Answer:
25/39
Step-by-step explanation:
1 [tex]\frac{2}{3}[/tex] = [tex]\frac{5}{3}[/tex] (Multiply the denominator (3) by the whole number (1). Then add the numerator (2) to get the new numerator and convert to improper form).
3 × 1 + 2 = 5
2 [tex]\frac{3}{5}[/tex] = [tex]\frac{13}{5}[/tex] (Multiply the denominator (5) by the whole number (2). Then add the numerator (3) to get it the new numerator and convert to improper form).
5 × 2 + 3 = 13
Now we can more easily divide [tex]\frac{5}{3}[/tex] ÷ [tex]\frac{13}{5}[/tex].
To divide by [tex]\frac{13}{5}[/tex], we can multiply by it's reciprocal: [tex]\frac{5}{13}[/tex] (switch the numerator and denominator).
[tex]\frac{5}{3}[/tex] × [tex]\frac{5}{13}[/tex] = [tex]\frac{5*5}{3*13}[/tex] = [tex]\frac{25}{39}[/tex]. There are no common factors between 25 and 39 besides 1. So it's already simplified.
