Solve (1)/(3)+((2)/(5)+((7)/(6)-(3)/(5)))-((7)/(8)-(3)/(4)) | 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

$$\frac{ 1 }{ 3 } +( \frac{ 2 }{ 5 } +( \frac{ 7 }{ 6 } - \frac{ 3 }{ 5 } ))-( \frac{ 7 }{ 8 } - \frac{ 3 }{ 4 } )$$

Evaluate

$\frac{47}{40}=1.175$

Solution Steps

Least common multiple of $3$ and $5$ is $15$. Convert $\frac{1}{3}$ and $\frac{2}{5}$ to fractions with denominator $15$.

$$\frac{5}{15}+\frac{6}{15}+\frac{7}{6}-\frac{3}{5}-\left(\frac{7}{8}-\frac{3}{4}\right)$$

Since $\frac{5}{15}$ and $\frac{6}{15}$ have the same denominator, add them by adding their numerators.

$$\frac{5+6}{15}+\frac{7}{6}-\frac{3}{5}-\left(\frac{7}{8}-\frac{3}{4}\right)$$

Add $5$ and $6$ to get $11$.

$$\frac{11}{15}+\frac{7}{6}-\frac{3}{5}-\left(\frac{7}{8}-\frac{3}{4}\right)$$

Least common multiple of $15$ and $6$ is $30$. Convert $\frac{11}{15}$ and $\frac{7}{6}$ to fractions with denominator $30$.

$$\frac{22}{30}+\frac{35}{30}-\frac{3}{5}-\left(\frac{7}{8}-\frac{3}{4}\right)$$

Since $\frac{22}{30}$ and $\frac{35}{30}$ have the same denominator, add them by adding their numerators.

$$\frac{22+35}{30}-\frac{3}{5}-\left(\frac{7}{8}-\frac{3}{4}\right)$$

Add $22$ and $35$ to get $57$.

$$\frac{57}{30}-\frac{3}{5}-\left(\frac{7}{8}-\frac{3}{4}\right)$$

Reduce the fraction $\frac{57}{30}$ to lowest terms by extracting and canceling out $3$.

$$\frac{19}{10}-\frac{3}{5}-\left(\frac{7}{8}-\frac{3}{4}\right)$$

Least common multiple of $10$ and $5$ is $10$. Convert $\frac{19}{10}$ and $\frac{3}{5}$ to fractions with denominator $10$.

$$\frac{19}{10}-\frac{6}{10}-\left(\frac{7}{8}-\frac{3}{4}\right)$$

Since $\frac{19}{10}$ and $\frac{6}{10}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{19-6}{10}-\left(\frac{7}{8}-\frac{3}{4}\right)$$

Subtract $6$ from $19$ to get $13$.

$$\frac{13}{10}-\left(\frac{7}{8}-\frac{3}{4}\right)$$

Least common multiple of $8$ and $4$ is $8$. Convert $\frac{7}{8}$ and $\frac{3}{4}$ to fractions with denominator $8$.

$$\frac{13}{10}-\left(\frac{7}{8}-\frac{6}{8}\right)$$

Since $\frac{7}{8}$ and $\frac{6}{8}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{10}-\frac{7-6}{8}$$

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

$$\frac{13}{10}-\frac{1}{8}$$

Least common multiple of $10$ and $8$ is $40$. Convert $\frac{13}{10}$ and $\frac{1}{8}$ to fractions with denominator $40$.

$$\frac{52}{40}-\frac{5}{40}$$

Since $\frac{52}{40}$ and $\frac{5}{40}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{52-5}{40}$$

Subtract $5$ from $52$ to get $47$.

$$\frac{47}{40}$$

Factor

$\frac{47}{2 ^ {3} \cdot 5} = 1\frac{7}{40} = 1.175$