Class 7 Mathematics

Chapter 2 Solutions — Arithmetic Expressions

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Solutions

Overview

Step-by-step NCERT solutions for Arithmetic Expressions (Chapter 2, NCERT Class 7 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Arithmetic Expressions textbook chapter.

Solved

What these solutions cover

All 23 questions in Arithmetic Expressions are solved in the PDF. Here's what's inside, exercise by exercise:

Simple Expressions — Fill Blanks and Arrange

1.
Fill in the blanks to make the expressions equal on both sides of the = sign:
- (a) 13 + 4 = ___ + 6
- (b) 22 + ___ = 6 × 5
- (c) 8 × ___ = 64 ÷ 2
- (d) 34 − ___ = 25
2.
Arrange the following expressions in ascending (increasing) order of their values.
- (a) 67 − 19
- (b) 67 − 20
- (c) 35 + 25
- (d) 5 × 11
- (e) 120 ÷ 3

Comparing Expressions Without Full Calculation

1.
Use '>' or '<' or '=' in each of the following expressions to compare them. Can you do it without complicated calculations?
- (a) 245 + 289 ___ 246 + 285
- (b) 273 − 145 ___ 272 − 144
- (c) 364 + 587 ___ 363 + 589
- (d) 124 + 245 ___ 129 + 245
- (e) 213 − 77 ___ 214 − 76

Terms, Values, and Situations

1.
Find the values of the following expressions by writing the terms in each case.
- (a) 28 − 7 + 8
- (b) 39 − 2 × 6 + 11
- (c) 40 − 10 + 10 + 10
- (d) 48 − 10 × 2 + 16 ÷ 2
- (e) 6 × 3 − 4 × 8 × 5
2.
Write a story/situation for each of the following expressions and find their values.
- (a) 89 + 21 − 10
- (b) 5 × 12 − 6
- (c) 4 × 9 + 2 × 6
3.
For each of the following situations, write the expression describing the situation, identify its terms and find the value of the expression.
- (a) Queen Alia gave 100 gold coins to Princess Elsa and 100 gold coins to Princess Anna last year. Princess Elsa doubled her coins. Princess Anna has only half left. Write an expression for how many gold coins they together have.
- (b) A metro train ticket…

Removing Brackets — I

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 [box] ___
- (b) 38 + (___ [box] ___) = 38 + 9 − 4
- (c) 24 − (6 + 4) = 24 [box] 6 − 4
- (d) 24 − 6 − 4 = 24 − 6 [box] ___
- (e) 27 − (8 + 3) = 27 [box] 8 [box] 3
- (f) 27 − (___ [box] ___) = 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)
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)
4.
In each of the sets of expressions below, identify those that have the same value. Do not evaluate them; 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
5.
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
6.
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 − ___
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. (Example: 2 − 3 + 5 = 4 and 3 − (5 − 2) = 0.)
8.
Consider the two expressions: (A) 73 − 14 + 1 and (B) 73 − 14 − 1. For each, identify which of the following are equal to it:
- (a) 73 − (14 + 1)
- (b) 73 − (14 − 1)
- (c) 73 + (−14 + 1)
- (d) 73 + (−14 − 1)

Distributive Property — Removing Brackets II

1.
Fill in the blanks with numbers, and boxes by signs, so that the expressions on both sides are equal.
- (a) 3 × (6 + 7) = 3 × 6 + 3 × 7
- (b) (8 + 3) × 4 = 8 × 4 + 3 × 4
- (c) 3 × (5 + 8) = 3 × 5 [box] 3 × ___
- (d) (9 + 2) × 4 = 9 × 4 [box] 2 × ___
- (e) 3 × (___ + 4) = 3 × ___ + ___
- (f) (___ + 6) × 4 = 13 × 4 + ___
- (g) 3 × (___ + ___) = 3 × 5 + 3 × 2
- (h) (___ + ___) × ___ = 2 × 4 + 3 × 4
- (i) 5 × (9 − 2)…
2.
In the boxes below, fill '<', '>' or '=' after analysing the expressions on the LHS and RHS. Use reasoning and understanding of terms and brackets — not by evaluating.
- (a) (8 − 3) × 29 ___ (3 − 8) × 29
- (b) 15 + 9 × 18 ___ (15 + 9) × 18
- (c) 23 × (17 − 9) ___ 23 × 17 + 23 × 9
- (d) (34 − 28) × 42 ___ 34 × 42 − 28 × 42
Here is one way to make 14: 2 × (1 + 6) = 14. Find four other ways of getting 14 in the form ___ × (___ + ___) = 14.
Find out the sum of the numbers given in each picture below in at least two different ways. Describe how you solved it through expressions. Picture I: a 3 × 3 grid with alternating values — corners and centre = 4, edges = 8 (5 fours and 4 eights). Picture II: a 4 × 4 grid with values 5 and 6 alternating — 8 fives and 8 sixes.

