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NCERT Solutions · Maths Ch 2
Arithmetic Expressions
37 questions · 5 exercises
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Ex 2.1
Ex 2.2
Ex 2.3
Ex 2.4
Ex 2.5
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
10 QUESTIONS
Exercise 2.1
Q1
Choose your favourite number and write as many expressions as you can having that value.
(3 marks)
Q2
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
(5 marks)
Q3
Arrange the following expressions in ascending order of their values: (a) 67 − 19 (b) 67 − 20 (c) 35 + 25 (d) 5 × 11 (e) 120 ÷ 3
(3 marks)
Q4
Use '>', '(5 marks)
Q5
Check if replacing subtraction by addition of the inverse does not change the value, by taking different examples. Does changing the order in which terms are added give different values?
(3 marks)
Q6
Does adding the terms of an expression in any order give the same value? Take expressions with 3 terms and with more than 3 terms (including negative numbers).
(3 marks)
Q7
Manasa adds a long list of numbers in five minutes and gets 11749. She realises she forgot the fourth number, 9055. Does she have to start all over again?
(2 marks)
Q8
Four friends order items costing ₹23 each and give a tip of ₹5. If the number of friends goes up to 7 and the tip remains the same, how much will they have to pay? Write an expression and identify its terms.
(2 marks)
Q9
Ruby sits out and the other 33 students play a grouping game. When the teacher calls out '5', the students form groups of 5 and Ruby writes 6 × 5 + 3. (a) If the teacher had called out '4', what would Ruby write? (b) If the teacher had called out '7', what would Ruby write? Identify the terms. Write an expression like this for your class size.
(3 marks)
Q10
Write ₹432 as an expression of notes and coins in two ways and identify the terms. Can you think of some more ways of giving ₹432?
(3 marks)
2
4 QUESTIONS
Exercise 2.2
Q11
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
(5 marks)
Q12
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
(5 marks)
Q13
Write the expression for each situation, identify its terms and find the value. (a) Queen Alia gave 100 gold coins each to Princess Elsa and Princess Anna. Elsa doubled her coins; Anna has half left. How many coins do they have together? (b) A metro ticket is ₹40 for an adult and ₹20 for a child. Find the total cost (i) for four adults and three children (ii) for two groups having three adults each. (c) Find the total height of a window from the measurements in the picture (7 panes of 5 cm, 6 bars of 2 cm and 2 frames of 3 cm).
(5 marks)
Q14
Tinker the Terms: Some expressions are given in three columns. In each column one or more terms are changed from the first expression 53 + (−16) = 37. Fill in the blanks doing as little computation as possible.
(3 marks)
3
9 QUESTIONS
Exercise 2.3
Q15
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
(3 marks)
Q16
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 marks)
Q17
Find the values of the following expressions. For each pair, first 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)
(5 marks)
Q18
In each set of expressions identify those that have the same value, without evaluating, using 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
(2 marks)
Q19
Add brackets at appropriate places so that the expressions have the values indicated: (a) 34 − 9 + 12 = 13 (b) 56 − 14 − 8 = 34 (c) −22 − 12 − 10 + 22 = −22
(2 marks)
Q20
Using only reasoning of how terms change their values, fill the blanks to make the expressions equal: (a) 423 + ____ = 419 + ____ (b) 207 − 68 = 210 − ____
(3 marks)
Q21
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.
(3 marks)
Q22
Whenever Jasoda has to subtract 9 from a number, she subtracts 10 and adds 1. 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?
(3 marks)
Q23
Consider the expressions (A) 73 − 14 + 1 and (B) 73 − 14 − 1. Identify the expressions equal to each from: (a) 73 − (14 + 1) (b) 73 − (14 − 1) (c) 73 + (−14 + 1) (d) 73 + (−14 − 1)
(2 marks)
4
EXERCISE 2.4 · 8 QUESTIONS
Distributive Property
Q24
Three friends each order the same two items costing ₹43 and ₹24. If another friend, Sangmu, joins and orders the same items, what is the expression for the total amount to be paid?
(2 marks)
Q25
5 × 4 + 3 ≠ 5 × (4 + 3). Can you explain why? Is 5 × (4 + 3) = 5 × (3 + 4) = (3 + 4) × 5?
(3 marks)
Q26
Use the distributive method to find the products: (a) 95 × 8 (b) 104 × 15 (c) 49 × 50. Is this quicker than the usual multiplication procedure? Which other products might be quicker to find like this?
(5 marks)
Q27
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 □ 3 × ___ (d) (9 + 2) × 4 = 9 × 4 □ 2 × ___ (e) 3 × (___ + 4) = 3 × ___ + ___ (f) (___ + 6) × 4 = 13 × 4 + ___ (g) 3 × (___ + ___) = 3 × 5 + 3 × 2 (h) (___ + ___) × ___ = 2 × 4 + 3 × 4
(3 marks)
Q28
Continue filling in: (i) 5 × (9 − 2) = 5 × 9 − 5 × ___ (j) (5 − 2) × 7 = 5 × 7 − 2 × ___ (k) 5 × (8 − 3) = 5 × 8 □ 5 × ___ (l) (8 − 3) × 7 = 8 × 7 □ 3 × 7 (m) 5 × (12 − ___) = ___ □ 5 × ___ (n) (15 − ___) × 7 = ___ □ 6 × 7 (o) 5 × (___ − ___) = 5 × 9 − 5 × 4 (p) (___ − ___) × ___ = 17 × 7 − 9 × 7
(3 marks)
Q29
Fill in '' or '=' by reasoning (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
(3 marks)
Q30
Here is one way to make 14: 2 × (1 + 6) = 14. Find other ways: ___ × (___ + ___) = 14, four times.
(3 marks)
Q31
Find the sum of the numbers in each picture in at least two different ways and describe how you solved it through expressions. pictures (I) and (II) on page 41 show numbers arranged in groups.
(3 marks)
5
6 QUESTIONS
Exercise 2.5
Q32
Write appropriate expressions for each situation and find their values. (a) Rahim supplies 9 kg of mangoes each day and Shyam supplies 11 kg each day to a market that operates on all seven days of the week. Find the number of kg supplied by them 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 she save by the end of the year? (c) A snail climbs 3 cm up a 10 cm post during the day and slips down 2 cm at night. In how many days will the snail get the treat at the top?
(5 marks)
Q33
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 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 marks)
Q34
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
(3 marks)
Q35
Compare the following pairs using '' or '=' or by reasoning: (a) 49 − 7 + 8 and 49 − 7 + 8 (b) 83 × 42 − 18 and 83 × 40 − 18 (c) 145 − 17 × 8 and 145 − 17 × 6 (d) 23 × 48 − 35 and 23 × (48 − 35) (e) (16 − 11) × 12 and −11 × 12 + 16 × 12 (f) (76 − 53) × 88 and 88 × (53 − 76) (g) 25 × (42 + 16) and 25 × (43 + 15) (h) 36 × (28 − 16) and 35 × (27 − 15)
(5 marks)
Q36
Identify which expressions are equal to the given expression without computation. (a) 83 − 37 − 12: (i) 84 − 38 − 12 (ii) 84 − (37 + 12) (iii) 83 − 38 − 13 (iv) −37 + 83 − 12 (b) 93 + 37 × 44 + 76: (i) 37 + 93 × 44 + 76 (ii) 93 + 37 × 76 + 44 (iii) (93 + 37) × (44 + 76) (iv) 37 × 44 + 93 + 76
(3 marks)
Q37
Choose a number and create ten different expressions having that value.
(3 marks)