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NCERT Class 7 Maths Chapter 2 Arithmetic Expressions Solutions Question Answer
Ganita Prakash Class 7 Chapter 2 Solutions Arithmetic Expressions
NCERT Class 7 Maths Ganita Prakash Chapter 2 Arithmetic Expressions Solutions Question Answer
2.1 Simple Expressions
NCERT In-Text Questions (Page 24)
Choose your favourite number and write as many expressions as you can having that value.
Solution:
Let us choose the number 20.
We can write the arithmetic expressions for the number as follows:
12 + 8 = 20; 4 × 5 = 20; 40 ÷ 2 = 20, etc.
Figure it Out (Page 25)
Question 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
Solution:
(a) 13 + 4 = 17
11 + 6 = 17
Therefore, 13 + 4 = 11 + 6
(b) Since 6 × 5 = 30
22 + 8 = 30
Therefore, 22 + 8 = 6 × 5
(c) Since 64 ÷ 2 = 32
8 × 4 = 32
Therefore, 8 × 4 = 64 ÷ 2
(d) Since 34 – 25 = 9
Therefore, 34 – 9 = 25
Question 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
Solution:
(a) 67 – 19 = 48
(b) 67 – 20 = 47
(c) 35 + 25 = 60
(d) 5 × 11 = 55
(e) 120 ÷ 3 = 40
Clearly, 40 < 47 < 48 < 55 < 60
Therefore, 120 ÷ 3 < 67 – 20 < 67 – 19 < 5 × 11 < 35 + 25
Thus, (e) < (b) < (a) < (d) < (c).
Comparing Expressions
NCERT In-Text Questions (Page 26)
Use ‘>’ or ‘<’ or ‘=’ in each of the following expressions to compare them. Can you do it without complicated calculations? Explain your thinking in each case.
(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
Solution:
Terms in Expressions
NCERT In-Text Questions (Pages 28-29)
Check if replacing subtraction by addition in this way does not change the value of the expression, by taking different examples.
Solution:
Let us take numbers 56 and 17.
56 – 17 = 39
Now, 56 + (-17) = 39
Hence, if we replace the subtraction sign with the addition sign in this way, the value of the expression does not change.
(Answer may vary by taking the different numbers.)
Can you explain why subtracting a number is the same as adding its inverse, using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Solution:
Do it yourself.
In the following table, some expressions are given. Complete the table.
Solution:
Does changing the order in which the terms are added give different values?
Solution:
No. Since in the expression, each term is separated by a ‘+’ sign.
So, changing the order in which the terms are added does not change the value.
As, 4 + 15 +(-9) = 10 or (-9) + 15 + 4 = 10
Swapping and Grouping
NCERT In-Text Questions (Pages 29-31)
Will this also hold when there are terms having negative numbers as well? Take some more expressions and check.
Solution:
Yes, swapping the terms having negative numbers does not change the sum.
As (-3) + (-2) = -5 or (-2) + (-3) = -5
(Answer may vary)
Can you explain why this is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Solution:
Yes
Will this also hold when there are terms having negative numbers as well? Take some more expressions and check.
Solution:
Yes, while adding the terms having negative numbers, grouping them in any order gives the same result.
As,
Can you explain why this is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Solution:
Yes
Does adding the terms of an expression in any order give the same value? Take some more expressions and check. Consider expressions with more than 3 terms also.
Solution:
Can you explain why this is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Solution:
Do it yourself.
Manasa is adding a long list of numbers. It took her five minutes to add them all and she got the answer 11749. Then she realised that she had forgotten to include the fourth number 9055. Does she have to start all over again?
Solution:
No, there is no need to start all over again. She has to add fourth number that is 9055 to the sum she got (11749) to get the correct sum of the list of given numbers.
That is 11749 + 9055 = 20804
More Expressions and Their Terms
NCERT In-Text Questions (Pages 32-33)
If the total number of friends goes up to 7 and the tip remains the same, how much will they have to pay? Write an expression for this situation and identify its terms.
