and $6$ to get $-5$.

$$6=\frac{-\frac{5}{6}}{\frac{4}{5}-\frac{2}{3}+\frac{3}{2}}$$

Least common multiple of $5$ and $3$ is $15$. Convert $\frac{4}{5}$ and $\frac{2}{3}$ to fractions with denominator $15$.

$$6=\frac{-\frac{5}{6}}{\frac{12}{15}-\frac{10}{15}+\frac{3}{2}}$$

Since $\frac{12}{15}$ and $\frac{10}{15}$ have the same denominator, subtract them by subtracting their numerators.

$$6=\frac{-\frac{5}{6}}{\frac{12-10}{15}+\frac{3}{2}}$$

Subtract $10$ from $12$ to get $2$.

$$6=\frac{-\frac{5}{6}}{\frac{2}{15}+\frac{3}{2}}$$

Least common multiple of $15$ and $2$ is $30$. Convert $\frac{2}{15}$ and $\frac{3}{2}$ to fractions with denominator $30$.

$$6=\frac{-\frac{5}{6}}{\frac{4}{30}+\frac{45}{30}}$$

Since $\frac{4}{30}$ and $\frac{45}{30}$ have the same denominator, add them by adding their numerators.

$$6=\frac{-\frac{5}{6}}{\frac{4+45}{30}}$$

Add $4$ and $45$ to get $49$.

$$6=\frac{-\frac{5}{6}}{\frac{49}{30}}$$

Divide $-\frac{5}{6}$ by $\frac{49}{30}$ by multiplying $-\frac{5}{6}$ by the reciprocal of $\frac{49}{30}$.

$$6=-\frac{5}{6}\times \frac{30}{49}$$

Multiply $-\frac{5}{6}$ times $\frac{30}{49}$ by multiplying numerator times numerator and denominator times denominator.

$$6=\frac{-5\times 30}{6\times 49}$$

Do the multiplications in the fraction $\frac{-5\times 30}{6\times 49}$.

$$6=\frac{-150}{294}$$

Reduce the fraction $\frac{-150}{294}$ to lowest terms by extracting and canceling out $6$.

$$6=-\frac{25}{49}$$

Convert $6$ to fraction $\frac{294}{49}$.

$$\frac{294}{49}=-\frac{25}{49}$$

Compare $\frac{294}{49}$ and $-\frac{25}{49}$.

$$\text{false}$$