NCERT Solutions for Ch2 Arithmetic Expressions Class 7 Math
Book Solutions1
Answer
Let’s choose the number 12. Expressions with the value 12 are:• 10 + 2 = 12
• 15 - 3 = 12
• 3 × 4 = 12
• 24 ÷ 2 = 12 etc.
2
(a) 13 + 4 = ______ + 6
(b) 22 + ______ = 6 × 5
(c) 8 × ______ = 64 ÷ 2
(d) 34 - ______ = 25
Answer
(a) 13 + 4 = 17, so 11 + 6 = 17. The blank is 11.(b) 6 × 5 = 30, so 22 + 8 = 30. The blank is 8.
(c) 64 ÷ 2 = 32, so 8 × 4 = 32. The blank is 4.
(d) 34 - 9 = 25. The blank is 9.
3
(a) 67 - 19
(b) 67 - 20
(c) 35 + 25
(d) 5 × 11
(e) 120 ÷ 3
Answer
Calculate each expression:• 67 - 19 = 48
• 67 - 20 = 47
• 35 + 25 = 60
• 5 × 11 = 55
• 120 ÷ 3 = 40
Ascending order: 40 < 47 < 48 < 55 < 60
So, the order is: 120 ÷ 3 < 67 - 20 < 67 - 19 < 5 × 11 < 35 + 25.
Thus, (e) < (b) < (a) < (d) < (c).
4
Answer
(a) 245 + 289 > 246 + 285
245 is 1 less than 246
But 289 is 4 more than 285
So overall, the left side is 3 more than the right side.
(b) 273 − 145 = 272 − 144
273 is 1 more than 272
145 is also 1 more than 144
So both changes cancel each other.
(c) 364 + 587 < 363 + 589
364 is 1 more than 363
But 587 is 2 less than 589
So overall, the left side is 1 less.
(d) 124 + 245 < 129 + 245
124 is 5 less than 129
245 is the same on both sides
So the left side is 5 less.
(e) 213 − 77 < 214 − 76
213 is 1 less than 214
But 77 is 1 more than 76
So the left side becomes 2 less.
5
Suppose we have the expression 30 + 5 × 4 without any brackets. Does it have no meaning? When there are expressions having multiple operations, and the order of operations is not specified by the brackets, we use the notion of terms to determine the order. Terms are the parts of an expression separated by a ‘+’ sign. For example, in 12+7, the terms are 12 and 7, as marked below.
We will keep marking each term of an expression as above. Note that this way of marking the terms is not a usual practice. This will be done until you become familiar with this concept. Now, what are the terms in 83 – 14? We know that subtracting a number is the same as adding the inverse of the number. Recall that the inverse of a given number has the sign opposite to it. For example, the inverse of 14 is –14, and the inverse of –14 is 14. Thus, subtracting 14 from 83 is the same as adding –14 to 83. That is,
Thus, the terms of the expression 83 – 14 are 83 and –14.
Q1: Check if replacing subtraction by addition in this way does not change the value of the expression, by taking different examples.
Answer
Subtraction can be written as adding the inverse. For example:• 83 - 14 = 83 + (-14). Calculate: 83 - 14 = 69, and 83 + (-14) = 69.
• 20 - 5 = 20 + (-5). Calculate: 20 - 5 = 15, and 20 + (-5) = 15.
In both cases, the value remains the same.
6
Answer
In the Token Model of Integers:
• +1 token = positive number
• −1 token = negative number
Subtracting a number means removing positive tokens.
But removing +1 tokens is the same as adding −1 tokens.
Example:
• 5 − 3 → Remove 3 positive tokens from 5 → Left with 2
• 5 + (−3) → Add 3 negative tokens to 5 → They cancel with 3 positives → Left with 2
Conclusion:
Subtracting a number is the same as adding its opposite.
So, 5 − 3 = 5 + (−3).
7
Answer
8
Answer
No, changing the order of addition does not change the value. For example, 6 + (-4) = 2, and (-4) + 6 = 2.This is due to the commutative property of addition.
9
Answer
Yes, it holds. For example:• (-5) + 7 = 2, and 7 + (-5) = 2.
• (-3) + (-2) = -5, and (-2) + (-3) = -5.
Swapping terms does not change the value.
10
Answer
Token Model of Integers :
• +1 token = positive number
• −1 token = negative number
• A +1 and −1 together cancel each other (because +1 + (−1) = 0)
Example:
Start with 0.
Add 5 positive and 5 negative tokens:
They cancel each other in pairs → Final total = 0
Why it matters:
Positive and negative tokens balance each other.
