Solve 10/9+3/5+11/4-1/9-3/4+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

$$10/9+3/5+11/4-1/9-3/4+2/5$$

Evaluate

$4$

Solution Steps

Least common multiple of $9$ and $5$ is $45$. Convert $\frac{10}{9}$ and $\frac{3}{5}$ to fractions with denominator $45$.

$$\frac{50}{45}+\frac{27}{45}+\frac{11}{4}-\frac{1}{9}-\frac{3}{4}+\frac{2}{5}$$

Since $\frac{50}{45}$ and $\frac{27}{45}$ have the same denominator, add them by adding their numerators.

$$\frac{50+27}{45}+\frac{11}{4}-\frac{1}{9}-\frac{3}{4}+\frac{2}{5}$$

Add $50$ and $27$ to get $77$.

$$\frac{77}{45}+\frac{11}{4}-\frac{1}{9}-\frac{3}{4}+\frac{2}{5}$$

Least common multiple of $45$ and $4$ is $180$. Convert $\frac{77}{45}$ and $\frac{11}{4}$ to fractions with denominator $180$.

$$\frac{308}{180}+\frac{495}{180}-\frac{1}{9}-\frac{3}{4}+\frac{2}{5}$$

Since $\frac{308}{180}$ and $\frac{495}{180}$ have the same denominator, add them by adding their numerators.

$$\frac{308+495}{180}-\frac{1}{9}-\frac{3}{4}+\frac{2}{5}$$

Add $308$ and $495$ to get $803$.

$$\frac{803}{180}-\frac{1}{9}-\frac{3}{4}+\frac{2}{5}$$

Least common multiple of $180$ and $9$ is $180$. Convert $\frac{803}{180}$ and $\frac{1}{9}$ to fractions with denominator $180$.

$$\frac{803}{180}-\frac{20}{180}-\frac{3}{4}+\frac{2}{5}$$

Since $\frac{803}{180}$ and $\frac{20}{180}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{803-20}{180}-\frac{3}{4}+\frac{2}{5}$$

Subtract $20$ from $803$ to get $783$.

$$\frac{783}{180}-\frac{3}{4}+\frac{2}{5}$$

Reduce the fraction $\frac{783}{180}$ to lowest terms by extracting and canceling out $9$.

$$\frac{87}{20}-\frac{3}{4}+\frac{2}{5}$$

Least common multiple of $20$ and $4$ is $20$. Convert $\frac{87}{20}$ and $\frac{3}{4}$ to fractions with denominator $20$.

$$\frac{87}{20}-\frac{15}{20}+\frac{2}{5}$$

Since $\frac{87}{20}$ and $\frac{15}{20}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{87-15}{20}+\frac{2}{5}$$

Subtract $15$ from $87$ to get $72$.

$$\frac{72}{20}+\frac{2}{5}$$

Reduce the fraction $\frac{72}{20}$ to lowest terms by extracting and canceling out $4$.

$$\frac{18}{5}+\frac{2}{5}$$

Since $\frac{18}{5}$ and $\frac{2}{5}$ have the same denominator, add them by adding their numerators.

$$\frac{18+2}{5}$$

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

$$\frac{20}{5}$$

Divide $20$ by $5$ to get $4$.

$$4$$

Factor

$2^{2}$