Problem 3 · 1998 AJHSME
Easy
Fractions, Decimals & Percents
fraction-arithmetic
38 + 7845=
Show answer
Answer: B — 25/16.
Show hints
Hint 1 of 2
A big fraction-over-a-fraction is just a division: (top) ÷ (bottom). Notice the two pieces on top already share the same denominator, so adding them is a freebie.
Still stuck? Show hint 2 →
Hint 2 of 2
Dividing by a fraction means flipping it and multiplying. Watch for the same fraction showing up twice.
Show solution
Approach: the bar means divide; flipping turns it into a square
- The top adds easily because the bottoms match: 3/8 + 7/8 = 10/8 = 5/4.
- The big bar means divide by 4/5, and dividing by a fraction means flip-and-multiply: (5/4) ÷ (4/5) = (5/4) × (5/4).
- That's the same fraction times itself: (5/4)² = 25/16.
- Why this transfers: a fraction stacked over a fraction is always a division in disguise — rewrite it as ÷, then flip the bottom. And a sanity check: 5/4 is a bit over 1, so its square should be a bit over 1; 25/16 ≈ 1.56 fits.
Mark:
· log in to save