Mixed Problems — Expressions and Reasoning

1.
Read the situations given below. Write appropriate expressions for each of them and find their values.
- (a) The district market in Begur operates all seven days. Rahim supplies 9 kg and Shyam supplies 11 kg of mangoes each day. Find the total mangoes supplied in a week.
- (b) Binu earns ₹20,000 per month. She spends ₹5,000 on rent, ₹5,000 on food, and ₹2,000 on other expenses every month. What will…
2.
Melvin reads a two-page story every day except on Tuesdays and Saturdays. How many stories would he complete reading in 8 weeks? Which of the following expressions describes this scenario?
- (a) 5 × 2 × 8
- (b) (7 − 2) × 8
- (c) 8 × 7
- (d) 7 × 2 × 8
- (e) 7 × 5 − 2
- (f) (7 + 2) × 8
- (g) 7 × 8 − 2 × 8
- (h) (7 − 5) × 8
3.
Find different ways of evaluating the following expressions:
- (a) 1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + 9 − 10
- (b) 1 − 1 + 1 − 1 + 1 − 1 + 1 − 1 + 1 − 1
4.
Compare the following pairs of expressions using '<', '>' or '=' or by reasoning.
- (a) 49 − 7 + 8 ___ 49 − 7 + 8
- (b) 83 × 42 − 18 ___ 83 × 40 − 18
- (c) 145 − 17 × 8 ___ 145 − 17 × 6
- (d) 23 × 48 − 35 ___ 23 × (48 − 35)
- (e) (16 − 11) × 12 ___ −11 × 12 + 16 × 12
- (f) (76 − 53) × 88 ___ 88 × (53 − 76)
- (g) 25 × (42 + 16) ___ 25 × (43 + 15)
- (h) 36 × (28 − 16) ___ 35 × (27 − 15)
5.
Identify which of the following expressions are equal to the given expression without computation. There can be more than one.
- (a) Given: 83 − 37 − 12
- (i) 84 − 38 − 12
- (ii) 84 − (37 + 12)
- (iii) 83 − 38 − 13
- (iv) −37 + 83 − 12
- (b) Given: 93 + 37 × 44 + 76
- (i) 37 + 93 × 44 + 76
- (ii) 93 + 37 × 76 + 44
- (iii) (93 + 37) × (44 + 76)
- (iv) 37 × 44 + 93 + 76

Sample

Worked examples

2 questions from Arithmetic Expressions, solved step by step.

Removing Brackets — I

In each of the sets of expressions below, identify those that have the same value. Do not evaluate them; 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

(a) Write each as a sum of terms and compare:

319 + 537: terms are +319 and +537.

319 − 537: terms are +319 and −537.

−537 + 319: terms are −537 and +319 — same as 319 − 537.

537 − 319: terms are +537 and −319 — different from all above.

Same value: 319 − 537 = −537 + 319.

(b) Identify the terms of each:

87 + 46 − 109: terms +87, +46, −109. (Appears three times — all equal.)

87 − 46 + 109: terms +87, −46, +109. Different.

87 − (46 + 109) = 87 − 46 − 109: terms +87, −46, −109. Different from above.

(87 − 46) + 109 = 87 − 46 + 109: terms +87, −46, +109. Same as 87 − 46 + 109.

Same value: the three expressions '87 + 46 − 109' (×3) have equal values.

Also: '87 − 46 + 109' and '(87 − 46) + 109' have equal values.

Answer: (a) 319 − 537 and −537 + 319 are equal. (b) The first three (87 + 46 − 109) are equal to each other; 87 − 46 + 109 and (87 − 46) + 109 are equal to each other.

Removing Brackets — I

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. (Example: 2 − 3 + 5 = 4 and 3 − (5 − 2) = 0.)

Listing distinct arrangements:

2 + 3 + 5 = 10

2 + 3 − 5 = 0

2 − 3 + 5 = 4

2 − 3 − 5 = −6

3 − 2 − 5 = −4

5 − 3 + 2 = 4 (same as 2 − 3 + 5)

5 + 3 − 2 = 6

3 − (5 − 2) = 3 − 3 = 0 (same value as 2 + 3 − 5)

2 − (3 + 5) = 2 − 8 = −6 (same as 2 − 3 − 5)

2 − (3 − 5) = 2 + 2 = 4 (same as 2 − 3 + 5)

5 − (3 + 2) = 0

5 − (2 − 3) = 5 + 1 = 6

3 + (5 − 2) = 6

Distinct values obtained: −6, −4, 0, 4, 6, 10.

Answer: Distinct values: −6, −4, 0, 4, 6, 10

All 23 questions in Arithmetic Expressions are solved step by step in the Solutions PDF above.

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Chapter 2 Solutions — Arithmetic Expressions

Overview

What these solutions cover

Simple Expressions — Fill Blanks and Arrange

Comparing Expressions Without Full Calculation

Terms, Values, and Situations

Removing Brackets — I

Distributive Property — Removing Brackets II

Mixed Problems — Expressions and Reasoning

Worked examples

In each of the sets of expressions below, identify those that have the same value. Do not evaluate them; 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

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. (Example: 2 − 3 + 5 = 4 and 3 − (5 − 2) = 0.)

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