AMO Masterclass — Fractions & Problem Solving
Grade 6 · Australian Maths Olympiad
Completed 0 / 12
Practice Complete
0/12
Type 1
🔄 Work Backwards
Start from the final result and reverse each operation. The #1 AMO strategy!
1
Example · Work Backwards
Chocolate Bar 🍫
A chocolate bar is shared. First 14 is eaten. Then 13 of the remaining is eaten. 12 pieces are left. How many pieces were there at first?
We need to work backwards from the final answer. The final number is 12 pieces. Start here!
✏️ Write Your Solution
Write your solution here with your pen or finger ✍️
2
Example · Work Backwards
Money Spent 💰
Tom spent 1/3 of his money on a book, then 1/2 of the remainder on a pen. He has $12 left. How much did he start with?
Work backwards from $12. The last thing Tom did was spend 1/2 of his remaining money on a pen.
✏️ Write Your Solution
Write your solution here with your pen or finger ✍️
3
Advanced · Work Backwards
Triple Operation 🔥
A number is halved, then 6 is added, then the result is multiplied by 3 to give 30. What was the original number?
Work backwards from 30. The last operation was "multiply by 3". What's the reverse of multiplying by 3?
✏️ Write Your Solution
Write your solution here with your pen or finger ✍️
Type 2
📊 Sequential Remainder
Track what's LEFT after each step. Watch the trap: "1/3 of remaining" ≠ "1/3 of total"!
4
Example · Sequential Remainder
Pizza Party 🍕
At a party, 1/3 of a pizza is eaten first. Then 1/2 of the remaining pizza is eaten. What fraction of the original pizza is left?
Start with the whole pizza = 1. After 1/3 is eaten, what fraction is left?
✏️ Write Your Solution
Write your solution here with your pen or finger ✍️
5
Example · Sequential Remainder
Book Pages 📖
Anna reads 1/4 of a book on Monday, then 1/3 of the remaining pages on Tuesday. If 36 pages are left, how many pages does the book have?
After Monday: Anna read 1/4, so what fraction is left? → 1 − 1/4 = 3/4
✏️ Write Your Solution
Write your solution here with your pen or finger ✍️
6
Advanced · Sequential Remainder
Three Steps 🔥
A tank is filled. First 1/3 is drained, then 1/4 of the remainder is drained, then 1/5 of the remainder is drained. 24 litres remain. How many litres were initially in the tank?
After step 1: 1/3 drained, so 2/3 remains.
✏️ Write Your Solution
Write your solution here with your pen or finger ✍️
Type 3
🔷 Geometric Fractions
Fractions of shapes. Break it down: fraction of a fraction = multiply!
7
Example · Geometric Fractions
Shaded Rectangle 🔷
A rectangle is divided into 4 equal columns and 3 equal rows. If 2 columns are fully shaded and 2 rows are also shaded, what fraction of the total area is shaded?
Think about fractions instead of cells. 2 out of 4 columns shaded = 1/2 of the area.
✏️ Write Your Solution
Write your solution here with your pen or finger ✍️
8
Example · Geometric Fractions
Folded Paper 📄
A square piece of paper is folded in half, then in half again, then in half again. If the final folded area is 5 cm², what was the original area?
Each fold halves the area. After fold 1: the area is 1/2 of the original.
✏️ Write Your Solution
Write your solution here with your pen or finger ✍️
9
Advanced · Geometric Fractions
Overlapping Circles 🔥
Two identical circles overlap. The overlapping area is 1/3 of each circle's area. What fraction of the total combined area (both circles, counting overlap once) is the overlapping region?
Let each circle = 1 unit of area. The overlap = 1/3 of one circle = 1/3 unit.
✏️ Write Your Solution
Write your solution here with your pen or finger ✍️
Type 4
⚖️ Comparison & Difference
Find what each person KEEPS, then compare. The difference reveals the answer.
10
Example · Comparison & Difference
Sweets Sharing 🍬
Amy and Ben have the same number of sweets. Amy gives 1/3 of hers away. Ben gives 1/4 of his away. Who has more left, and by what fraction of the original?
Find what Amy keeps. She gives away 1/3, so she keeps: 1 − 1/3 = 2/3
✏️ Write Your Solution
Write your solution here with your pen or finger ✍️
11
Example · Comparison & Difference
Distance Race 🏃
Three runners each run 1200 m. Runner A completes 3/4 of the distance, Runner B completes 2/3, and Runner C completes 5/6. Who ran the longest distance and how far?
To compare 3/4, 2/3, and 5/6, convert them all to a common denominator. The LCM of 4, 3, and 6 is 12.
✏️ Write Your Solution
Write your solution here with your pen or finger ✍️
12
Advanced · Comparison & Difference
Price Comparison 🔥
Shop A sells a toy for $80. Shop B sells the same toy at 3/4 of Shop A's price. Shop C sells it at 4/5 of Shop B's price. What is the difference between the cheapest and most expensive price?
Start with Shop A: price = $80.
✏️ Write Your Solution
Write your solution here with your pen or finger ✍️