The final value depends on which type is more.
Example:
3 − 5 → 3 positives, 5 negatives
Cancel 3 pairs → Left with 2 negatives → Answer: −2
This shows how subtraction can lead to negative numbers using the token model.
11
Answer
Yes, adding the terms of an expression in any order gives the same value. This is because addition is commutative and associative, which means:
• Commutative: Changing the order of numbers doesn’t change the sum.
(Example: 4 + 5 = 5 + 4 = 9)
• Associative: Grouping numbers differently doesn’t change the sum.
(Example: (2 + 3) + 4 = 2 + (3 + 4) = 9)
Let’s check with more terms:
Example 1:
7 + (-2) + 5 + (-3)
Try adding in different orders:
• (7 + 5) + (-2) + (-3) = 12 - 2 - 3 = 7
• 7 + (-2) + (-3) + 5 = 7 - 2 - 3 + 5 = 7
• (-2 + 5) + (-3 + 7) = 3 + 4 = 7
All give the same result.
12
Answer
In the Token Model:
• Positive numbers are shown as positive tokens (+1 each)
• Negative numbers are shown as negative tokens (–1 each)
• A positive token and a negative token together cancel out (because +1 + (–1) = 0)
Example:
Suppose you have 3 positive tokens (+3) and you add 2 more positive tokens (+2): +3 + +2 = +5
You now have 5 positive tokens.
If you change the order:
+2 + +3 = +5
You still get 5 tokens. So, the order doesn't matter.
13
Answer
No, she doesn’t need to start over.She can add 9055 to 11749: 11749 + 9055 = 20804.
This is because addition is commutative and associative.
14
Answer
Cost of 4 dosas = 4 × 23Can the total amount with tip be written as 4 × 23 + 5? Evaluating it, we get
Thus, 4 × 23 + 5 is a correct way of writing the expression.
15
Answer
Cost of 7 dosas = 7 × 23. Total cost with tip = 7 × 23 + 5.Terms: 7 × 23, 5.
Evaluate: 7 × 23 = 161, 161 + 5 = 166. They pay ₹166.
The terms in the expression 7 × 23 + 5 are 7 × 23, 5.
16
Answer
Ruby wrote 6 × 5 + 3 (understood as 3 more than 6 × 5)
17
Answer
Ruby observed what happened in the game:
• The children had to form groups of 5.
She noticed that there were 6 full groups of 5 students each.
• That makes 6 × 5 = 30 students.
• But the total number of children playing was 33.
• So, 3 children were left out who could not fit into a full group of 5.
Therefore, Ruby wrote:
6 × 5 + 3,
which means:
• 30 students are in complete groups (6 groups of 5),
• And 3 students are left out.
Final Expression:
6 × 5 + 3 — written as a sum of terms:
(6 × 5) + 3
18
If the teacher had called out ‘4’, Ruby would write ____________
If the teacher had called out ‘7’, Ruby would write ____________
Answer
• If the teacher had called out ‘4’, Ruby would writeExpression: 8 × 4 + 1.
Terms: 8 × 4, 1.
• If the teacher had called out ‘4’, Ruby would write
Expression: 4 × 7 + 5.
Terms: 4 × 7, 5.
19
Answer
Do it Yourself!20
Answer
There is more than one possibility. For example,432 = 4 × 100 + 1 × 20 + 1 × 10 + 2 × 1
Meaning: 4 notes of ₹100, 1 note of ₹20, 1 note of ₹10 and 2 notes of ₹1
432 = 8 × 50 + 1 × 10 + 4 × 5 + 2 × 1
Meaning: 8 notes of ₹50, 1 note of ₹10, 4 notes of ₹5 and 2 notes of ₹1
21
Answer
• 432 = 4 × 100 + 1 × 20 + 1 × 10 + 2 × 1.Terms: 4 × 100, 1 × 20, 1 × 10, 2 × 1.
• 432 = 8 × 50 + 1 × 10 + 4 × 5 + 2 × 1.
Terms: 8 × 50, 1 × 10, 4 × 5, 2 × 1.
22
Answer
Some more ways to gave ₹432 to someone are as follows:• 4 × 100 + 3 × 10 + 2 × 1 = 400 + 30 + 2 = 432.
Terms: 4 × 100, 3 × 10, 2 × 1.
• 2 × 100 + 4 × 50 + 3 × 10 + 2 × 1 = 200 + 200 + 30 + 2 = 432.
