Solve Simplify (1- 2 3 )/[( 2 3 +( 2 3 +( 2 3 - 1 4 )+ 1 2 ]+ 1 2 ] | 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

$$( 1 - \frac { 2 } { 3 } ) \div [ ( \frac { 2 } { 3 } + ( \frac { 2 } { 3 } + ( \frac { 2 } { 3 } + \frac { 1 } { 4 } ) + \frac { 1 } { 2 } y + \frac { 1 } { 2 } ]$$

Evaluate

$\frac{4}{3\left(2y+11\right)}$

Solution Steps

Convert $1$ to fraction $\frac{3}{3}$.

$$\frac{\frac{3}{3}-\frac{2}{3}}{\frac{2}{3}+\frac{2}{3}+\frac{2}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Since $\frac{3}{3}$ and $\frac{2}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-2}{3}}{\frac{2}{3}+\frac{2}{3}+\frac{2}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Subtract $2$ from $3$ to get $1$.

$$\frac{\frac{1}{3}}{\frac{2}{3}+\frac{2}{3}+\frac{2}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Since $\frac{2}{3}$ and $\frac{2}{3}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{2+2}{3}+\frac{2}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Add $2$ and $2$ to get $4$.

$$\frac{\frac{1}{3}}{\frac{4}{3}+\frac{2}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Since $\frac{4}{3}$ and $\frac{2}{3}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{4+2}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Add $4$ and $2$ to get $6$.

$$\frac{\frac{1}{3}}{\frac{6}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Divide $6$ by $3$ to get $2$.

$$\frac{\frac{1}{3}}{2+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Convert $2$ to fraction $\frac{8}{4}$.

$$\frac{\frac{1}{3}}{\frac{8}{4}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Since $\frac{8}{4}$ and $\frac{1}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{8+1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Add $8$ and $1$ to get $9$.

$$\frac{\frac{1}{3}}{\frac{9}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Least common multiple of $4$ and $2$ is $4$. Convert $\frac{9}{4}$ and $\frac{1}{2}$ to fractions with denominator $4$.

$$\frac{\frac{1}{3}}{\frac{9}{4}+\frac{1}{2}y+\frac{2}{4}}$$

Since $\frac{9}{4}$ and $\frac{2}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{9+2}{4}+\frac{1}{2}y}$$

Add $9$ and $2$ to get $11$.

$$\frac{\frac{1}{3}}{\frac{11}{4}+\frac{1}{2}y}$$

Express $\frac{\frac{1}{3}}{\frac{11}{4}+\frac{1}{2}y}$ as a single fraction.

$$\frac{1}{3\left(\frac{11}{4}+\frac{1}{2}y\right)}$$

Use the distributive property to multiply $3$ by $\frac{11}{4}+\frac{1}{2}y$.

$$\frac{1}{3\times \frac{11}{4}+3\times \frac{1}{2}y}$$

Express $3\times \frac{11}{4}$ as a single fraction.

$$\frac{1}{\frac{3\times 11}{4}+3\times \frac{1}{2}y}$$

Multiply $3$ and $11$ to get $33$.

$$\frac{1}{\frac{33}{4}+3\times \frac{1}{2}y}$$

Multiply $3$ and $\frac{1}{2}$ to get $\frac{3}{2}$.

$$\frac{1}{\frac{33}{4}+\frac{3}{2}y}$$

Expand

$\frac{1}{3\left(\frac{y}{2}+\frac{11}{4}\right)}$

Solution Steps

Convert $1$ to fraction $\frac{3}{3}$.

$$\frac{\frac{3}{3}-\frac{2}{3}}{\frac{2}{3}+\frac{2}{3}+\frac{2}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Since $\frac{3}{3}$ and $\frac{2}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-2}{3}}{\frac{2}{3}+\frac{2}{3}+\frac{2}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Subtract $2$ from $3$ to get $1$.

$$\frac{\frac{1}{3}}{\frac{2}{3}+\frac{2}{3}+\frac{2}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Since $\frac{2}{3}$ and $\frac{2}{3}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{2+2}{3}+\frac{2}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Add $2$ and $2$ to get $4$.

$$\frac{\frac{1}{3}}{\frac{4}{3}+\frac{2}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Since $\frac{4}{3}$ and $\frac{2}{3}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{4+2}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Add $4$ and $2$ to get $6$.

$$\frac{\frac{1}{3}}{\frac{6}{3}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Divide $6$ by $3$ to get $2$.

$$\frac{\frac{1}{3}}{2+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Convert $2$ to fraction $\frac{8}{4}$.

$$\frac{\frac{1}{3}}{\frac{8}{4}+\frac{1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Since $\frac{8}{4}$ and $\frac{1}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{8+1}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Add $8$ and $1$ to get $9$.

$$\frac{\frac{1}{3}}{\frac{9}{4}+\frac{1}{2}y+\frac{1}{2}}$$

Least common multiple of $4$ and $2$ is $4$. Convert $\frac{9}{4}$ and $\frac{1}{2}$ to fractions with denominator $4$.

$$\frac{\frac{1}{3}}{\frac{9}{4}+\frac{1}{2}y+\frac{2}{4}}$$

Since $\frac{9}{4}$ and $\frac{2}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{9+2}{4}+\frac{1}{2}y}$$

Add $9$ and $2$ to get $11$.

$$\frac{\frac{1}{3}}{\frac{11}{4}+\frac{1}{2}y}$$

Express $\frac{\frac{1}{3}}{\frac{11}{4}+\frac{1}{2}y}$ as a single fraction.

$$\frac{1}{3\left(\frac{11}{4}+\frac{1}{2}y\right)}$$

Use the distributive property to multiply $3$ by $\frac{11}{4}+\frac{1}{2}y$.

$$\frac{1}{3\times \frac{11}{4}+3\times \frac{1}{2}y}$$

Express $3\times \frac{11}{4}$ as a single fraction.

$$\frac{1}{\frac{3\times 11}{4}+3\times \frac{1}{2}y}$$

Multiply $3$ and $11$ to get $33$.

$$\frac{1}{\frac{33}{4}+3\times \frac{1}{2}y}$$

Multiply $3$ and $\frac{1}{2}$ to get $\frac{3}{2}$.

$$\frac{1}{\frac{33}{4}+\frac{3}{2}y}$$