Question

what is the next fraction in this sequence? simplify your answer.
\frac{4}{5}, \frac{7}{10}, \frac{3}{5}, \frac{1}{2}, ...

Explanation:

Step1: Convert to common denominator

Convert all fractions to tenths: $\frac{4}{5}=\frac{8}{10}$, $\frac{3}{5}=\frac{6}{10}$, $\frac{1}{2}=\frac{5}{10}$. Now the sequence is $\frac{8}{10}, \frac{7}{10}, \frac{6}{10}, \frac{5}{10},...$

Step2: Identify the pattern

The numerator decreases by 1 each time. So next numerator: $5 - 1 = 4$. The denominator remains 10. So the fraction is $\frac{4}{10}$.

Step3: Simplify the fraction

Simplify $\frac{4}{10}$ by dividing numerator and denominator by 2: $\frac{4\div2}{10\div2}=\frac{2}{5}$.

Answer:

$\frac{2}{5}$