Class 7 | Ganita Prakash | Chapter 2
๐ Arithmetic Expressions
Terms ยท Brackets ยท BODMAS ยท Comparing
๐ 2.1 โ Simple Expressions
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What is an Arithmetic Expression?
A mathematical phrase using numbers and operations: +, โ, ร, รท
Examples: 13 + 2, 20 โ 4, 12 ร 5, 18 รท 3
Every expression has a value โ 13 + 2 = 15
A mathematical phrase using numbers and operations: +, โ, ร, รท
Examples: 13 + 2, 20 โ 4, 12 ร 5, 18 รท 3
Every expression has a value โ 13 + 2 = 15
Different expressions can have the same value!
Ways to write 12: 10 + 2, 15 โ 3, 3 ร 4, 24 รท 2
Ways to write 12: 10 + 2, 15 โ 3, 3 ร 4, 24 รท 2
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๐งฎ Comparing Expressions
We compare using =, <, >
Example: 10 + 2 > 7 + 1 โ because 12 > 8 โ
Example: 13 โ 2 < 4 ร 3 โ because 11 < 12 โ
Example: 10 + 2 > 7 + 1 โ because 12 > 8 โ
Example: 13 โ 2 < 4 ร 3 โ because 11 < 12 โ
Smart Shortcut โ No calculation needed! ๐ง
1023 + 125 vs 1022 + 128
โ 1022 has 1 less, but 128 has 3 more. So 1022 + 128 is bigger!
113 โ 25 vs 112 โ 24
โ Start: 113 has 1 more. Lose: 25 has 1 more. โ They are EQUAL!
1023 + 125 vs 1022 + 128
โ 1022 has 1 less, but 128 has 3 more. So 1022 + 128 is bigger!
113 โ 25 vs 112 โ 24
โ Start: 113 has 1 more. Lose: 25 has 1 more. โ They are EQUAL!
๐ Pattern!
If we add the same amount to both numbers in a sum, the difference stays the same.
If both numbers decrease/increase by same amount in subtraction, result stays same!
If we add the same amount to both numbers in a sum, the difference stays the same.
If both numbers decrease/increase by same amount in subtraction, result stays same!
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๐ข 2.2 โ Complex Expressions & Brackets
The Marble Problem ๐ฑ
Mallesh has 30 marbles. Arun has 5 bags with 4 marbles each.
Total = 30 + 5 ร 4
โ Wrong: (30 + 5) ร 4 = 35 ร 4 = 140
โ Right: 30 + (5 ร 4) = 30 + 20 = 50
Mallesh has 30 marbles. Arun has 5 bags with 4 marbles each.
Total = 30 + 5 ร 4
โ Wrong: (30 + 5) ร 4 = 35 ร 4 = 140
โ Right: 30 + (5 ร 4) = 30 + 20 = 50
Brackets tell us what to solve FIRST! ๐
Example: 100 โ (15 + 56) = 100 โ 71 = 29 โ
(NOT 100 โ 15 + 56 = 141 โ)
Solve everything inside brackets first
Then do multiplication/division (left to right)
Finally do addition/subtraction (left to right)
Example: 100 โ (15 + 56) = 100 โ 71 = 29 โ
(NOT 100 โ 15 + 56 = 141 โ)
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๐ฆ Terms in Expressions
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What are Terms?
Terms = parts of an expression separated by + signs
In 12 + 7: terms are 12 and 7
In 83 โ 14: write as 83 + (โ14) โ terms are 83 and โ14
In 6ร5 + 3: terms are 6ร5 and 3
Terms = parts of an expression separated by + signs
In 12 + 7: terms are 12 and 7
In 83 โ 14: write as 83 + (โ14) โ terms are 83 and โ14
In 6ร5 + 3: terms are 6ร5 and 3
Key Rule: Convert all subtractions to addition of the inverse!
โ18 โ 3 = (โ18) + (โ3) โ terms: โ18, โ3
2 โ 10 + 4ร6 = 2 + (โ10) + 4ร6 โ terms: 2, โ10, 4ร6
โ18 โ 3 = (โ18) + (โ3) โ terms: โ18, โ3
2 โ 10 + 4ร6 = 2 + (โ10) + 4ร6 โ terms: 2, โ10, 4ร6
| Expression | Terms |
|---|---|
| 13 โ 2 + 6 | 13, โ2, 6 |
| 5 + 6ร3 | 5, 6ร3 |
| 4 + 15 โ 9 | 4, 15, โ9 |
| 23 โ 2ร4 + 16 | 23, โ2ร4, 16 |
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๐ Swapping & Grouping
Swapping Terms (Commutativity):
6 + (โ4) = โ4 + 6 = 2 โ (Order doesn't matter!)
Grouping Terms (Associativity):
(a + b) + c = a + (b + c) โ we can group any way!
6 + (โ4) = โ4 + 6 = 2 โ (Order doesn't matter!)
Grouping Terms (Associativity):
(a + b) + c = a + (b + c) โ we can group any way!
๐ Using Terms to Evaluate Expressions (without brackets):
Each TERM is evaluated on its own, then added.
30 + 5 ร 4
Terms: 30 and 5 ร 4
Values: 30 + 20 = 50 โ
Multiplication binds more tightly โ it happens inside the term first!
Each TERM is evaluated on its own, then added.
30 + 5 ร 4
Terms: 30 and 5 ร 4
Values: 30 + 20 = 50 โ
Multiplication binds more tightly โ it happens inside the term first!
BODMAS / PEMDAS remember? ๐ฏ
Brackets โ Orders (powers) โ Division โ Multiplication โ Addition โ Subtraction
The "terms" idea is just a cleaner way to say the same thing!
Brackets โ Orders (powers) โ Division โ Multiplication โ Addition โ Subtraction
The "terms" idea is just a cleaner way to say the same thing!
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๐ Quick Summary
Expression = numbers + operations
e.g. 13+2, 5ร4-3
e.g. 13+2, 5ร4-3
Brackets FIRST!
(5+3)ร2 = 16
NOT 5+(3ร2)=11
(5+3)ร2 = 16
NOT 5+(3ร2)=11
Terms = parts
separated by +
Evaluate each first!
separated by +
Evaluate each first!
Swapping โ
Grouping โ
Order doesn't matter for +
Grouping โ
Order doesn't matter for +
| Concept | Meaning | Example |
|---|---|---|
| Expression | Numbers + operations | 30 + 5ร4 |
| Brackets | Solve inside first | (30+5)ร4 = 140 |
| Terms | Parts separated by + | 30 and 5ร4 |
| Inverse | Opposite sign | Inverse of 14 is โ14 |
๐ Chapter 2 Complete! ๐
Made with โค๏ธ by @edugrown
Made with โค๏ธ by @edugrown