Terms: 2 × 100, 4 × 50, 3 × 10, 2 × 1.
23
(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
Answer
(a) Terms: 28, -7, 8.
Expression: 28 + (-7) + 8 = 21 + 8 = 29.
(b) Terms: 39, -2 × 6, 11.
Expression: 39 + (-2 × 6) + 11 = 39 - 12 + 11 = 27 + 11 = 38.
(c) Terms: 40, -10, 10, 10.
Expression: 40 + (-10) + 10 + 10 = 30 + 10 + 10 = 40 + 10 = 50.
(d) Terms: 48, -10 × 2, 16 ÷ 2.
Expression: 48 + (-10 × 2) + (16 ÷ 2) = 48 - 20 + 8 = 36.
(e) Terms: 6 × 3, -4 × 8 × 5.
Expression: 6 × 3 + (-4 × 8 × 5) = 18 + (-160) = -142.
24
(a) 89 + 21 – 10
(b) 5 × 12 – 6
(c) 4 × 9 + 2 × 6
Answer
(a) Story: Ria had 89 candies, got 21 more, and gave 10 to her friend. How many candies does she have now?
Value: 89 + 21 + (-10) = 100.
(b) Story: A shop sells 5 packs of 12 pencils each but removes 6 defective ones. How many pencils are left?
Value: 5 × 12 - 6 = 60 + (-6) = 54.
(c) Story: A family buys 4 pizzas costing ₹9 each and 2 drinks costing ₹6 each. What is the total cost?
Value: 4 × 9 + 2 × 6 = 36 + 12 = 48.
25
(a) 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 tickets:
(i) for four adults and three children?
(ii) for two groups having three adults each?
Answer
(a) Number of gold coins Princess Elsa got = 100Number 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 = 100/2
Therefore, the total number of gold coins Princess Elsa and Princess Anna have together = 2 × 100 + 100/2
Thus, the expression describing the above situation is 2 × 100 + 100/2
Terms: 2 × 100, 100/2
Now, 2 × 100 + 100/2 = 200 + 50 = 250
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 × 3Now, 7 × 5 + 6 × 2 + 2 × 3 = 35 + 12 + 6 = 47 + 6 = 53
26
What happens to the value of an expression if we increase or decrease the value of one of its terms?
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.
Answer
27
Answer
Yes, –15 is one more than –16, so the value will be 1 more than 37.28
Answer
Yes, –17 is one less than –16, so the value will be 1 less than 37.29
(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 Answer
(a) 24 + (6 - 4) = 24 + 6 - 4 = 26(b) 38 + (9 - 4) = 38 + 9 - 4 = 43
(c) 24 - (6 + 4) = 24 - 6 - 4 = 14
(d) 24 - 6 - 4 = 24 - 6 - 4 = 14
(e) 27 - (8 + 3) = 27 - 8 - 3 = 16
(f) 27 - (8 - 3) = 27 - 8 + 3 = 22
30
(a) 14 + (12 + 10)
(b) 14 - (12 + 10)
(c) 14 + (12 - 10)
(d) 14 - (12 - 10)
(e) -14 + 12 – 10
(f) 14 - (-12 - 10)
Answer
(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) No brackets to remove. Expression: -14 + 12 - 10 = -14 + 2 = -12
(f) 14 - (-12 - 10) = 14 + 12 + 10 = 14 + 22 = 36
31
(a) (6 + 10) - 2 and 6 + (10 - 2)
(b) 16 - (8 - 3) and (16 - 8) – 3
(c) 27 - (18 + 4) and 27 + (-18 - 4)
Answer
(a) Initial Guess: Different, due to bracket placement.
Values: (6 + 10) - 2 = 16 - 2 = 14,
6 + (10 - 2) = 6 + 8 = 14.
Conclusion: They are equal because (a + b) - c = a + (b - c).
(b) Initial Guess: Different.
Values: 16 - (8 - 3) = 16 - 5 = 11,
(16 - 8) - 3 = 8 - 3 = 5.
Conclusion: They are not equal.
(c) Initial Guess: Same, as - (a + b) = -a - b.
Values: 27 - (18 + 4) = 27 - 22 = 5,
27 + (-18 - 4) = 27 - 18 - 4 = 5.
Conclusion: They are equal.
32
(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
Answer
Expressions having the same terms have the same value. Therefore, the expressions that have the same value are:
• 319 – 537
• –537 + 319
(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.
33
Q5: 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
Answer
(a) To get 13, we need to first subtract 9 from 34, then add 12.
