Solve [(1/2 - 5/4)(3 - 7/2) + (1/12 - 2/3) * 3/2] / (3/2) - 1/6 | 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

$$[(\frac{1}{2}-\frac{5}{4})\cdot(3-\frac{7}{2})+(\frac{1}{12}-\frac{2}{3})\cdot\frac{3}{2}]:\frac{3}{2}-\frac{1}{6}$$

Evaluate

$-\frac{1}{2}=-0.5$

Solution Steps

Least common multiple of $2$ and $4$ is $4$. Convert $\frac{1}{2}$ and $\frac{5}{4}$ to fractions with denominator $4$.

$$\frac{\left(\frac{2}{4}-\frac{5}{4}\right)\left(3-\frac{7}{2}\right)+\left(\frac{1}{12}-\frac{2}{3}\right)\times \frac{3}{2}}{\frac{3}{2}}-\frac{1}{6}$$

Since $\frac{2}{4}$ and $\frac{5}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2-5}{4}\left(3-\frac{7}{2}\right)+\left(\frac{1}{12}-\frac{2}{3}\right)\times \frac{3}{2}}{\frac{3}{2}}-\frac{1}{6}$$

Subtract $5$ from $2$ to get $-3$.

$$\frac{-\frac{3}{4}\left(3-\frac{7}{2}\right)+\left(\frac{1}{12}-\frac{2}{3}\right)\times \frac{3}{2}}{\frac{3}{2}}-\frac{1}{6}$$

Convert $3$ to fraction $\frac{6}{2}$.

$$\frac{-\frac{3}{4}\left(\frac{6}{2}-\frac{7}{2}\right)+\left(\frac{1}{12}-\frac{2}{3}\right)\times \frac{3}{2}}{\frac{3}{2}}-\frac{1}{6}$$

Since $\frac{6}{2}$ and $\frac{7}{2}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{3}{4}\times \frac{6-7}{2}+\left(\frac{1}{12}-\frac{2}{3}\right)\times \frac{3}{2}}{\frac{3}{2}}-\frac{1}{6}$$

Subtract $7$ from $6$ to get $-1$.

$$\frac{-\frac{3}{4}\left(-\frac{1}{2}\right)+\left(\frac{1}{12}-\frac{2}{3}\right)\times \frac{3}{2}}{\frac{3}{2}}-\frac{1}{6}$$

Multiply $-\frac{3}{4}$ times $-\frac{1}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-3\left(-1\right)}{4\times 2}+\left(\frac{1}{12}-\frac{2}{3}\right)\times \frac{3}{2}}{\frac{3}{2}}-\frac{1}{6}$$

Do the multiplications in the fraction $\frac{-3\left(-1\right)}{4\times 2}$.

$$\frac{\frac{3}{8}+\left(\frac{1}{12}-\frac{2}{3}\right)\times \frac{3}{2}}{\frac{3}{2}}-\frac{1}{6}$$

Least common multiple of $12$ and $3$ is $12$. Convert $\frac{1}{12}$ and $\frac{2}{3}$ to fractions with denominator $12$.

$$\frac{\frac{3}{8}+\left(\frac{1}{12}-\frac{8}{12}\right)\times \frac{3}{2}}{\frac{3}{2}}-\frac{1}{6}$$

Since $\frac{1}{12}$ and $\frac{8}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{8}+\frac{1-8}{12}\times \frac{3}{2}}{\frac{3}{2}}-\frac{1}{6}$$

Subtract $8$ from $1$ to get $-7$.

$$\frac{\frac{3}{8}-\frac{7}{12}\times \frac{3}{2}}{\frac{3}{2}}-\frac{1}{6}$$

Multiply $-\frac{7}{12}$ times $\frac{3}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3}{8}+\frac{-7\times 3}{12\times 2}}{\frac{3}{2}}-\frac{1}{6}$$

Do the multiplications in the fraction $\frac{-7\times 3}{12\times 2}$.

$$\frac{\frac{3}{8}+\frac{-21}{24}}{\frac{3}{2}}-\frac{1}{6}$$

Reduce the fraction $\frac{-21}{24}$ to lowest terms by extracting and canceling out $3$.

$$\frac{\frac{3}{8}-\frac{7}{8}}{\frac{3}{2}}-\frac{1}{6}$$

Since $\frac{3}{8}$ and $\frac{7}{8}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-7}{8}}{\frac{3}{2}}-\frac{1}{6}$$

Subtract $7$ from $3$ to get $-4$.

$$\frac{\frac{-4}{8}}{\frac{3}{2}}-\frac{1}{6}$$

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

$$\frac{-\frac{1}{2}}{\frac{3}{2}}-\frac{1}{6}$$

Divide $-\frac{1}{2}$ by $\frac{3}{2}$ by multiplying $-\frac{1}{2}$ by the reciprocal of $\frac{3}{2}$.

$$-\frac{1}{2}\times \frac{2}{3}-\frac{1}{6}$$

Multiply $-\frac{1}{2}$ times $\frac{2}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2}{2\times 3}-\frac{1}{6}$$

Cancel out $2$ in both numerator and denominator.

$$\frac{-1}{3}-\frac{1}{6}$$

Fraction $\frac{-1}{3}$ can be rewritten as $-\frac{1}{3}$ by extracting the negative sign.

$$-\frac{1}{3}-\frac{1}{6}$$

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

$$-\frac{2}{6}-\frac{1}{6}$$

Since $-\frac{2}{6}$ and $\frac{1}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2-1}{6}$$

Subtract $1$ from $-2$ to get $-3$.

$$\frac{-3}{6}$$

Reduce the fraction $\frac{-3}{6}$ to lowest terms by extracting and canceling out $3$.

$$-\frac{1}{2}$$

Factor

$-\frac{1}{2} = -0.5$