Solve (1 1/4 + 4/5) * of(1 1/4 - 4/5) / (5/6 + 1 1/5) * of(1 1/5 - 5/6) 111 111 11 | 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

$$( 1 \frac { 1 } { 4 } + \frac { 4 } { 5 } ) ( 1 \frac { 1 } { 4 } - \frac { 4 } { 5 } ) \div ( \frac { 5 } { 6 } + 1 \frac { 1 } { 5 } ) ( 1 \frac { 1 } { 5 } - \frac { 5 } { 6 } )$$

Evaluate

$\frac{4059}{24400}\approx 0.166352459$

Solution Steps

Multiply $1$ and $4$ to get $4$.

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

Add $4$ and $1$ to get $5$.

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

Least common multiple of $4$ and $5$ is $20$. Convert $\frac{5}{4}$ and $\frac{4}{5}$ to fractions with denominator $20$.

$$\frac{\left(\frac{25}{20}+\frac{16}{20}\right)\left(\frac{1\times 4+1}{4}-\frac{4}{5}\right)}{\frac{5}{6}+\frac{1\times 5+1}{5}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Since $\frac{25}{20}$ and $\frac{16}{20}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{25+16}{20}\left(\frac{1\times 4+1}{4}-\frac{4}{5}\right)}{\frac{5}{6}+\frac{1\times 5+1}{5}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Add $25$ and $16$ to get $41$.

$$\frac{\frac{41}{20}\left(\frac{1\times 4+1}{4}-\frac{4}{5}\right)}{\frac{5}{6}+\frac{1\times 5+1}{5}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Multiply $1$ and $4$ to get $4$.

$$\frac{\frac{41}{20}\left(\frac{4+1}{4}-\frac{4}{5}\right)}{\frac{5}{6}+\frac{1\times 5+1}{5}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Add $4$ and $1$ to get $5$.

$$\frac{\frac{41}{20}\left(\frac{5}{4}-\frac{4}{5}\right)}{\frac{5}{6}+\frac{1\times 5+1}{5}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Least common multiple of $4$ and $5$ is $20$. Convert $\frac{5}{4}$ and $\frac{4}{5}$ to fractions with denominator $20$.

$$\frac{\frac{41}{20}\left(\frac{25}{20}-\frac{16}{20}\right)}{\frac{5}{6}+\frac{1\times 5+1}{5}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Since $\frac{25}{20}$ and $\frac{16}{20}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{41}{20}\times \frac{25-16}{20}}{\frac{5}{6}+\frac{1\times 5+1}{5}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Subtract $16$ from $25$ to get $9$.

$$\frac{\frac{41}{20}\times \frac{9}{20}}{\frac{5}{6}+\frac{1\times 5+1}{5}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Multiply $\frac{41}{20}$ times $\frac{9}{20}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{41\times 9}{20\times 20}}{\frac{5}{6}+\frac{1\times 5+1}{5}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Do the multiplications in the fraction $\frac{41\times 9}{20\times 20}$.

$$\frac{\frac{369}{400}}{\frac{5}{6}+\frac{1\times 5+1}{5}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Multiply $1$ and $5$ to get $5$.

$$\frac{\frac{369}{400}}{\frac{5}{6}+\frac{5+1}{5}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Add $5$ and $1$ to get $6$.

$$\frac{\frac{369}{400}}{\frac{5}{6}+\frac{6}{5}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Least common multiple of $6$ and $5$ is $30$. Convert $\frac{5}{6}$ and $\frac{6}{5}$ to fractions with denominator $30$.

$$\frac{\frac{369}{400}}{\frac{25}{30}+\frac{36}{30}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Since $\frac{25}{30}$ and $\frac{36}{30}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{369}{400}}{\frac{25+36}{30}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Add $25$ and $36$ to get $61$.

$$\frac{\frac{369}{400}}{\frac{61}{30}}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Divide $\frac{369}{400}$ by $\frac{61}{30}$ by multiplying $\frac{369}{400}$ by the reciprocal of $\frac{61}{30}$.

$$\frac{369}{400}\times \frac{30}{61}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Multiply $\frac{369}{400}$ times $\frac{30}{61}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{369\times 30}{400\times 61}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Do the multiplications in the fraction $\frac{369\times 30}{400\times 61}$.

$$\frac{11070}{24400}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Reduce the fraction $\frac{11070}{24400}$ to lowest terms by extracting and canceling out $10$.

$$\frac{1107}{2440}\left(\frac{1\times 5+1}{5}-\frac{5}{6}\right)$$

Multiply $1$ and $5$ to get $5$.

$$\frac{1107}{2440}\left(\frac{5+1}{5}-\frac{5}{6}\right)$$

Add $5$ and $1$ to get $6$.

$$\frac{1107}{2440}\left(\frac{6}{5}-\frac{5}{6}\right)$$

Least common multiple of $5$ and $6$ is $30$. Convert $\frac{6}{5}$ and $\frac{5}{6}$ to fractions with denominator $30$.

$$\frac{1107}{2440}\left(\frac{36}{30}-\frac{25}{30}\right)$$

Since $\frac{36}{30}$ and $\frac{25}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1107}{2440}\times \frac{36-25}{30}$$

Subtract $25$ from $36$ to get $11$.

$$\frac{1107}{2440}\times \frac{11}{30}$$

Multiply $\frac{1107}{2440}$ times $\frac{11}{30}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{1107\times 11}{2440\times 30}$$

Do the multiplications in the fraction $\frac{1107\times 11}{2440\times 30}$.

$$\frac{12177}{73200}$$

Reduce the fraction $\frac{12177}{73200}$ to lowest terms by extracting and canceling out $3$.

$$\frac{4059}{24400}$$

Factor

$\frac{3 ^ {2} \cdot 11 \cdot 41}{2 ^ {4} \cdot 5 ^ {2} \cdot 61} = 0.16635245901639345$