NCERT Solutions Class 7 Maths Chapter 2: Arithmetic Expressions (Ganita Prakash) covers Lesson 2.3, which focuses on expression simplification and manipulation using the Distributive Property, as well as managing or handling brackets. This exercise is essential for helping students learn the rules for removing brackets, which they will use as they continue to study algebra.
The activities in Exercise 2.3 train you to balance equations with properties and simplify complex expressions with multiple operations and signs. Developing mastery of these tasks assists in eliminating many common calculation errors and also leads to developing a systematic approach to a mathematics problem.
You can obtain the complete and step-by-step solutions for NCERT Class 7 Maths Chapter 2 Exercise 2.3 in a downloadable PDF format. You can use these solutions to revise work, practice questions, and get the logic behind modifying expressions.
1. Fill in the blanks with numbers, and boxes with operation signs such that the expressions on both sides are equal.
(a) 24+(6−4)=24+6□ □ .
(b) 38+ ____ □ ____ ) =38+9−4
(c) 24−(6+4)=24 □ 6-4
(d) 24−6−4=24−6 □ □ ____
(e) 27−(8+3)=27 □ 8 □ 3
(f) 27−( ____ □ ____ ) =27−8+3
Sol. (a) 24+(6−4)=24+6−4
(b) 38+(9−4)=38+9−4
(c) 24−(6+4)=24−6−4
(d) 24−6−4=24−6−4
(e) 27−(8+3)=27−8−3
(f) 27−(8−3)=27−8+3
2. Remove the brackets and write the expression having the same value.
(a) 14+(12+10)
(b) 14−(12+10)
(c) 14+(12−10)
(d) 14−(12−10)
(e) −14+12−10
(f) 14−(−12−10)
Sol. (a) 14+(12+10)
=14+12+10=14+22=36
(b) 14−(12+10)
=14−12−10=14−22=−8
(c) 14+(12−10)
=14+12−10=14+2=16
(d) 14−(12−10)
=14−12+10=14−2=12
(e) −14+12−10
=−14+2=−12
(f) 14−(−12−10)=14+12+10=14+22=36
3. Find the values of the following expressions. For each pair, first try to guess whether they have the same value. When are the two expressions equal?
(a) (6+10)−2 and 6+(10−2)
(b) 16−(8−3) and (16-8) - 3
(c) 27−(18+4) and 27+(−18−4)
Sol. (a) (6+10)−2 and 6+(10−2)
(6+10)−2=16−2=14
and 6+(10−2)=6+8=14
Clearly, (6+10)−2=6+(10−2)
Hence, the expressions in part (a) have the same value.
(b) 16 - (8-3) and (16-8) - 3
16−(8−3)=16−5=11
and (16−8)−3=8−3=5
16−(8−3)=(16−8)−3
Hence, the expressions in part (b) do not have the same value.
(c) 27−(18+4) and 27+(−18−4)
27−(18+4)=27−22=5
and 27+(−18−4)=27+(−22)=5
Clearly, 27−(18+4)=27+(−18−4)
Hence, the expressions in part (c) have the same value.
4. In each of the sets of expressions below, identify those that have the same value. Do not evaluate them, but rather use your understanding of terms.
(a) 319+537,319−537,−537+319, 537-319
(b) 87+46−109,87+46−109,87+46−109,87−46+109,87−(46+109), (87−46)+109
Sol. (a)
Expressions having the same terms have equal values.
Therefore, 319−537,−537+319 have the same value.
(b)
Expressions having the same terms have equal values.
Therefore, 87+46−109,87+46−109, 87+46−109 have the same value.
Also, 87-46+109 and (87-46) + 109 have the same value.
4. Add brackets at appropriate places in the expressions such that they lead to the values indicated.
(a) 34−9+12=13
(b) 56−14−8=34
(c) −22−12+10+22=−22
Sol. Here, the expressions with correctly placed brackets are
(a) 34−(9+12)=13
(b) 56−(14+8)=34
(c) −22−(12+10)+22=−22
5. Using only reasoning of how terms change their values, fill the blanks to make the expressions on either side of the equality (=) equal.
(a) 423+…=419+ ____
(b) 207−68=210− ____
Sol. Here are the expressions with the correct values bases on reasoning.
(a) 423+4=419+8
(b) 207−68=210−71
By analysing how numbers shift, we maintain balance in the equation without direct calculation.
6. Using the numbers 2,3 and 5 , and the operators ' + ' and ' - ', and brackets, as necessary, generate expressions to give as many different values as possible. For example, 2−3+5=4 and 3−(5−2)=0.
Sol. Here are different expressions using the numbers, 2, 3 and 5 along with the operators ' + ' and ' - ' and brackets
(i) 2+3+5=10
(ii) 2+(5−3)=4
(iii) (5+3)−2=6
(iv) 5−(3+2)=0
(v) 2−(3+5)=−6
7. Whenever Jasoda has to subtract 9 from a number, she subtracts 10 and adds 1 to it. For example, 36−9=26+1.
(a) Do you think she always gets the correct answer? Why?
(b) Can you think of other similar strategies? Give some examples.
Sol. (a) Yes, Jasoda always gets the correct answer. Her strategy works because subtracting 10 removes one extra than needed, so adding 1 afterward restores the correct value. Mathematically, her method follows a−9=(a−10)+1 [here, a is any number]
This method is useful because subtracting 10 is often easier to calculate mentally than subtracting 9.
(b) Similar strategies include
Subtracting 99
Instead of subtracting 99, subtract 100 and add 1
e.g. We have,
245−99=(245−100)+1=145+1 = 146
Adding 9
Instead of adding 9, add 10 and subtract 1 .
e.g. We have, 37+9=(37+10)−1=47−1=46
Multiplying by 5
Instead of multiplying by 5, multiply by 10 and divide by 2 .
e.g. We have,
36×5=(36×10)÷2=360÷2=180
8. Consider the two expressions:
(a) 73−14+1, (b) 73−14−1. For each of these expressions, identify the expressions from the following collection that are equal to it.
(i) 73−(14+1)
(ii) 73−(14−1)
(iii) 73+(−14+1)
(iv) 73+(−14−1)
Sol. Given expressions:
73−14+1=60 and 73−14−1=58
Now,
(i) 73−(14+1)=73−15=58
(ii) 73−(14−1)=73−13=60
(iii) 73+(−14+1)=73−13=60
(iv) 73+(−14−1)=73+(−15)=58
Hence, expressions (ii) and (iii) are equal to the expression 73-14+1, i.e. (a) and expressions (i) and (iv) are equal to the expression 73-14-1. i.e. (b)
(Session 2026 - 27)