BananaLearnLearning LibraryGamesThree fifths of 40 learners bring lunch. How many do not?
- One fifth of 40 is 8; three fifths is 24.
- The remaining number is 40 − 24 = 16.
- Check 24 + 16 = 40; the question asked for those who do not.
Dates and official context
SOF lists IMO dates including 26 November and 10 December 2026. Your school selects the date and manages participation. Check its instructions and the current official syllabus before choosing additional practice. Do not assume that a date on this page means registration is still open at your school.
Make the hidden assumption visible
A reasoning problem may require whole boxes, equal shares or a fixed total. Write that condition before calculating. If 53 children travel in vehicles with eight seats each, 53÷8=6 remainder 5 means seven vehicles, not six and not a fractional vehicle.
An answer can be numerically correct for the wrong quantity. In a price problem, distinguish cost per item, number of items and total cost. In a shape problem, distinguish boundary length from covered area.
Use representations strategically
A bar helps with a fraction of a total; an array helps with equal groups; a table helps organise cases. The representation should reduce the difficulty. Drawing every object is unnecessary when a labelled bar or multiplication statement communicates the same relationship.
For “three fifths of 40”, split the bar into five equal parts of eight, then select three: 24. For a missing whole, reverse the steps: if three fifths is 24, one fifth is eight and the whole is 40.
Check the reasonableness before opening solutions
Estimate a decimal calculation and check units. A 2.5 m ribbon cannot leave 25 m after a short cut. For a finite pattern, follow the stated or simplest intended rule, but recognise that a short sequence alone does not mathematically determine every future term.
This independent workbook is not an official full-length mock or a prediction of question distribution. Use the official syllabus and your school’s chosen exam date to decide what else to practise.
Worked examples: follow each decision
A rectangle is 9 cm by 6 cm. A square has the same perimeter. Find its side.
- Rectangle perimeter = 2 × (9 + 6) = 30 cm.
- Square side = 30 ÷ 4 = 7.5 cm.
- Equal perimeter does not imply equal area.
20 questions with explained answers
Attempt a short group of questions before opening the solutions. Use a drawing or written method where helpful. Explain the answer, then try a similar question with a detail changed.
2/3 of 36
Show answer and reasoning
24
One third is 12; double it.
A 2.4 m rope is cut into 0.6 m pieces.
Show answer and reasoning
4 pieces
2.4 ÷ 0.6 = 4.
15, 22, 29, 36, next term?
Show answer and reasoning
43
Add 7 each time.
Average of 6, 8 and 10
Show answer and reasoning
8
Sum 24 divided by 3.
A ₹240 book has 25% off. Sale price?
Show answer and reasoning
₹180
One quarter of 240 is 60; subtract it.
3 hours 15 minutes in minutes
Show answer and reasoning
195 minutes
3 × 60 + 15.
A box has volume 4 × 3 × 2 cm³.
Show answer and reasoning
24 cm³
Multiply the three dimensions.
Is 0.7 larger than 0.65?
Show answer and reasoning
Yes
0.7 = 0.70, which is greater than 0.65.
53 children, 8 seats per vehicle. Minimum vehicles?
Show answer and reasoning
7
Six vehicles hold 48, leaving five children.
Three fifths of a number is 24. Find the number.
Show answer and reasoning
40
One fifth is 8; five fifths is 40.
A 2.5 m ribbon loses 0.75 m. Length left?
Show answer and reasoning
1.75 m
2.50−0.75=1.75.
A rectangle is 8 cm by 3 cm. Perimeter and area?
Show answer and reasoning
22 cm; 24 cm²
2(8+3)=22; 8×3=24.
Continue 2, 6, 12, 20 using differences 4, 6, 8, ...
Show answer and reasoning
30
The next difference is 10.
A clock shows 10:35. What is 1 hour 50 minutes later?
Show answer and reasoning
12:25
Add one hour, then 50 minutes.
Which is greater: 5/8 or 3/4?
Show answer and reasoning
3/4
3/4=6/8.
A bag has 3 red and 5 blue counters. What fraction are red?
Show answer and reasoning
3/8
The total is 8, not 5.
A 3-by-3 grid: count squares of all sizes.
Show answer and reasoning
14
9 small +4 of side 2 +1 of side 3.
Four identical pens cost ₹36. Seven cost?
Show answer and reasoning
₹63
One costs ₹9.
A rectangle has perimeter 30 cm and length 9 cm. Width?
Show answer and reasoning
6 cm
Length+width=15.
A number rounds to 500 to the nearest hundred. Could it be 549?
Show answer and reasoning
Yes
549 is below the halfway point 550.
Check what you can now explain
- Attempt independently before checking.
- Explain why the answer works.
- Retry the underlying skill with a changed example.
Keep these distinctions clear
- Keep units visible through a multi-step calculation.
- Read the final question again: it may ask for the remaining amount rather than the part you first calculated.
Save a useful copy
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Keep the ideas connected
- Finding a fraction of an amount
- Area and perimeter: the difference, examples and practice
- Grade 5 Writing Algebraic Expressions from Words
- Choose a Maths practice game by skill
For help with an ongoing school-learning difficulty, read how Maths tutoring works or ask about English or Science support. Share a specific example your child found difficult.
Sources and scope
Original explanations, examples, visual models and practice by BananaLearn. This guide is not an official textbook extract, exam paper or endorsed assessment resource.