So, (34 – 9) + 12 = 25 + 12 = 37 (not correct).
Instead, try 34 – (9 + 12):
34 – (9 + 12) = 34 – 21 = 13.
So, the expression is 34 – (9 + 12) = 13.
(b) To get 34, we need to subtract 14 and 8 from 56 in the correct order.
(56 – 14) – 8 = 42 – 8 = 34.
So, the expression is (56 – 14) – 8 = 34.
(c) To get 22, we need to group the terms carefully.
–22 – (12 + 10) + 22 = –22 – 22 + 22 = –22.
So, the expression is –22 – (12 + 10) + 22 = –22.
34
(a) 423 + ______= 419 + ______
(b) 207 – 68 = 210 – ______
Answer
(a) We need to make both sides equal.
423 + ___ = 419 + ___.
423 is 4 more than 419 (423 – 419 = 4).
So, the number on the right side should be 4 more than the number on the left side.
If we put 0 on the left, then 0 + 4 = 4 on the right.
423 + 0 = 419 + 4.
So, the blanks are 0 and 4.
(b) 210 is 3 more than 207
So to keep both sides equal, we also need to make the second number on the right side 3 more than 68.
207 − 68 = 210 – 71
Because increasing the first number by 3 and also increasing the second number by 3 keeps the value the same.
35
Answer
Let’s use 2, 3, and 5 with + and – to get different values:• 2 + 3 + 5 = 10,
• 2 + 3 – 5 = 0,
• 2 – 3 + 5 = 4,
• 2 – (3 + 5) = –6,
• 5 + 3 – 2 = 6, etc.
36
(a) Do you think she always gets the correct answer? Why?
(b) Can you think of other similar strategies? Give some examples.
Answer
(a) Yes, Jasoda always gets the correct answer.
Subtracting 10 and adding 1 is the same as subtracting 9 because 10 – 1 = 9.
For example, 36 – 9 = 27.
Jasoda does (36 – 10) + 1 = 26 + 1 = 27, which is correct.
(b) Yes, we can use other strategies:
Instead of subtracting 9, subtract 8 and subtract 1 more: 36 – 9 = 36 – 8 – 1 = 28 – 1 = 27.
Or, subtract 5 and subtract 4 more: 36 – 9 = 36 – 5 – 4 = 31 – 4 = 27.
Both give the correct answer.
37
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)
Answer
(a) 73 – (14 + 1) = 73 – 15 = 58.
Expression a) 73 – 14 + 1 = 59 + 1 = 60 (not equal).
Expression b) 73 – 14 – 1 = 59 – 1 = 58 (equal).
So, it matches expression b).
(b) 73 – (14 – 1) = 73 – 13 = 60.
Expression a) 73 – 14 + 1 = 60 (equal).
Expression b) 73 – 14 – 1 = 58 (not equal).
So, it matches expression a).
(c) 73 + (–14 + 1) = 73 + (–13) = 73 – 13 = 60.
Expression a) 73 – 14 + 1 = 60 (equal).
Expression b) 73 – 14 – 1 = 58 (not equal).
So, it matches expression a).
(d) 73 + (–14 – 1) = 73 + (–15) = 73 – 15 = 58.
Expression a) 73 – 14 + 1 = 60 (not equal).
Expression b) 73 – 14 – 1 = 58 (equal).
So, it matches expression b).
38
Answer
As each of them had one vegetable cutlet and one rasagulla, each of their shares can be represented by 43 + 24.39
Answer
Each person had 1 vegetable cutlet and 1 rasgulla.Cost of one vegetable cutlet = ₹43
Cost of one rasgulla = ₹24
Correct expression is: 2 × (43 + 24)
40
Answer
Cost of one vegetable cutlet = ₹43
Cost of one rasgulla = ₹24
Total cost for one person = 43 + 24 = ₹67
Now, there are 3 people (Lhamo, Norbu, and Sangmu).
So, the total amount to be paid = 3 × (43 + 24)
= 3 × 67 = ₹201
Expression: 3 × (43 + 24)
41
Answer
As 63 × 18 means 63 times 18,63 × 18 = (53 + 10) × 18
= 53 ×18 + 10×18
= 954 + 180
= 1134.
42
(a) 95 × 8
(b) 104 × 15
(c) 49 × 50
Answer
(a) Write 95 as (100 – 5): 100 × 8 = 800
5 × 8 = 40
800 – 40 = 760
So, 95 × 8 = 760.
(b) Write 104 as (100 + 4): 100 × 15 = 1500
4 × 15 = 60
1500 + 60 = 1560
So, 104 × 15 = 1560.
