Class 7MathematicsChapter 2NCERT • Ganita Prakash
Arithmetic Expressions
Learn how to read, write, compare and evaluate mathematical expressions using terms, brackets and useful properties.
Chapter Snapshot
- An arithmetic expression combines numbers and operations.
- Every expression has a value.
- Different expressions can have the same value.
- Brackets tell us which part to calculate first.
- Expressions can be understood as a sum of terms.
- Addition terms can be rearranged and regrouped.
- Removing brackets requires attention to signs.
- The distributive property helps simplify calculations.
What You Will Learn
- ✓Understand arithmetic expressions
- ✓Find the value of simple expressions
- ✓Compare two expressions
- ✓Use brackets correctly
- ✓Identify terms in an expression
- ✓Evaluate expressions with several operations
- ✓Remove brackets correctly
- ✓Use the distributive property
Exam PriorityBoardsVery HighFoundationHigh
Chapter Overview
We often use mathematical expressions without realising it.
For example:
13 + 2
20 - 4
12 × 5
18 ÷ 3
Each of these represents a mathematical calculation.
Arithmetic expressions help us describe real-life situations clearly and solve them step by step.
1. Arithmetic Expressions
Examples:
18+7
50−16
8×6
72÷9
Every expression has a value.
For example:
13+2=15
Here:
13 + 2 is the expression.
15 is its value.
Quick Check
What is the value of the expression 15 + 8?
Show answer
23
2. Different Expressions, Same Value
Different expressions can give the same answer.
For example:
10+2=12
15−3=12
3×4=12
24÷2=12
All four expressions have the same value.
3. Comparing Expressions
Expressions can be compared using:
For example:
10+5>8+4
because:
15>12
Compare Expressions
Question
Compare 113 - 25 and 112 - 24.
Solution
Evaluate both:
113−25=88112−24=88Therefore:
113−25=112−24Quick Check
Compare 25 + 10 and 24 + 12.
Show answer
25 + 10 < 24 + 12 because 35 < 36.
4. Why Do We Need Brackets?
Consider:
30+5×4
If we first calculate:
5×4=20
then:
30+20=50
But if someone adds 30 and 5 first, they may get a different answer.
Brackets remove this confusion.
For example:
30+(5×4)
First calculate:
5×4=20
Then:
30+20=50
Using Brackets
A shopkeeper receives ₹100.
The cost of two items is ₹15 and ₹56.
The change is:
100−(15+56)First:
15+56=71Then:
100−71=29So the change is ₹29.
5. Terms in an Expression
Expressions can be understood by separating them into terms.
Consider:
13−2+6
We can write it as:
13+(−2)+6
The terms are:
Another example:
5+6×3
The terms are:
6. Evaluating Expressions with Terms
For an expression containing several operations:
- evaluate brackets first;
- evaluate each term;
- add the values of the terms.
Evaluate an Expression
Question
Find the value of 39 - 2 × 6 + 11.
Solution
Write it in terms:
39+(−2×6)+11Calculate the product:
2×6=12So:
39−12+11=27+11=38Therefore:
38Expression with Brackets
Question
Find the value of 5 × (3 + 2) + 7 × 8 + 3.
Solution
First evaluate the bracket:
3+2=5Now:
5×5+7×8+3Evaluate the products:
25+56+3Therefore:
847. Swapping Terms in Addition
Consider:
6+(−4)
Its value is:
2
Now swap the terms:
(−4)+6
The value is still:
2
So changing the order of terms in addition does not change the sum.
Commutative Property of Addition
a+b=b+a
For example:
18+25=25+18
8. Grouping Terms
Consider:
5+10+20
We may calculate:
(5+10)+20
or:
5+(10+20)
Both give:
35
Associative Property of Addition
(a+b)+c=a+(b+c)
9. Removing Brackets
Brackets can sometimes be removed.
The sign before the bracket is important.
Bracket Preceded by a Plus Sign
Consider:
28+(35−10)
We can write:
28+35−10
The signs inside remain unchanged.
Bracket Preceded by a Minus Sign
Consider:
200−(40+3)
Removing the bracket gives:
200−40−3
Therefore:
200−(40+3)=157
Another example:
500−(250−100)
Removing the bracket gives:
500−250+100
Therefore:
500−(250−100)=350
10. Distributive Property
The distributive property connects multiplication with addition and subtraction.