Solution:
Since the total number of friends = 7
and the cost of each dosa = ₹ 23
Therefore, the total cost of 7 dosas = 7 × 23
As the tip remains the same, that is ₹ 5.
So, the expression for describing the total cost is 7 × 23 + 5 = 7 × 23 + 5 = 161 + 5 = ₹ 166.
The terms in the expression 7 × 23 + 5 are 7 × 23, 5.
Think and discuss why she wrote this.
The expression written as a sum of terms is-
Solution:
Do it yourself.
For each of the cases below, write the expression and identify its terms:
If the teacher had called out ‘4’, Ruby would write _________
If the teacher had called out ‘7’, Ruby would write _________
Solution:
If the teacher had called our ‘4’, Ruby would write 8 × 4 + 1
Terms: 8 × 4, 1
If the teacher had called our ‘7’, Ruby would write 4 × 7 + 5
Terms: 4 × 7, 5
Write an expression like the above for your class size.
Solution:
Do it yourself.
Identify the terms in the two expressions above.
Solution:
432 = 4 × 100 + 1 × 20 + 1 × 10 + 2 × 1
Terms: 4 × 100, 1 × 20, 1 × 10, and 2 × 1
432 = 8 × 50 + 1 × 10 + 4 × 5 + 2 × 1
Terms: 8 × 50, 1 × 10, 4 × 5, and 2 × 1
Can you think of some more ways of giving ₹ 432 to someone?
Solution:
Do it yourself.
Figure it Out (Pages 34-35)
Question 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
Solution:
(a) 28 – 7 + 8 = 28 + (-7) + 8
Terms: 28, -7, and 8
28 – 7 + 8
= 28 + (-7) + 8
= 21 + 8 = 29
(b) 39 – 2 × 6 + 11 = 39 + (-2 × 6) + 11
Terms: 39, -2 × 6, and 11
39 – 2 × 6 + 11
= 39 + (-2 × 6) + 11
= 39 + (-12) + 11
= 27 + 11
= 38
(c) 40 – 10 + 10 + 10 = 40 + (-10) + 10 + 10
Terms: 40, -10, 10, and 10
40 – 10 + 10 + 10
= 40 + (-10) + 10 + 10
= 30 + 10 + 10
= 40 + 10
= 50
(d) 48 – 10 × 2 + 16 + 2 = 48 + (-10 × 2) + (16 + 2)
Terms: 48, -10 × 2, 16 + 2
48 – 10 × 2 + 16 + 2
= 48 + (-10 × 2) + (16 + 2)
= 48 + (-20) + (8)
= 28 + 8 = 36
(e) 6 × 3 – 4 × 8 × 5 = (6 × 3) + (-4 × 8 × 5)
Terms: 6 × 3, 4 × 8 × 5
6 × 3 – 4 × 8 × 5
= (6 × 3) + (-4 × 8 × 5)
= 18 + (-160)
= -142
Question 2.
Write a story/situation for each of the following expressions and find their values.
(а) 89 + 21 – 10
(b) 5 × 12 – 6
(c) 4 × 9 + 2 × 6
Solution:
(a) 89 + 21 – 10
Riya and Siya are cousins. They went to the beach, from where Riya collected 89 stones and Siya collected 21 stones. When they reached home, their other younger sister asked them for some stones. They give her 10 stones from their collection. How many stones were left with both Riya and Siya?
89 + 21 – 10 = 89 + 21 + (-10) = 89 + 11 = 100
(b) 5 × 12 – 6
Radha bought 5 pens from a stationery shop. The cost of each pen is ₹ 12. The shopkeeper also gave her a discount of ₹ 6 on the total cost. Find the total amount that she has to pay to the shopkeeper.
5 × 12 – 6 = 5 × 12 + (-6) = 60 + (-6) = 54
(c) 4 × 9 + 2 × 6
Sumit bought 4 pencils, the cost of each pencil is ₹ 9, and he also bought 2 erasers, which cost ₹ 6 each. How much money does he have to spend to buy these items?
