Solve - 12/5 - 7/20 + 3/14 + 1/7 - 1/10 | 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

$$\frac{-12}{5}-\frac{7}{20}+\frac{3}{14}+\frac{1}{7}-\frac{1}{10}$$

Evaluate

$-\frac{349}{140}\approx -2.492857143$

Solution Steps

Fraction $\frac{-12}{5}$ can be rewritten as $-\frac{12}{5}$ by extracting the negative sign.

$$-\frac{12}{5}-\frac{7}{20}+\frac{3}{14}+\frac{1}{7}-\frac{1}{10}$$

Least common multiple of $5$ and $20$ is $20$. Convert $-\frac{12}{5}$ and $\frac{7}{20}$ to fractions with denominator $20$.

$$-\frac{48}{20}-\frac{7}{20}+\frac{3}{14}+\frac{1}{7}-\frac{1}{10}$$

Since $-\frac{48}{20}$ and $\frac{7}{20}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-48-7}{20}+\frac{3}{14}+\frac{1}{7}-\frac{1}{10}$$

Subtract $7$ from $-48$ to get $-55$.

$$\frac{-55}{20}+\frac{3}{14}+\frac{1}{7}-\frac{1}{10}$$

Reduce the fraction $\frac{-55}{20}$ to lowest terms by extracting and canceling out $5$.

$$-\frac{11}{4}+\frac{3}{14}+\frac{1}{7}-\frac{1}{10}$$

Least common multiple of $4$ and $14$ is $28$. Convert $-\frac{11}{4}$ and $\frac{3}{14}$ to fractions with denominator $28$.

$$-\frac{77}{28}+\frac{6}{28}+\frac{1}{7}-\frac{1}{10}$$

Since $-\frac{77}{28}$ and $\frac{6}{28}$ have the same denominator, add them by adding their numerators.

$$\frac{-77+6}{28}+\frac{1}{7}-\frac{1}{10}$$

Add $-77$ and $6$ to get $-71$.

$$-\frac{71}{28}+\frac{1}{7}-\frac{1}{10}$$

Least common multiple of $28$ and $7$ is $28$. Convert $-\frac{71}{28}$ and $\frac{1}{7}$ to fractions with denominator $28$.

$$-\frac{71}{28}+\frac{4}{28}-\frac{1}{10}$$

Since $-\frac{71}{28}$ and $\frac{4}{28}$ have the same denominator, add them by adding their numerators.

$$\frac{-71+4}{28}-\frac{1}{10}$$

Add $-71$ and $4$ to get $-67$.

$$-\frac{67}{28}-\frac{1}{10}$$

Least common multiple of $28$ and $10$ is $140$. Convert $-\frac{67}{28}$ and $\frac{1}{10}$ to fractions with denominator $140$.

$$-\frac{335}{140}-\frac{14}{140}$$

Since $-\frac{335}{140}$ and $\frac{14}{140}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-335-14}{140}$$

Subtract $14$ from $-335$ to get $-349$.

$$-\frac{349}{140}$$

Factor

$-\frac{349}{140} = -2\frac{69}{140} = -2.492857142857143$