Solve 5/6+(-3)/8-6/7+(-3)/14-2/5-8/(-15) | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$5/6+(-3)/8-6/7+(-3)/14-2/5-8/(-15)$$

Evaluate

$-\frac{403}{840}\approx -0.479761905$

Solution Steps

Fraction $\frac{-3}{8}$ can be rewritten as $-\frac{3}{8}$ by extracting the negative sign.

$$\frac{5}{6}-\frac{3}{8}-\frac{6}{7}+\frac{-3}{14}-\frac{2}{5}-\frac{8}{-15}$$

Least common multiple of $6$ and $8$ is $24$. Convert $\frac{5}{6}$ and $\frac{3}{8}$ to fractions with denominator $24$.

$$\frac{20}{24}-\frac{9}{24}-\frac{6}{7}+\frac{-3}{14}-\frac{2}{5}-\frac{8}{-15}$$

Since $\frac{20}{24}$ and $\frac{9}{24}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-9}{24}-\frac{6}{7}+\frac{-3}{14}-\frac{2}{5}-\frac{8}{-15}$$

Subtract $9$ from $20$ to get $11$.

$$\frac{11}{24}-\frac{6}{7}+\frac{-3}{14}-\frac{2}{5}-\frac{8}{-15}$$

Least common multiple of $24$ and $7$ is $168$. Convert $\frac{11}{24}$ and $\frac{6}{7}$ to fractions with denominator $168$.

$$\frac{77}{168}-\frac{144}{168}+\frac{-3}{14}-\frac{2}{5}-\frac{8}{-15}$$

Since $\frac{77}{168}$ and $\frac{144}{168}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{77-144}{168}+\frac{-3}{14}-\frac{2}{5}-\frac{8}{-15}$$

Subtract $144$ from $77$ to get $-67$.

$$-\frac{67}{168}+\frac{-3}{14}-\frac{2}{5}-\frac{8}{-15}$$

Fraction $\frac{-3}{14}$ can be rewritten as $-\frac{3}{14}$ by extracting the negative sign.

$$-\frac{67}{168}-\frac{3}{14}-\frac{2}{5}-\frac{8}{-15}$$

Least common multiple of $168$ and $14$ is $168$. Convert $-\frac{67}{168}$ and $\frac{3}{14}$ to fractions with denominator $168$.

$$-\frac{67}{168}-\frac{36}{168}-\frac{2}{5}-\frac{8}{-15}$$

Since $-\frac{67}{168}$ and $\frac{36}{168}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-67-36}{168}-\frac{2}{5}-\frac{8}{-15}$$

Subtract $36$ from $-67$ to get $-103$.

$$-\frac{103}{168}-\frac{2}{5}-\frac{8}{-15}$$

Least common multiple of $168$ and $5$ is $840$. Convert $-\frac{103}{168}$ and $\frac{2}{5}$ to fractions with denominator $840$.

$$-\frac{515}{840}-\frac{336}{840}-\frac{8}{-15}$$

Since $-\frac{515}{840}$ and $\frac{336}{840}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-515-336}{840}-\frac{8}{-15}$$

Subtract $336$ from $-515$ to get $-851$.

$$-\frac{851}{840}-\frac{8}{-15}$$

Fraction $\frac{8}{-15}$ can be rewritten as $-\frac{8}{15}$ by extracting the negative sign.

$$-\frac{851}{840}-\left(-\frac{8}{15}\right)$$

The opposite of $-\frac{8}{15}$ is $\frac{8}{15}$.

$$-\frac{851}{840}+\frac{8}{15}$$

Least common multiple of $840$ and $15$ is $840$. Convert $-\frac{851}{840}$ and $\frac{8}{15}$ to fractions with denominator $840$.

$$-\frac{851}{840}+\frac{448}{840}$$

Since $-\frac{851}{840}$ and $\frac{448}{840}$ have the same denominator, add them by adding their numerators.

$$\frac{-851+448}{840}$$

Add $-851$ and $448$ to get $-403$.

$$-\frac{403}{840}$$

Factor

$-\frac{403}{840} = -0.4797619047619048$