4 × 9 + 2 × 6 = 36 + 12 = 48
Question 3.
For each of the following situations, write the expression describing the situation, identify its terms, and find the value of the expression.
(а) Queen Alia gave 100 gold coins to Princess Elsa and 100 gold coins to Princess Anna last year. Princess Elsa used the coins to start a business and doubled her coins. Princess Anna bought jewellery and has only half of the coins left. Write an expression describing how many gold coins Princess Elsa and Princess Anna together have.
(b) A metro train ticket between two stations is ₹ 40 for an adult and ₹ 20 for a child. What is the total cost of the tickets?
(i) for four adults and three children?
(ii) for two groups having three adults each?
(c) Find the total height of the window by writing an expression describing the relationship among the measurements shown in the picture.
Solution:
(a) Number of gold coins Princess Elsa got = 100
Number of gold coins Princess Anna got = 100
Princess Elsa used the coins to start the business and doubled her coins.
So, the number of coins Princess Elsa has = 2 × 100
Princess Anna bought jewellery and has only half of the coins left.
So, the number of coins Princess Anna has = \(\frac{100}{2}\)
Therefore, the total number of gold coins Princess Elsa and Princess Anna have together = 2 × 100 + \(\frac{100}{2}\)
Thus, the expression describing the above situation is 2 × 100 + \(\frac{100}{2}\)
Terms: 2 × 100, \(\frac{100}{2}\)
Now, 2 × 100 + \(\frac{100}{2}\) = 200 + 50 = 250
(b) (i) Metro train ticket for an adult = ₹ 40
So, the metro train ticket for four adults = 4 × 40
Metro train ticket for a child = ₹ 20
So, the metro train ticket for three children = 3 × 20
Therefore, the expression describing the total cost of tickets for four adults and three children is 4 × 40 + 3 × 20
Terms: 4 × 40, 3 × 20
Now, 4 × 40 + 3 × 20 = 160 + 60 = 220
(ii) Metro train ticket for an adult = ₹ 40
So, the metro train ticket for a group of three adults = 3 × 40
Therefore, the expression describing the total cost of tickets for the two groups having three adults each is 2 × (3 × 40).
Terms: 2 × (3 × 40)
Now, 2 × (3 × 40) = 2 × 120 = 240
(c) By observing the given picture, the total height of the window = number of gaps × 5 cm + number of grills × 2 cm + number of borders × 3 cm = 7 × 5 + 6 × 2 + 2 × 3
Terms: 7 × 5, 6 × 2, 2 × 3
Now, 7 × 5 + 6 × 2 + 2 × 3 = 35 + 12 + 6 = 47 + 6 = 53
Tinker the Terms I
NCERT In-Text Questions (Pages 36-37)
Some expressions are given in the following three columns. In each column, one or more terms are changed from the first expression. Go through the example (in the first column) and fill in the blanks, doing as little computation as possible.
Solution:
Figure it Out (Pages 37-38)
Question 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
Solution:
(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
Question 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)
Solution:
(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
Question 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)
Solution:
(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.
Question 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
Solution:
(a)
Expressions having the same terms have the same value. Therefore, 319 – 537 and -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.
Question 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
Solution:
(a) 34 – (9 + 12) = 34 – 21 = 13
(b) (56 – 14) – 8 = 42 – 8 = 34
(c) -22 – (12 + 10) + 22 = -22 – 22 + 22 = -22
Question 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 – ________
Solution:
(a) 423 + 419 = 419 + 423
(b) 207 – 68 = 210 – 71
Question 7.
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
Solution:
Here are a few expressions formed by using numbers 2, 3, and 5 and the operators ‘+’ and ‘-‘ and brackets having different values.
