Question Answer For All Chapters – Ganita Prakash Class 7th
2.1 Simple Expressions (Page 24)
Choose your favourite number and write as many expressions as you can having that value.
Ans: We can write different arithmetic expressions for this number as follows:
12 + 8 = 20
4 × 5 = 20
40 ÷ 2 = 20
25 – 5 = 20
2 × 10 = 20
100 ÷ 5 = 20
Thus, many different expressions can represent the value 20.
Figure it Out (Page 25)
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
Ans:
(a) 13 + 4 = ____ + 6
13 + 4 = 17
So, ____ + 6 = 17
____ = 17 – 6 = 11
13 + 4 = 11 + 6
(b) 22 + ____ = 6 × 5
6 × 5 = 30
So, 22 + ____ = 30
____ = 30 – 22 = 8
22 + 8 = 6 × 5
(c) 8 × ____ = 64 ÷ 2
64 ÷ 2 = 32
So, 8 × ____ = 32
____ = 32 ÷ 8 = 4
8 × 4 = 64 ÷ 2
(d) 34 – ____ = 25
So, ____ = 34 – 25 = 9
34 – 9 = 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
Ans: (a) 67 – 19 = 48
(b) 67 – 20 = 47
(c) 35 + 25 = 60
(d) 5 × 11 = 55
(e) 120 ÷ 3 = 40
Now, arrange them in ascending (increasing) order:
40, 47, 48, 55, 60
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.
Ans:
(a) Compare 245 + 289 and 246 + 285.
→ If we increase 245 by 1, it becomes 246, but we increase 285 by 1 it becomes 286.
(245 + 1) + 289 ______ 246 + (285 +1)
246 + 289 ______ 246 + 286
246 + 289 > 246 + 286
So left side is 3 more than right side.
∴ LHS > RHS
(b) Compare 273 – 145 and 272 – 144.
We add 1 to both sides
273 + 1 – 145 ______ 272 + 1 – 144
274 – 145 ______ 273 – 144
Both sides are same.
∴ LHS = RHS
(c) Compare 364 + 587 and 363 + 589.
→ If we increase 587 by 1, it becomes 588, but increase 363 by 1, it becomes 364.
364 + (587 + 1) ______ (363 + 1 )+ 589
364 + 588 ______ 364 + 589
364 + 588 ______ 364 + 589
So left side is 2 less than right side.
∴ LHS < RHS
(d) Compare 124 + 245 and 129 + 245.
→ If we increase 124 by 5, it becomes 129. The second term is same (245).
(124 + 5) + 245 ______ 129 + 245
So,
124 + 245 < 129 + 245
Because left side was 5 less.
∴ LHS < RHS
Now, (e) Try To Do yourself.
Terms in Expressions (Pages 28-29)
(Q.) Check if replacing subtraction by addition in this way does not change the value of the expression, by taking different examples.
Ans: Expression: 15 – 7
Replace subtraction: 15 + (–7)
Now, 15 – 7 = 8
15 + (–7) = 8
Same value.
(Q.) Complete the Table:-
Ans:
Does changing the order in which the terms are added give different values?
For example, in the expression 7+(−3)+8:
If we add in the given order: 7+(−3)+8=4+8=12
If we change the order: (−3)+8+7=5+7=12
Swapping and Grouping (Pages 29-31)
(Q.) Will this also hold when there are terms having negative numbers as well? Take some more expressions and check.
Ans: Even if the numbers are negative, changing their order does not affect the sum. For example:
(−3)+(−2)=−5 and if we swap them: (−2)+(−3)=−5
The result is the same in both cases, showing that the sum remains unchanged.
(Q.) Can you explain why this is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Ans: 6+(−4)+2 = 2+2 = 4
Swapped order: (−4)+2+6 = −2+6 = 4
Another order: 2+6+(−4) = 8+(−4) = 4
The sum remains 4 in all cases.
(Q.) Will this also hold when there are terms having negative numbers as well? Take some more expressions and check.
Ans: Yes, this rule holds true even when negative numbers are included. Let’s test it with some examples:
(−7)+4+3
Original order: (−7)+4+3 = −3+3 = 0
Changed order: 4+3+(−7) = 7+(−7) = 0
Sum is the same.
(Q.) Can you explain why this is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Ans: 5+(−3)
Represented as 5 blue tokens and 3 red tokens.
Pair each red with a blue → 3 pairs cancel.
Leftover = 2 blue tokens = +2.
Now, if we swap: (−3)+5
Start with 3 red tokens and add 5 blue tokens.
After cancellation, again 2 blue tokens remain.
Order does not change the result.
(Q.) 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.
Ans: Yes
(Q.) Can you explain why this is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Ans:
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