Solve Date - 2 5 *( 3 10 + 1 15 )=( -2 5 * 3 10 )+( -2 5 * 1 15 | 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

$$- \frac { 2 } { 5 } \times ( \frac { 3 } { 10 } + 1 ) = ( - \frac { 2 } { 5 } \times \frac { 3 } { 10 } ) + ( - \frac { 2 } { 5 } \times \frac { 1 } { 15 }$$

Verify

$\text{false}$

Solution Steps

Convert $1$ to fraction $\frac{10}{10}$.

$$-\frac{2}{5}\left(\frac{3}{10}+\frac{10}{10}\right)=-\frac{2}{5}\times \frac{3}{10}-\frac{2}{5}\times \frac{1}{15}$$

Since $\frac{3}{10}$ and $\frac{10}{10}$ have the same denominator, add them by adding their numerators.

$$-\frac{2}{5}\times \frac{3+10}{10}=-\frac{2}{5}\times \frac{3}{10}-\frac{2}{5}\times \frac{1}{15}$$

Add $3$ and $10$ to get $13$.

$$-\frac{2}{5}\times \frac{13}{10}=-\frac{2}{5}\times \frac{3}{10}-\frac{2}{5}\times \frac{1}{15}$$

Multiply $-\frac{2}{5}$ times $\frac{13}{10}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\times 13}{5\times 10}=-\frac{2}{5}\times \frac{3}{10}-\frac{2}{5}\times \frac{1}{15}$$

Do the multiplications in the fraction $\frac{-2\times 13}{5\times 10}$.

$$\frac{-26}{50}=-\frac{2}{5}\times \frac{3}{10}-\frac{2}{5}\times \frac{1}{15}$$

Reduce the fraction $\frac{-26}{50}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{13}{25}=-\frac{2}{5}\times \frac{3}{10}-\frac{2}{5}\times \frac{1}{15}$$

Multiply $-\frac{2}{5}$ times $\frac{3}{10}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{13}{25}=\frac{-2\times 3}{5\times 10}-\frac{2}{5}\times \frac{1}{15}$$

Do the multiplications in the fraction $\frac{-2\times 3}{5\times 10}$.

$$-\frac{13}{25}=\frac{-6}{50}-\frac{2}{5}\times \frac{1}{15}$$

Reduce the fraction $\frac{-6}{50}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{13}{25}=-\frac{3}{25}-\frac{2}{5}\times \frac{1}{15}$$

Multiply $-\frac{2}{5}$ times $\frac{1}{15}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{13}{25}=-\frac{3}{25}+\frac{-2}{5\times 15}$$

Do the multiplications in the fraction $\frac{-2}{5\times 15}$.

$$-\frac{13}{25}=-\frac{3}{25}+\frac{-2}{75}$$

Fraction $\frac{-2}{75}$ can be rewritten as $-\frac{2}{75}$ by extracting the negative sign.

$$-\frac{13}{25}=-\frac{3}{25}-\frac{2}{75}$$

Least common multiple of $25$ and $75$ is $75$. Convert $-\frac{3}{25}$ and $\frac{2}{75}$ to fractions with denominator $75$.

$$-\frac{13}{25}=-\frac{9}{75}-\frac{2}{75}$$

Since $-\frac{9}{75}$ and $\frac{2}{75}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{25}=\frac{-9-2}{75}$$

Subtract $2$ from $-9$ to get $-11$.

$$-\frac{13}{25}=-\frac{11}{75}$$

Least common multiple of $25$ and $75$ is $75$. Convert $-\frac{13}{25}$ and $-\frac{11}{75}$ to fractions with denominator $75$.

$$-\frac{39}{75}=-\frac{11}{75}$$

Compare $-\frac{39}{75}$ and $-\frac{11}{75}$.

$$\text{false}$$