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

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

Verify

$\text{false}$

Solution Steps

Fraction $\frac{-2}{3}$ can be rewritten as $-\frac{2}{3}$ by extracting the negative sign.

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

Convert $2$ to fraction $\frac{6}{3}$.

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

Since $\frac{6}{3}$ and $\frac{2}{3}$ have the same denominator, subtract them by subtracting their numerators.

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

Subtract $2$ from $6$ to get $4$.

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

Least common multiple of $3$ and $4$ is $12$. Convert $\frac{4}{3}$ and $\frac{3}{4}$ to fractions with denominator $12$.

$$\frac{16}{12}+\frac{9}{12}=2+\frac{2}{3}+\frac{-3}{5}$$

Since $\frac{16}{12}$ and $\frac{9}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{16+9}{12}=2+\frac{2}{3}+\frac{-3}{5}$$

Add $16$ and $9$ to get $25$.

$$\frac{25}{12}=2+\frac{2}{3}+\frac{-3}{5}$$

Convert $2$ to fraction $\frac{6}{3}$.

$$\frac{25}{12}=\frac{6}{3}+\frac{2}{3}+\frac{-3}{5}$$

Since $\frac{6}{3}$ and $\frac{2}{3}$ have the same denominator, add them by adding their numerators.

$$\frac{25}{12}=\frac{6+2}{3}+\frac{-3}{5}$$

Add $6$ and $2$ to get $8$.

$$\frac{25}{12}=\frac{8}{3}+\frac{-3}{5}$$

Fraction $\frac{-3}{5}$ can be rewritten as $-\frac{3}{5}$ by extracting the negative sign.

$$\frac{25}{12}=\frac{8}{3}-\frac{3}{5}$$

Least common multiple of $3$ and $5$ is $15$. Convert $\frac{8}{3}$ and $\frac{3}{5}$ to fractions with denominator $15$.

$$\frac{25}{12}=\frac{40}{15}-\frac{9}{15}$$

Since $\frac{40}{15}$ and $\frac{9}{15}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{25}{12}=\frac{40-9}{15}$$

Subtract $9$ from $40$ to get $31$.

$$\frac{25}{12}=\frac{31}{15}$$

Least common multiple of $12$ and $15$ is $60$. Convert $\frac{25}{12}$ and $\frac{31}{15}$ to fractions with denominator $60$.

$$\frac{125}{60}=\frac{124}{60}$$

Compare $\frac{125}{60}$ and $\frac{124}{60}$.

$$\text{false}$$