Solve (1)/(2)\div((1)/(3)\div(2)/(5))=((1)/(2)\div-(1)/(3))\div2\div5

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$\frac{ 1 }{ 2 } \div ( \frac{ 1 }{ 3 } \div \frac{ 2 }{ 5 } )=( \frac{ 1 }{ 2 } \div - \frac{ 1 }{ 3 } ) \div 2 \div 5$$

Verify

$\text{false}$

Solution Steps

Multiply both sides of the equation by $5$.

$$6\times \frac{1}{2}=\frac{\frac{\frac{1}{2}}{-\frac{1}{3}}}{2}$$

Multiply $6$ and $\frac{1}{2}$ to get $\frac{6}{2}$.

$$\frac{6}{2}=\frac{\frac{\frac{1}{2}}{-\frac{1}{3}}}{2}$$

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

$$3=\frac{\frac{\frac{1}{2}}{-\frac{1}{3}}}{2}$$

Express $\frac{\frac{\frac{1}{2}}{-\frac{1}{3}}}{2}$ as a single fraction.

$$3=\frac{\frac{1}{2}}{-\frac{1}{3}\times 2}$$

Express $-\frac{1}{3}\times 2$ as a single fraction.

$$3=\frac{\frac{1}{2}}{\frac{-2}{3}}$$

Fraction $\frac{-2}{3}$ can be rewritten as $-\frac{2}{3}$ by extracting the negative sign.

$$3=\frac{\frac{1}{2}}{-\frac{2}{3}}$$

Divide $\frac{1}{2}$ by $-\frac{2}{3}$ by multiplying $\frac{1}{2}$ by the reciprocal of $-\frac{2}{3}$.

$$3=\frac{1}{2}\left(-\frac{3}{2}\right)$$

Multiply $\frac{1}{2}$ times $-\frac{3}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$3=\frac{1\left(-3\right)}{2\times 2}$$

Do the multiplications in the fraction $\frac{1\left(-3\right)}{2\times 2}$.

$$3=\frac{-3}{4}$$

Fraction $\frac{-3}{4}$ can be rewritten as $-\frac{3}{4}$ by extracting the negative sign.

$$3=-\frac{3}{4}$$

Convert $3$ to fraction $\frac{12}{4}$.

$$\frac{12}{4}=-\frac{3}{4}$$

Compare $\frac{12}{4}$ and $-\frac{3}{4}$.

$$\text{false}$$

Show Solution