IMO Practice Test — Operations with Fractions (Unlike Denominators)
6 Questions • 25 min • Olympiad level
25:00
Question 1 of 6
hard
Find the missing number: ⅔ + __ = 1¼
⅓
⁷⁄₁₂
⁵⁄₁₂
½
Explanation: 1¼=5/4, subtract 2/3: 5/4-2/3=15/12-8/12=7/12
Question 2 of 6
hard
Which is larger: ½ × ¾ or ½ ÷ ¾?
Same
First is larger
Second is larger
Cannot tell
Explanation: ½×¾=3/8=0.375, ½÷¾=½×4/3=4/6=0.666, 2nd larger
Question 3 of 6
hard
Simplify: (⅔ + ½) ÷ (¾ - ⅓)
¹⁴⁄₅
¹¹⁄₅
²²⁄₁₅
¹⁰⁄₉
Explanation: Top: 4/6+3/6=7/6. Bottom: 9/12-4/12=5/12. (7/6)÷(5/12)=7/6×12/5=84/30=14/5
Question 4 of 6
hard
A recipe needs 1½ cups flour. You have ⅔ cup. How much more?
⅚
⁵⁄₆
¾
⅔
Explanation: 1½=3/2, 3/2-2/3=9/6-4/6=5/6
Question 5 of 6
hard
What is half of ¾?
⅜
³⁄₈
⅓
¼
Explanation: ½×¾=3/8
Question 6 of 6
hard
If ⅘ of a number is 12, what is the number?
15
20
9.6
15
Explanation: Let x = number. 4/5×x=12, x=12×5/4=60/4=15