Divide and simplify: \(\frac{2x}{3} \div \frac{5x}{6}\)
Understand the Problem
The question asks to divide and simplify the expression (\frac{2x}{3} \div \frac{5x}{6}). We will solve this by multiplying by the reciprocal.
Answer
$\frac{4}{5}$
Answer for screen readers
$\frac{4}{5}$
Steps to Solve
-
Rewrite the division as multiplication by the reciprocal To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{5x}{6}$ is $\frac{6}{5x}$. $$ \frac{2x}{3} \div \frac{5x}{6} = \frac{2x}{3} \cdot \frac{6}{5x} $$
-
Multiply the fractions Multiply the numerators and denominators. $$ \frac{2x}{3} \cdot \frac{6}{5x} = \frac{2x \cdot 6}{3 \cdot 5x} = \frac{12x}{15x} $$
-
Simplify the fraction Simplify the fraction by canceling the common factor of $x$ in the numerator and denominator. $$ \frac{12x}{15x} = \frac{12}{15} $$
-
Reduce the fraction to lowest terms Both 12 and 15 are divisible by 3. $$ \frac{12}{15} = \frac{12 \div 3}{15 \div 3} = \frac{4}{5} $$
$\frac{4}{5}$
More Information
The result of dividing $\frac{2x}{3}$ by $\frac{5x}{6}$ is $\frac{4}{5}$. This is a constant value independent of $x$ (as long as $x \ne 0$).
Tips
A common mistake is forgetting to take the reciprocal of the second fraction before multiplying. Another mistake is not simplifying the fraction to its lowest terms at the end.
AI-generated content may contain errors. Please verify critical information
