Solve 4 2/5 - 3 1/10 - 4 8/9 + 2 1/10 | 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

$$4\frac{2}{5}-3\frac{1}{10}-4\frac{8}{9}+2\frac{1}{10}$$

Evaluate

$-\frac{67}{45}\approx -1.488888889$

Solution Steps

Multiply $4$ and $5$ to get $20$.

$$\frac{20+2}{5}-\frac{3\times 10+1}{10}-\frac{4\times 9+8}{9}+\frac{2\times 10+1}{10}$$

Add $20$ and $2$ to get $22$.

$$\frac{22}{5}-\frac{3\times 10+1}{10}-\frac{4\times 9+8}{9}+\frac{2\times 10+1}{10}$$

Multiply $3$ and $10$ to get $30$.

$$\frac{22}{5}-\frac{30+1}{10}-\frac{4\times 9+8}{9}+\frac{2\times 10+1}{10}$$

Add $30$ and $1$ to get $31$.

$$\frac{22}{5}-\frac{31}{10}-\frac{4\times 9+8}{9}+\frac{2\times 10+1}{10}$$

Least common multiple of $5$ and $10$ is $10$. Convert $\frac{22}{5}$ and $\frac{31}{10}$ to fractions with denominator $10$.

$$\frac{44}{10}-\frac{31}{10}-\frac{4\times 9+8}{9}+\frac{2\times 10+1}{10}$$

Since $\frac{44}{10}$ and $\frac{31}{10}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{44-31}{10}-\frac{4\times 9+8}{9}+\frac{2\times 10+1}{10}$$

Subtract $31$ from $44$ to get $13$.

$$\frac{13}{10}-\frac{4\times 9+8}{9}+\frac{2\times 10+1}{10}$$

Multiply $4$ and $9$ to get $36$.

$$\frac{13}{10}-\frac{36+8}{9}+\frac{2\times 10+1}{10}$$

Add $36$ and $8$ to get $44$.

$$\frac{13}{10}-\frac{44}{9}+\frac{2\times 10+1}{10}$$

Least common multiple of $10$ and $9$ is $90$. Convert $\frac{13}{10}$ and $\frac{44}{9}$ to fractions with denominator $90$.

$$\frac{117}{90}-\frac{440}{90}+\frac{2\times 10+1}{10}$$

Since $\frac{117}{90}$ and $\frac{440}{90}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{117-440}{90}+\frac{2\times 10+1}{10}$$

Subtract $440$ from $117$ to get $-323$.

$$-\frac{323}{90}+\frac{2\times 10+1}{10}$$

Multiply $2$ and $10$ to get $20$.

$$-\frac{323}{90}+\frac{20+1}{10}$$

Add $20$ and $1$ to get $21$.

$$-\frac{323}{90}+\frac{21}{10}$$

Least common multiple of $90$ and $10$ is $90$. Convert $-\frac{323}{90}$ and $\frac{21}{10}$ to fractions with denominator $90$.

$$-\frac{323}{90}+\frac{189}{90}$$

Since $-\frac{323}{90}$ and $\frac{189}{90}$ have the same denominator, add them by adding their numerators.

$$\frac{-323+189}{90}$$

Add $-323$ and $189$ to get $-134$.

$$\frac{-134}{90}$$

Reduce the fraction $\frac{-134}{90}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{67}{45}$$

Factor

$-\frac{67}{45} = -1\frac{22}{45} = -1.488888888888889$