(2 + 3) – 5 = 5 – 5 = 0,
5 + (3 – 2) = 5 + 1 = 6,
-5 + (2 – 3) = -5 + (-1) = -6,
(-2 + 3) – 5 = 1 – 5 = – 4, etc.
Question 8.
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.
Solution:
(a) Yes, she will always get the correct answer if she subtracts 10 from a number and then adds 1 to the result instead of directly subtracting 9 from the number, because subtracting 10 and adding 1, i.e., -10 + 1 = -9, is equivalent to subtracting 9 from the number.
As 36 – 9 = 27 or (36 – 10) + 1 = 26 + 1 = 27
(b) Do it yourself.
Question 9.
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.
(a) 73 – (14 + 1)
(b) 73 – (14 – 1)
(c) 73 + (-14 + 1)
(d) 73 + (-14 – 1)
Solution:
Given expressions:
73 – 14 + 1 = 60 and 73 – 14 – 1 = 58
Now,
(a) 73 – (14 + 1) = 73- 15 = 58
(b) 73 – (14 – 1) = 73 – 13 = 60
(c) 73 + (-14 + 1) = 73 – 13 = 60
(d) 73 + (-14 – 1) = 73 + (-15) = 58
Hence, expressions (b) and (c) are equal to the expression 73 – 14 + 1, and expressions (a) and (d) are equal to the expression 73 – 14 – 1.
Removing Brackets-II
NCERT In-Text Questions (Pages 39-40)
If another friend, Sangmu, joins them and orders the same items, what will be the expression for the total amount to be paid?
Solution:
If another friend, Sangmu, joins them (Lhamo and Norbu) and orders the same items, then the expression for the total amount will be 3 × (43 + 24).
5 × 4 + 3 ≠ 5 × (4 + 3). Can you explain why?
Is 5 × (4 + 3) = 5 × (3 + 4) = (3 + 4) × 5?
Solution:
Expression 5 × 4 + 3 means 3 more than 5 × 4, which is equal to 23, but 5 × (4 + 3) means 5 times (4 + 3), which is equal to 35.
Hence, 5 × 4 + 3 ≠ 5 × (4 + 3)
5 × (4 + 3), 5 × (3 + 4), and (3 + 4) × 5 have the same meaning, which is 5 times the sum of 3 and 4, and give the same value.
Hence, 5 × (4 + 3) = 5 × (3 + 4) = (3 + 4) × 5
Tinker the Terms II
NCERT In-Text Questions (Page 41)
Use this method to find the following products:
(а) 95 × 8
(b) 104 × 15
(c) 49 × 50
Is this quicker than the multiplication procedure you use generally?
Solution:
(a) 95 × 8 = (100 – 5) × 8
= 100 × 8 – 5 × 8
= 800 – 40
= 760
(b) 104 × 15 = (100 + 4) × 15
= 100 × 15 + 4 × 15
= 1500 + 60
= 1560
(c) 49 × 50 = (50 – 1) × 50
= 50 × 50 – 50 × 1
= 2500 – 50
= 2450
Yes, this procedure is quicker than the general multiplication procedure.
Which other products might be quicker to find, like the ones above?
Solution:
Do it yourself.
Figure it Out (Pages 41-42)
Question 1.
Fill in the blanks with numbers and boxes by signs, so that the expressions on both sides are equal.
(а) 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
(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
Solution:
(а) 3 × (6 + 7) = 3 × 6 + 3 × 7
(b) (8 + 3) × 4 = 8 × 4 + 3 × 4
(c) 3 × (5 + 8) = 3 × 5 + 3 × 8
(d) (9 + 2) × 4 = 9 × 4 + 2 × 4
(e) 3 × (10 + 4) = 30 + 12
(f) (13 + 6) × 4 = 13 × 4 + 24
(g) 3 × (5 + 2) = 3 × 5 + 3 × 2
(h) (2 + 3) × 4 = 2 × 4 + 3 × 4
(i) 5 × (9 – 2) = 5 × 9 – 5 × 2
(j) (5 – 2) × 7 = 5 × 7 – 2 × 7
(k) 5 × (8 – 3) = 5 × 8 – 5 × 3
(l) (8 – 3) × 7 = 8 × 7 – 3 × 7
(m) 5 × (12 – 3) = 60 – 5 × 3
(n) (15 – 6) × 7 = 105 – 6 × 7
(o) 5 × (9 – 4) = 5 × 9 – 5 × 4
(p) (17 – 9) × 7 = 17 × 7 – 9 × 7
Question 2.
