Solve (- 2/5 + 4/9) + (- 3/4) = - 2/5 + \{4/9 + (- 3/4)\}

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Question

$$(-\frac{2}{5}+\frac{4}{9})+(-\frac{3}{4})=-\frac{2}{5}+\{\frac{4}{9}+(-\frac{3}{4})\}$$

Verify

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Solution Steps

Least common multiple of $5$ and $9$ is $45$. Convert $-\frac{2}{5}$ and $\frac{4}{9}$ to fractions with denominator $45$.

$$-\frac{18}{45}+\frac{20}{45}-\frac{3}{4}=-\frac{2}{5}+\frac{4}{9}-\frac{3}{4}$$

Since $-\frac{18}{45}$ and $\frac{20}{45}$ have the same denominator, add them by adding their numerators.

$$\frac{-18+20}{45}-\frac{3}{4}=-\frac{2}{5}+\frac{4}{9}-\frac{3}{4}$$

Add $-18$ and $20$ to get $2$.

$$\frac{2}{45}-\frac{3}{4}=-\frac{2}{5}+\frac{4}{9}-\frac{3}{4}$$

Least common multiple of $45$ and $4$ is $180$. Convert $\frac{2}{45}$ and $\frac{3}{4}$ to fractions with denominator $180$.

$$\frac{8}{180}-\frac{135}{180}=-\frac{2}{5}+\frac{4}{9}-\frac{3}{4}$$

Since $\frac{8}{180}$ and $\frac{135}{180}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-135}{180}=-\frac{2}{5}+\frac{4}{9}-\frac{3}{4}$$

Subtract $135$ from $8$ to get $-127$.

$$-\frac{127}{180}=-\frac{2}{5}+\frac{4}{9}-\frac{3}{4}$$

Least common multiple of $5$ and $9$ is $45$. Convert $-\frac{2}{5}$ and $\frac{4}{9}$ to fractions with denominator $45$.

$$-\frac{127}{180}=-\frac{18}{45}+\frac{20}{45}-\frac{3}{4}$$

Since $-\frac{18}{45}$ and $\frac{20}{45}$ have the same denominator, add them by adding their numerators.

$$-\frac{127}{180}=\frac{-18+20}{45}-\frac{3}{4}$$

Add $-18$ and $20$ to get $2$.

$$-\frac{127}{180}=\frac{2}{45}-\frac{3}{4}$$

Least common multiple of $45$ and $4$ is $180$. Convert $\frac{2}{45}$ and $\frac{3}{4}$ to fractions with denominator $180$.

$$-\frac{127}{180}=\frac{8}{180}-\frac{135}{180}$$