๐ What this Exercise Covers
Exercise 2.5 is a mixed application exercise. It combines:
- Patterns in whole numbers
- Use of properties (commutative, distributive, etc.)
- Observations and logical thinking
๐ It helps you apply concepts learned in Exercises 2.2 and 2.3
๐ข 1. Patterns Using Multiplication
Example:
- 9 ร 1 = 9
- 9 ร 2 = 18
- 9 ร 3 = 27
๐ Pattern: Multiples increase regularly
๐ 2. Using Distributive Property in Patterns
aร(b+c)=aรb+aรca \times (b + c) = a \times b + a \times caร(b+c)=aรb+aรc
Example:
- 8 ร 15 = 8 ร (10 + 5)
= (8ร10) + (8ร5)
= 80 + 40 = 120
๐ Helps in fast calculation
๐ง 3. Observing Number Patterns
Example:
- 1 ร 1 = 1
- 11 ร 11 = 121
- 111 ร 111 = 12321
๐ Pattern formation using digits
๐ 4. Important Learning
- Patterns make maths easy and fun
- Properties help in breaking big calculations
- Encourages logical thinking
โ๏ธ Exercise 2.5 โ Worksheet (50 Questions)
๐ข Section A: Observe and Complete the Pattern (1โ15)
- 2 ร 1 = 2
2 ร 2 = 4
2 ร 3 = ___
2 ร 4 = ___ - 5 ร 1 = 5
5 ร 2 = 10
5 ร 3 = ___
5 ร 4 = ___ - 10 ร 1 = 10
10 ร 2 = 20
10 ร 3 = ___
10 ร 4 = ___ - 3 ร 1 = 3
3 ร 2 = 6
3 ร 3 = ___
3 ร 4 = ___ - 1 ร 1 = 1
11 ร 11 = 121
111 ร 111 = ___ - 4 ร 5 = 20
4 ร 6 = ___
4 ร 7 = ___ - 6 ร 2 = 12
6 ร 3 = ___
6 ร 4 = ___ - 7 ร 1 = 7
7 ร 2 = 14
7 ร 3 = ___ - 9 ร 1 = 9
9 ร 2 = 18
9 ร 3 = ___ - 8 ร 1 = 8
8 ร 2 = 16
8 ร 3 = ___
11โ15. Continue similar multiplication patterns
โ๏ธ Section B: Use Distributive Property (16โ25)
- 7 ร 12
- 8 ร 15
- 9 ร 11
- 6 ร 14
- 5 ร 18
- 10 ร 25
- 4 ร 21
- 3 ร 19
- 12 ร 13
- 15 ร 12
๐ง Section C: Identify Pattern (26โ35)
- 1, 11, 111 โ ______
- 2, 22, 222 โ ______
- 3, 6, 9 โ ______
- 5, 10, 15 โ ______
- 4, 8, 12 โ ______
- 10, 100, 1000 โ ______
- 9, 18, 27 โ ______
- 6, 12, 18 โ ______
- 7, 14, 21 โ ______
- 8, 16, 24 โ ______
๐ Section D: Simplify Using Properties (36โ45)
- 25 ร 16
- 50 ร 12
- 99 ร 7
- 100 ร 18
- 75 ร 4
- 8 ร 125
- 20 ร 15
- 15 ร 15
- 9 ร 99
- 12 ร 25
๐งฉ Section E: Case-Based Questions (46โ50)
๐ฆ Case Study: Packing Boxes
A shopkeeper packs 12 items in each box. He packs (10 + 5) boxes.
- How many boxes in total?
- Total items using distributive property
- Which property is used?
๐ซ Case Study: Classroom Rows
Each row has 8 students. There are 12 rows.
- Total students using distributive method
- What is 8 ร 12?
โ Answer Key
Section A (Sample)
- 6, 8
- 15, 20
- 30, 40
- 9, 12
- 12321
- 24, 28
- 18, 24
- 21
- 27
- 24
Section B
- 84
- 120
- 99
- 84
- 90
- 250
- 84
- 57
- 156
- 180
Section C
- Repeating digits
- Repeating digits
- +3
- +5
- +4
- ร10
- +9
- +6
- +7
- +8
Section D
- 400
- 600
- 693
- 1800
- 300
- 1000
- 300
- 225
- 891
- 300
Section E
- 15
- 12ร10 + 12ร5 = 120 + 60 = 180
- Distributive property
- 8ร10 + 8ร2 = 80 + 16 = 96
- 96
