Problem 12 · 1989 AJHSME
Hard
Fractions, Decimals & Percents
simplify-complex-fraction
1 − 131 − 12=
Show answer
Answer: E — 4⁄3.
Show hints
Hint 1 of 3
A big fraction is really just 'top ÷ bottom.' Collapse the top into one fraction and the bottom into one fraction before you do anything else.
Still stuck? Show hint 2 →
Hint 2 of 3
1 − 1⁄3 means 'a whole minus one of its thirds' — picture three thirds, take one away. Same idea for 1 − 1⁄2.
Still stuck? Show hint 3 →
Hint 3 of 3
To divide by a fraction, flip it and multiply: ÷(1⁄2) becomes ×2.
Show solution
Approach: simplify top and bottom, then flip-and-multiply
- Treat the bar as a division sign and clean each half first. Top: 1 − 1⁄3 = 2⁄3 (three thirds minus one third). Bottom: 1 − 1⁄2 = 1⁄2 (two halves minus one half).
- Now (2⁄3) ÷ (1⁄2). Dividing by 1⁄2 asks 'how many halves fit in 2⁄3?' — and there are twice as many, so flip and multiply: (2⁄3) × 2 = 4⁄3.
- Why this transfers: never wrestle a stacked fraction all at once — reduce the top to a single fraction, the bottom to a single fraction, then it's one clean division. Sanity check: the answer is more than 1, which makes sense since the top 2⁄3 is bigger than the bottom 1⁄2.
Mark:
· log in to save