Solve 3/4 - 3/5 - 2/3 + 5/8 - 4/15 | 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

$$\frac{3}{4}-\frac{3}{5}-\frac{2}{3}+\frac{5}{8}-\frac{4}{15}$$

Evaluate

$-\frac{19}{120}\approx -0.158333333$

Solution Steps

Least common multiple of $4$ and $5$ is $20$. Convert $\frac{3}{4}$ and $\frac{3}{5}$ to fractions with denominator $20$.

$$\frac{15}{20}-\frac{12}{20}-\frac{2}{3}+\frac{5}{8}-\frac{4}{15}$$

Since $\frac{15}{20}$ and $\frac{12}{20}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-12}{20}-\frac{2}{3}+\frac{5}{8}-\frac{4}{15}$$

Subtract $12$ from $15$ to get $3$.

$$\frac{3}{20}-\frac{2}{3}+\frac{5}{8}-\frac{4}{15}$$

Least common multiple of $20$ and $3$ is $60$. Convert $\frac{3}{20}$ and $\frac{2}{3}$ to fractions with denominator $60$.

$$\frac{9}{60}-\frac{40}{60}+\frac{5}{8}-\frac{4}{15}$$

Since $\frac{9}{60}$ and $\frac{40}{60}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-40}{60}+\frac{5}{8}-\frac{4}{15}$$

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

$$-\frac{31}{60}+\frac{5}{8}-\frac{4}{15}$$

Least common multiple of $60$ and $8$ is $120$. Convert $-\frac{31}{60}$ and $\frac{5}{8}$ to fractions with denominator $120$.

$$-\frac{62}{120}+\frac{75}{120}-\frac{4}{15}$$

Since $-\frac{62}{120}$ and $\frac{75}{120}$ have the same denominator, add them by adding their numerators.

$$\frac{-62+75}{120}-\frac{4}{15}$$

Add $-62$ and $75$ to get $13$.

$$\frac{13}{120}-\frac{4}{15}$$

Least common multiple of $120$ and $15$ is $120$. Convert $\frac{13}{120}$ and $\frac{4}{15}$ to fractions with denominator $120$.

$$\frac{13}{120}-\frac{32}{120}$$

Since $\frac{13}{120}$ and $\frac{32}{120}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{13-32}{120}$$

Subtract $32$ from $13$ to get $-19$.

$$-\frac{19}{120}$$

Factor

$-\frac{19}{120} = -0.15833333333333333$