In the boxes below, fill in ‘<’, ‘>’ or ‘=’ after analysing the expressions on the LHS and RHS. Use reasoning and understanding of terms and brackets to figure this out, and not by evaluating the expressions.
(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
Solution:
(a) (8 – 3) × 29 > (3 – 8) × 29
Because, (3 – 8) × 29 = -(8 – 3) × 29
⇒ (8 – 3) × 29 > (3 – 8) × 29
(b) 15 + 9 × 18 < (15 + 9) × 18
Because, (15 + 9) × 18 = 15 × 18 + 9 × 18 and 15 × 18 > 15
So, 15 + 9 × 18 < (15 + 9) × 18
(c) 23 × (17 – 9) < 23 × 17 + 23 × 9
Because, 23 × (17 – 9) = 23 × 17 – 23 × 9
Clearly, 23 × 17 > 23 × 17 – 23 × 9
⇒ 23 × (17 – 9) < 23 × 17 + 23 × 9
(d) (34 – 28) × 42 = 34 × 42 – 28 × 42
Question 3.
Here is one way to make 14: 2 × (1 + 6) = 14. Are there other ways of getting 14? Fill them out below:
(a) ________ × (________ + ________) = 14
(b) ________ × (________ + ________) = 14
(c) ________ × (________ + ________) = 14
(d) ________ × (________ + ________) = 14
Solution:
(a) 2 × (5 + 2) = 14
(b) 2 × (3 + 4) = 14
(c) 2 × (4 + 3) = 14
(d) 2 × (6 + 1) = 14
Question 4.
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.
Solution:
For I: 5 × 4 + 4 × 8 = 20 + 32 = 52
or 4 × (4 + 8) + 4 = 4 × 12 + 4 = 52
For II: 8 × (5 + 6) = 8 × 11 = 88
or 8 × 5 + 8 × 6 = 40 + 48 = 88
Figure it Out (Pages 42-44)
Question 1.
Read the situations given below. Write appropriate expressions for each of them and find their values.
(a) The district market in Begur operates on all seven days of the week. Rahim supplies 9 kg of mangoes each day from his orchard, and Shyam supplies 11 kg of mangoes each day from his orchard to this market. Find the number of mangoes supplied by them in a week to the local district market.
(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 is the amount Binu will save by the end of the year?
(c) During the daytime, a snail climbs 3 cm up a post, and during the night, while asleep, accidentally slips down by 2 cm. The post is 10 cm high, and a delicious treat is on top. In how many days will the snail get the treat?
Solution:
(a) Supplies of mangoes by Rahim in the market each day = 9 kg
Supplies of mangoes by Shyam in the market each day = 11 kg
Total supplies of mangoes in the market on each day = (9 + 11) kg
Therefore, total supplies of mangoes in the market in all 7 days = 7 × (9 + 11) kg
= 7 × 20
= 140 kg
(b) Binu’s per month earning = ₹ 20,000
Binu’s total monthly expenditures = ₹ 5,000 on rent + ₹ 5,000 on food + ₹ 2,000 on other expenses
= 5,000 + 5,000 + 2,000
Therefore, Binu’s monthly savings = ₹ 20,000 – ₹(5,000 + 5,000 + 2,000)
= ₹ 20,000 – ₹ 12,000
= ₹ 8,000
Thus, Binu’s total yearly savings = 12 × 8000 = 96000
Hence, Binu will save ₹ 96000 by the end of the year.
