Solve 3/7 - 4/9 - 11/7 + 7/9 | 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

$$\frac{3}{7}+\frac{-4}{9}+\frac{-11}{7}+\frac{7}{9}$$

Evaluate

$-\frac{17}{21}\approx -0.80952381$

Solution Steps

Fraction $\frac{-4}{9}$ can be rewritten as $-\frac{4}{9}$ by extracting the negative sign.

$$\frac{3}{7}-\frac{4}{9}+\frac{-11}{7}+\frac{7}{9}$$

Least common multiple of $7$ and $9$ is $63$. Convert $\frac{3}{7}$ and $\frac{4}{9}$ to fractions with denominator $63$.

$$\frac{27}{63}-\frac{28}{63}+\frac{-11}{7}+\frac{7}{9}$$

Since $\frac{27}{63}$ and $\frac{28}{63}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-28}{63}+\frac{-11}{7}+\frac{7}{9}$$

Subtract $28$ from $27$ to get $-1$.

$$-\frac{1}{63}+\frac{-11}{7}+\frac{7}{9}$$

Fraction $\frac{-11}{7}$ can be rewritten as $-\frac{11}{7}$ by extracting the negative sign.

$$-\frac{1}{63}-\frac{11}{7}+\frac{7}{9}$$

Least common multiple of $63$ and $7$ is $63$. Convert $-\frac{1}{63}$ and $\frac{11}{7}$ to fractions with denominator $63$.

$$-\frac{1}{63}-\frac{99}{63}+\frac{7}{9}$$

Since $-\frac{1}{63}$ and $\frac{99}{63}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-99}{63}+\frac{7}{9}$$

Subtract $99$ from $-1$ to get $-100$.

$$-\frac{100}{63}+\frac{7}{9}$$

Least common multiple of $63$ and $9$ is $63$. Convert $-\frac{100}{63}$ and $\frac{7}{9}$ to fractions with denominator $63$.

$$-\frac{100}{63}+\frac{49}{63}$$

Since $-\frac{100}{63}$ and $\frac{49}{63}$ have the same denominator, add them by adding their numerators.

$$\frac{-100+49}{63}$$

Add $-100$ and $49$ to get $-51$.

$$\frac{-51}{63}$$

Reduce the fraction $\frac{-51}{63}$ to lowest terms by extracting and canceling out $3$.

$$-\frac{17}{21}$$

Factor

$-\frac{17}{21} = -0.8095238095238095$