The key ideas of this chapter, answered through the six guiding questions. Read them with your textbook.
🧠 Concept map: Multiplication and division
1What am I looking at?
Answer: Multiplying and dividing larger numbers using place value.
2What are its main parts or ideas?
Answer: Factors, product, dividend, divisor, quotient and remainder.
3How does it work?
Answer: Multiply by each digit and add the partial products; use long division (divide, multiply, subtract, bring down).
4Why is it important?
Answer: Used for costs of many items, sharing money and finding rates.
5What happens if something changes?
Answer: Multiplying by 10 or 100 adds zeros; division by 0 is not possible.
6What should I remember for the exam?
Answer: Long multiplication, long division and word problems with two steps.
📗 Full lesson: Multiplication and division strategies
This topic comes from GayaGnan's India-wide K–12 catalog. It is not copied from, or an official chapter of, any board's textbook: check your board's syllabus for the exact chapter and depth. Open as its own page →
🖼️ 2D concept map
Tap a word to see what it means.
Counters rearranged into all rectangles of 24
ℹ️ Counters stand for any objects.
🎯 Learning outcomes
Use arrays, doubling and splitting to multiply
Relate multiplication and division as inverse operations
Solve word problems with grouping and sharing
Before you start: Times tables and the meaning of multiplication.
📖 Explanation
Multiplication facts can be built from known ones. To find 6 × 8, double 3 × 8 = 24 to get 48. To find 9 × 7, think 10 × 7 − 7 = 63.
Splitting (the distributive idea) makes big products easier: 14 × 6 = 10 × 6 + 4 × 6 = 60 + 24 = 84.
Division undoes multiplication: if 7 × 9 = 63, then 63 ÷ 9 = 7 and 63 ÷ 7 = 9. A fact family has two multiplications and two divisions.
🇮🇳 Example from India
In a temple kitchen, 144 laddoos are packed 12 to a box. Since 12 × 12 = 144, there are 12 boxes.
⚠️ Common mistake
✗ 24 ÷ 6 and 6 ÷ 24 are the same ✓ Division order matters: 24 ÷ 6 = 4, but 6 ÷ 24 is a quarter.
🧪 Try this activity
Arrange 24 counters in as many rectangles as you can (1 × 24, 2 × 12, 3 × 8, 4 × 6). Write the multiplication and division fact for each.
✍️ Question bank with answers
Tap an option to check multiple-choice answers. Open “Answer” or “Marking points” for the others.
Multiple choice1 mark · easy
Which is the same as 15 × 4?
Answer
C. 10 × 4 + 5 × 4
Split 15 into 10 + 5 and multiply each part by 4.
Multiple choice1 mark · easy
If 8 × 7 = 56, then 56 ÷ 7 =
Answer
B. 8
Division is the inverse of multiplication.
Multiple choice1 mark · easy
9 × 6 can be found as
Answer
C. 10 × 6 − 6
9 sixes is one six less than 10 sixes: 60 − 6 = 54.
Very short answer1 mark · easy
Write the fact family for 5, 6 and 30.
Answer
5 × 6 = 30
6 × 5 = 30
30 ÷ 5 = 6
30 ÷ 6 = 5
Very short answer1 mark · easy
Double 35.
Answer
70
Short answer2 marks · medium
Use splitting to find 23 × 5.
Marking points
20 × 5 = 100
3 × 5 = 15
115
Long answer4 marks · hard
96 children go on a trip. Each van holds 8. How many vans? If each van costs ₹450, what is the total cost?
Marking points
96 ÷ 8 = 12 vans
12 × 450 = ₹5,400
Application2 marks · medium
Chairs in a hall are in 18 rows of 15. Is that enough for 250 people?
Answer
18 × 15 = 270
270 > 250, so yes
Diagram / label2 marks · medium
Draw an array for 3 × 7 and write two division facts from it.
Answer
3 rows of 7 dots
21 ÷ 3 = 7
21 ÷ 7 = 3
Worked problem2 marks · medium
Find 125 × 8 by doubling.
Answer
125 × 2 = 250
250 × 2 = 500
500 × 2 = 1,000
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