(c) Since the snail climbs 3 cm up the post in daytime and slips down by 2 cm at night.
So, the distance climbed by the snail of the post = 3 – 2 = 1 cm in a day.
∴ The distance climbed in 7 days = 7 cm
The height of the post is 10 cm.
The distance climbed on the 8th day before slipping = 7 + 3 = 10 cm
So, the snail will take 8 days to reach the top of the post and get the delicious treat.
Question 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 expressions below 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
Solution:
Number of days in a week except Tuesday and Saturday = 7 – 2
Since Melvin reads a two-page story every day except Tuesday and Saturday.
Therefore, number of stories read in a week = 1 × (7 – 2)
So, number of stories read in 8 weeks = 8 × 1 × (7 – 2)
= 8 × (7 – 2) or (7 – 2) × 8 [Expression (b)]
or 7 × 8 – 2 × 8 [Expression (g)]
Only expressions (b) and (g) describe this scenario.
Question 3.
Find different ways of evaluating the following expressions:
(а) 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10
(b) 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1
Solution:
(a) 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10
= (1 + 3 + 5 + 7 + 9) + (-2 – 4 – 6 – 8 – 10)
= 25 + (-30)
= -5
or
1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10
= (1 – 2) + (3 – 4) + (5 – 6) + (7 – 8) +(9 – 10)
= (-1) + (-1) + (-1) + (-1) + (-1)
= -5
(b) 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1
= (1 – 1) + (1 – 1) + (1 – 1) + (1 – 1) + (1 – 1)
= 0 + 0 + 0 + 0 + 0
= 0
or
1 – 1 + 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1
= (1 + 1 + 1 + 1 + 1) + (-1 – 1 – 1 – 1 – 1)
= 5 + (-5)
= 0
Question 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)
Solution:
(a) 49 – 7 + 8 = 49 – 7 + 8
(∵ All the terms on both sides are the same)
(b) 83 × 42 > 83 × 40
∴ 83 × 42 – 18 > 83 × 40 – 18
(c) 17 × 8 > 17 × 6
⇒ -17 × 8 < -17 × 6
∴ 145 – 17 × 8 < 145 – 17 × 6
(d) 23 × (48 – 35) = 23 × 48 – 23 × 35
and 35 < 23 × 35 23 × 48 – 35 > 23 × (48 – 35)
(e) (16 – 11) × 12 = 16 × 12 – 11 × 12 = -11 × 12 + 16 × 12
∴ (16 – 11) × 12 = -11 × 12 + 16 × 12
(f) (76 – 53) × 88 = 76 × 88 – 53 × 88 = -(53 – 76) × 88
∴ (76 – 53) × 88 > 88 × (53 – 76)
(g) 43 + 15 = 42 + 1 + 15 = 42 + 16
⇒ 25 × (43 + 15) = 25 × (42 + 16)
∴ 25 × (42 + 16) = 25 × (43 + 15)
(h) 35 × (27 – 15) = 35 × (28 – 16)
∴ 36 × (28 – 16) > 35 × (27 – 15)
Question 5.
Identify which of the following expressions are equal to the given expression without computation. You may rewrite the expressions using terms or removing brackets. There can be more than one expression that is equal to the given expression.
(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
Solution:
(a) 83 – 37 – 12 = 83 – 37 – 12 + (1 – 1)
= (83 + 1) – 37 – 1 – 12
= 84 – 38 – 12 (option (i))
= 34
Or
83 – 37 – 12 = -37 + 83 – 12
= 46 – 12
= 34 (option (iv))
Hence, (i) and (iv) are equal to the given expression 83 – 37 – 12.
(b) (iv) 37 × 44 + 93 + 76
Rearrange the terms, and we get 93 + 37 × 44 + 76, which is equal to the given expression.
Hence, (iv) is equal to the given expression 93 + 37 × 44 + 76.
Question 6.
Choose a number and create ten different expressions having that value.
Solution:
Do it yourself.
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