(c) Write 49 as (50 – 1): 50 × 50 = 2500
1 × 50 = 50
2500 – 50 = 2450
So, 49 × 50 = 2450.
43
Answer
Yes, this method can be quicker because it uses easier numbers like 100 or 50 and then adjusts with simple subtraction or addition, instead of doing long multiplication step by step.44
Answer
Products like 98 × 25, 99 × 10, 103 × 15, or 51 × 50 might be quicker because they can be written as (100 – 2) × 25, (100 – 1) × 10, (100 + 3) × 15, or (50 + 1) × 50, and solved using the same easy method.45
Answer
(a) 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
46
Answer
(a) (8 – 3) × 29 > (3 – 8) × 29
Explanation:
• (8 – 3) = 5, so the left side is 5 × 29 = 145
• (3 – 8) = –5, so right side is –5 × 29 = –145
Since 145 is greater than –145,
145 > –145
(b) 15 + 9 × 18 < (15 + 9) × 18
Explanation:
• Follow BODMAS:
Left side → 9 × 18 = 162 → 15 + 162 = 177
Right side → (15 + 9) × 18 = 24 × 18 = 432
⇒ 177 < 432
(c) 23 × (17 – 9) < 23 × 17 + 23 × 9
Explanation:
This shows the distributive property:
Left side: 23 × (17 – 9) = 23 × 8 = 184
Right side: 23 × 17 = 391, 23 × 9 = 207
391 + 207 = 598
⇒ 184 < 598
(d) (34 – 28) × 42 = 34 × 42 – 28 × 42
Explanation:
Left side: (34 – 28) × 42 = 6 × 42 = 252
Right side: 34 × 42 = 1428, 28 × 42 = 1176 → 1428 – 1176 = 252
Both sides are equal.
47
(a) ___ × (___ + ___ ) = 14
(b) ___ × (___ + ___ ) = 14
(c) ___ × (___ + ___ ) = 14
(d) ___ × (___ + ___ ) = 14
Answer
(a) 7 × (1 + 1) = 14(b) 2 × (5 + 2) = 14
(c) 1 × (10 + 4) = 14
(d) 14 × (1 + 0) = 14
48
Answer
(a) 5 × 4 + 4 × 8 = 20 + 32 = 52
or 4 × (4 + 8) + 4 = 4 × 12 + 4 = 52
(b) 8 × (5 + 6) = 8 × 11 = 88
or 8 × 5 + 8 × 6 = 40 + 48 = 88
49
(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 a 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 its top. In how many days will the snail get the treat?
Answer
(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.
50
(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
Answer
Number of days in a week except Tuesday and Saturday = 7 – 2Since 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.
51
(a) 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 – 10
(b) 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1
Answer
(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
52
(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)
Answer
(a) 49 - 7 + 8 = 49 - 7 + 8.
(∵ All the terms on both sides are the same)
(b) 83 × 42 = 83 × (40 + 2) = 83 × 40 + 83 × 2.
So, 83 × 42 - 18 > 83 × 40 - 18.
(c) 17 × 8 = 136, 17 × 6 = 102. 145 - 136 < 145 - 102.
So, 145 - 17 × 8 < 145 - 17 × 6.
(d) 23 × 48 - 35 > 23 × 13 (since 48 > 13).
So, 23 × 48 - 35 > 23 × (48 - 35).
(e) (16 - 11) × 12 = 5 × 12. -11 × 12 + 16 × 12 = (16 - 11) × 12 = 5 × 12.
So, (16 - 11) × 12 = -11 × 12 + 16 × 12.
(f) (76 - 53) = 23, (53 - 76) = -23.
So, 23 × 88 > -23 × 88.
Therefore, (76 - 53) × 88 > 88 × (53 - 76).
(g) 42 + 16 = 58, 43 + 15 = 58.
So, 25 × (42 + 16) = 25 × (43 + 15).
(h) 28 - 16 = 12, 27 - 15 = 12.
But 36 > 35.
So, 36 × (28 - 16) > 35 × (27 - 15).
53
Q5: 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 which 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
Answer
(a) (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) The expressions equal to 93 + 37 × 44 + 76 are:
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.
54
Answer
Let’s choose the number 10. Ten different expressions are:• 5 + 5
• 20 – 10
• 2 × 5
• 50 ÷ 5
• 15 – 5
• 7 + 3
• 4 × 2 + 2
• 30 – 20
• 10 × 1
• 25 – 15