Solve -(7)/(3)+(1)/(2)-5+(-(3)/(2)+4\times(-7+(1)/(4)\times(-3+(1)/(3)) | 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

$$- \frac{ 7 }{ 3 } + \frac{ 1 }{ 2 } -5+(- \frac{ 3 }{ 2 } +4 \times (-7+ \frac{ 1 }{ 4 } \times (-3+ \frac{ 1 }{ 3 } )$$

Evaluate

$-39$

Solution Steps

Least common multiple of $3$ and $2$ is $6$. Convert $-\frac{7}{3}$ and $\frac{1}{2}$ to fractions with denominator $6$.

$$-\frac{14}{6}+\frac{3}{6}-5-\frac{3}{2}+4\left(-7+\frac{1}{4}\left(-3+\frac{1}{3}\right)\right)$$

Since $-\frac{14}{6}$ and $\frac{3}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{-14+3}{6}-5-\frac{3}{2}+4\left(-7+\frac{1}{4}\left(-3+\frac{1}{3}\right)\right)$$

Add $-14$ and $3$ to get $-11$.

$$-\frac{11}{6}-5-\frac{3}{2}+4\left(-7+\frac{1}{4}\left(-3+\frac{1}{3}\right)\right)$$

Convert $5$ to fraction $\frac{30}{6}$.

$$-\frac{11}{6}-\frac{30}{6}-\frac{3}{2}+4\left(-7+\frac{1}{4}\left(-3+\frac{1}{3}\right)\right)$$

Since $-\frac{11}{6}$ and $\frac{30}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-11-30}{6}-\frac{3}{2}+4\left(-7+\frac{1}{4}\left(-3+\frac{1}{3}\right)\right)$$

Subtract $30$ from $-11$ to get $-41$.

$$-\frac{41}{6}-\frac{3}{2}+4\left(-7+\frac{1}{4}\left(-3+\frac{1}{3}\right)\right)$$

Least common multiple of $6$ and $2$ is $6$. Convert $-\frac{41}{6}$ and $\frac{3}{2}$ to fractions with denominator $6$.

$$-\frac{41}{6}-\frac{9}{6}+4\left(-7+\frac{1}{4}\left(-3+\frac{1}{3}\right)\right)$$

Since $-\frac{41}{6}$ and $\frac{9}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-41-9}{6}+4\left(-7+\frac{1}{4}\left(-3+\frac{1}{3}\right)\right)$$

Subtract $9$ from $-41$ to get $-50$.

$$\frac{-50}{6}+4\left(-7+\frac{1}{4}\left(-3+\frac{1}{3}\right)\right)$$

Reduce the fraction $\frac{-50}{6}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{25}{3}+4\left(-7+\frac{1}{4}\left(-3+\frac{1}{3}\right)\right)$$

Convert $-3$ to fraction $-\frac{9}{3}$.

$$-\frac{25}{3}+4\left(-7+\frac{1}{4}\left(-\frac{9}{3}+\frac{1}{3}\right)\right)$$

Since $-\frac{9}{3}$ and $\frac{1}{3}$ have the same denominator, add them by adding their numerators.

$$-\frac{25}{3}+4\left(-7+\frac{1}{4}\times \frac{-9+1}{3}\right)$$

Add $-9$ and $1$ to get $-8$.

$$-\frac{25}{3}+4\left(-7+\frac{1}{4}\left(-\frac{8}{3}\right)\right)$$

Multiply $\frac{1}{4}$ times $-\frac{8}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{25}{3}+4\left(-7+\frac{1\left(-8\right)}{4\times 3}\right)$$

Do the multiplications in the fraction $\frac{1\left(-8\right)}{4\times 3}$.

$$-\frac{25}{3}+4\left(-7+\frac{-8}{12}\right)$$

Reduce the fraction $\frac{-8}{12}$ to lowest terms by extracting and canceling out $4$.

$$-\frac{25}{3}+4\left(-7-\frac{2}{3}\right)$$

Convert $-7$ to fraction $-\frac{21}{3}$.

$$-\frac{25}{3}+4\left(-\frac{21}{3}-\frac{2}{3}\right)$$

Since $-\frac{21}{3}$ and $\frac{2}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{25}{3}+4\times \frac{-21-2}{3}$$

Subtract $2$ from $-21$ to get $-23$.

$$-\frac{25}{3}+4\left(-\frac{23}{3}\right)$$

Express $4\left(-\frac{23}{3}\right)$ as a single fraction.

$$-\frac{25}{3}+\frac{4\left(-23\right)}{3}$$

Multiply $4$ and $-23$ to get $-92$.

$$-\frac{25}{3}+\frac{-92}{3}$$

Fraction $\frac{-92}{3}$ can be rewritten as $-\frac{92}{3}$ by extracting the negative sign.

$$-\frac{25}{3}-\frac{92}{3}$$

Since $-\frac{25}{3}$ and $\frac{92}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-25-92}{3}$$

Subtract $92$ from $-25$ to get $-117$.

$$\frac{-117}{3}$$

Divide $-117$ by $3$ to get $-39$.

$$-39$$

Factor

$-39$