Consider:
5×(8+3)
We can multiply 5 by both numbers:
5×8+5×3
Therefore:
5×(8+3)=5×8+5×3
Distributive Property
Over addition:
a×(b+c)=a×b+a×cOver subtraction:
a×(b−c)=a×b−a×cUsing the Distributive Property
Question
Find 97 × 25 using a convenient method.
Solution
Write:
97=100−3So:
97×25=(100−3)×25Distribute 25:
100×25−3×25=2500−75=2425Therefore:
97×25=2425Important Terms
Key Terms
Arithmetic ExpressionValue of an ExpressionTermBracketCommutative PropertyAssociative PropertyDistributive Property
Common Mistakes
Exam Focus
Important Exam Topics
Focus on:
- meaning of arithmetic expressions;
- finding the value of an expression;
- comparing expressions;
- identifying terms;
- use of brackets;
- removing brackets;
- commutative property;
- associative property;
- distributive property;
- writing expressions from real-life situations.
Quick Revision
Quick Revision
- An arithmetic expression contains numbers and operations.
- Every arithmetic expression has a value.
- Different expressions may have the same value.
- Brackets tell us which part to calculate first.
- An expression can be written as a sum of terms.
- Products inside a term should be evaluated together.
- Addition is commutative: a+b=b+a.
- Addition is associative: (a+b)+c=a+(b+c).
- A plus sign before brackets keeps the inner signs unchanged.
- A minus sign before brackets changes the inner signs.
- Multiplication distributes over addition and subtraction.
Practice Questions
Multiple Choice Questions
Q1MCQEasyClass 7
What is the value of:
12+3×4A. 60
B. 24
C. 48
D. 15
View Solution
Evaluate the multiplication term first:
3×4=12Then:
12+12=24Answer: B. 24
Q2MCQEasyClass 7
Which expression has the same value as:
20−(8+2)A. 20−8+2
B. 20−8−2
C. 20+8−2
D. 20+8+2
View Solution
20−(8+2)=20−8−2Answer: B
Q3MCQEasyClass 7
Which property is shown by:
7+12=12+7A. Associative
B. Distributive
C. Commutative
D. Division
View Solution
The order of the terms has changed.
Answer: C. Commutative property
Q4MCQModerateClass 7
Which is equal to:
6×(10+4)A. 6×10+4
B. 6×10+6×4
C. 10+6×4
D. 6+10+4
View Solution
Using the distributive property:
6×(10+4)=6×10+6×4Answer: B
Short Answer Questions
Q5Short AnswerEasyClass 7
Identify the terms in:
18−5+7View Solution
Rewrite as:
18+(−5)+7The terms are:
Q6Short AnswerModerateClass 7
Remove the brackets:
50−(20−8)View Solution
The bracket is preceded by a minus sign, so the signs inside change:
50−20+8Q7Short AnswerModerateClass 7
Write an expression for:
“Five pencils cost ₹12 each and one eraser costs ₹8.”
View Solution
Cost of five pencils:
5×12Add the cost of the eraser:
5×12+8Numerical Questions
Q8NumericalModerateClass 7
Evaluate:
48−10×2+16÷2View Solution
Evaluate the multiplication and division terms:
10×2=2016÷2=8Now:
48−20+8=28+8=36Q9NumericalModerateClass 7
Use the distributive property to find:
104×15View Solution
Write:
104=100+4Therefore:
104×15=(100+4)×15=100×15+4×15=1500+60=1560Q10NumericalModerateFoundation
Evaluate:
25−(12−7)and then write it without brackets.
View Solution
First evaluate the bracket:
12−7=5Therefore:
25−5=20Without brackets:
25−12+7and:
25−12+7=20Apply Your Learning
Create Your Own Expression
Choose any number between 10 and 30.
Write at least four different arithmetic expressions having that value.
For example, for 20:
- 12+8
- 25−5
- 4×5
- 40÷2
Then challenge a friend to create different expressions for the same number.
Chapter Summary
Chapter Summary
- Arithmetic expressions contain numbers and mathematical operations.
- Every expression has a value.
- Different expressions can have equal values.
- Brackets specify which calculation should be done first.
- Expressions can be separated into terms.
- Addition terms can be reordered and regrouped without changing the sum.
- A minus sign before a bracket changes the signs of the terms inside when the bracket is removed.
- The distributive property connects multiplication with addition and subtraction.
- Understanding expressions makes complex calculations easier and clearer.
