Solve (9)/(3)+(4)/(5)+(4)/(3)\times(3)/(9)+(4)/(5)+(5)/(7) | 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

$$\frac{ 9 }{ 3 } + \frac{ 4 }{ 5 } + \frac{ 4 }{ 3 } \times \frac{ 3 }{ 9 } + \frac{ 4 }{ 5 } + \frac{ 5 }{ 7 }$$

Evaluate

$\frac{1814}{315}\approx 5.758730159$

Solution Steps

Divide $9$ by $3$ to get $3$.

$$3+\frac{4}{5}+\frac{4}{3}\times \frac{3}{9}+\frac{4}{5}+\frac{5}{7}$$

Convert $3$ to fraction $\frac{15}{5}$.

$$\frac{15}{5}+\frac{4}{5}+\frac{4}{3}\times \frac{3}{9}+\frac{4}{5}+\frac{5}{7}$$

Since $\frac{15}{5}$ and $\frac{4}{5}$ have the same denominator, add them by adding their numerators.

$$\frac{15+4}{5}+\frac{4}{3}\times \frac{3}{9}+\frac{4}{5}+\frac{5}{7}$$

Add $15$ and $4$ to get $19$.

$$\frac{19}{5}+\frac{4}{3}\times \frac{3}{9}+\frac{4}{5}+\frac{5}{7}$$

Reduce the fraction $\frac{3}{9}$ to lowest terms by extracting and canceling out $3$.

$$\frac{19}{5}+\frac{4}{3}\times \frac{1}{3}+\frac{4}{5}+\frac{5}{7}$$

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

$$\frac{19}{5}+\frac{4\times 1}{3\times 3}+\frac{4}{5}+\frac{5}{7}$$

Do the multiplications in the fraction $\frac{4\times 1}{3\times 3}$.

$$\frac{19}{5}+\frac{4}{9}+\frac{4}{5}+\frac{5}{7}$$

Least common multiple of $5$ and $9$ is $45$. Convert $\frac{19}{5}$ and $\frac{4}{9}$ to fractions with denominator $45$.

$$\frac{171}{45}+\frac{20}{45}+\frac{4}{5}+\frac{5}{7}$$

Since $\frac{171}{45}$ and $\frac{20}{45}$ have the same denominator, add them by adding their numerators.

$$\frac{171+20}{45}+\frac{4}{5}+\frac{5}{7}$$

Add $171$ and $20$ to get $191$.

$$\frac{191}{45}+\frac{4}{5}+\frac{5}{7}$$

Least common multiple of $45$ and $5$ is $45$. Convert $\frac{191}{45}$ and $\frac{4}{5}$ to fractions with denominator $45$.

$$\frac{191}{45}+\frac{36}{45}+\frac{5}{7}$$

Since $\frac{191}{45}$ and $\frac{36}{45}$ have the same denominator, add them by adding their numerators.

$$\frac{191+36}{45}+\frac{5}{7}$$

Add $191$ and $36$ to get $227$.

$$\frac{227}{45}+\frac{5}{7}$$

Least common multiple of $45$ and $7$ is $315$. Convert $\frac{227}{45}$ and $\frac{5}{7}$ to fractions with denominator $315$.

$$\frac{1589}{315}+\frac{225}{315}$$

Since $\frac{1589}{315}$ and $\frac{225}{315}$ have the same denominator, add them by adding their numerators.

$$\frac{1589+225}{315}$$

Add $1589$ and $225$ to get $1814$.

$$\frac{1814}{315}$$

Factor

$\frac{2 \cdot 907}{3 ^ {2} \cdot 5 \cdot 7} = 5\frac{239}{315} = 5.758730158730159$