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Mathematics
Arithmetic Expressions
NCERT Solutions
NCERT Solutions
Arithmetic Expressions
26 Solutions
Exercise:
All Exercises
Figure it Out 1
Figure it Out 2
Figure it Out 3
Figure it Out 4
Figure it Out 5
Figure it Out 6
Figure it Out 7
Q1
Figure it Out 1
Fill in the blanks to make the expressions equal on both sides of the = sign:
(a)
13
+
4
=
13+4=
13
+
4
=
______ + 6
(b)
22
+
22+
22
+
______
=
6
×
5
=6 \times 5
=
6
×
5
(c)
8
×
8 \times
8
×
______
=
64
÷
2
=64 \div 2
=
64
÷
2
(d)
34
−
34-
34
−
______
=
25
=25
=
25
Q2
Figure it Out 1
Arrange the following expressions in ascending (increasing) order of their values.
(a)
67-19
(b)
67-20
(c)
35
+
25
35+25
35
+
25
(d)
5
×
11
5 \times 11
5
×
11
(e)
120
÷
3
120 \div 3
120
÷
3
Q1
Figure it Out 2
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
245+289
245
+
289
| |
246
+
285
246+285
246
+
285
|
|---|---|---|---|
| (b) | 273-145 | | 272-144 |
| (c) | 364 + 587 | | 363 + 589 |
| (d) |
124
+
245
124+245
124
+
245
| |
129
+
245
129+245
129
+
245
|
| (e) | 213-77 | | 214-76 |
Q1
Figure it Out 3
In the following table, some expressions are given. Complete the table.
Expression
Expression as the sum of its terms
Terms
13
−
2
+
6
13-2+6
13
−
2
+
6
13
+
(
−
2
)
+
6
13+(-2)+6
13
+
(
−
2
)
+
6
13, - 2, 6
5
+
6
×
3
5+6 \times 3
5
+
6
×
3
4
+
15
−
9
4+15-9
4
+
15
−
9
23
−
2
×
4
+
16
23-2 \times 4+16
23
−
2
×
4
+
16
28
+
19
−
8
28+19-8
28
+
19
−
8
Q1
Figure it Out 4
Find the values of the following expressions by writing the terms in each case.
(a)
28
−
7
+
8
28-7+8
28
−
7
+
8
(b)
39
−
2
×
6
+
11
39-2 \times 6+11
39
−
2
×
6
+
11
(c)
40
−
10
+
10
+
10
40-10+10+10
40
−
10
+
10
+
10
(d)
48
−
10
×
2
+
16
÷
2
48-10 \times 2+16 \div 2
48
−
10
×
2
+
16
÷
2
(e)
6
×
3
−
4
×
8
×
5
6 \times 3-4 \times 8 \times 5
6
×
3
−
4
×
8
×
5
Q2
Figure it Out 4
Write a story/situation for each of the following expressions and find their values.
(a)
89
+
21
−
10
89+21-10
89
+
21
−
10
(b)
5
×
12
−
6
5 \times 12-6
5
×
12
−
6
(c)
4
×
9
+
2
×
6
4 \times 9+2 \times 6
4
×
9
+
2
×
6
Q3
Figure it Out 4
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 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?
(c)
Find the total height of the window by writing an expression describing the relationship among the measurements shown in the picture.
Q1
Figure it Out 5
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
24+(6-4)=24+6
24
+
(
6
−
4
)
=
24
+
6
☐ 4
(b)
38
+
(
38+(
38
+
(
______ ☐ ______
)
=
38
+
9
−
4
) = 38+9-4
)
=
38
+
9
−
4
(c)
24
−
(
6
+
4
)
=
24
24-(6+4)=24
24
−
(
6
+
4
)
=
24
☐ 6-4
(d)
24
−
6
−
4
=
24
−
(
6
24-6-4=24-(6
24
−
6
−
4
=
24
−
(
6
☐ ______)
(e)
27
−
(
8
+
3
)
=
27
27-(8+3)=27
27
−
(
8
+
3
)
=
27
☐ 8 ☐ 3
(f)
27
−
(
27-(
27
−
(
______ ☐ ______
)
=
27
−
8
+
3
) = 27-8+3
)
=
27
−
8
+
3
Q2
Figure it Out 5
Remove the brackets and write the expression having the same value.
(a)
14
+
(
12
+
10
)
14+(12+10)
14
+
(
12
+
10
)
(b)
14
−
(
12
+
10
)
14-(12+10)
14
−
(
12
+
10
)
(c)
14
+
(
12
−
10
)
14+(12-10)
14
+
(
12
−
10
)
(d)
14
−
(
12
−
10
)
14-(12-10)
14
−
(
12
−
10
)
(e)
−
14
+
12
−
10
-14+12-10
−
14
+
12
−
10
(f)
14
−
(
−
12
−
10
)
14-(-12-10)
14
−
(
−
12
−
10
)
Q3
Figure it Out 5
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
(6+10)-2
(
6
+
10
)
−
2
and
6
+
(
10
−
2
)
6+(10-2)
6
+
(
10
−
2
)
(b)
16
−
(
8
−
3
)
16-(8-3)
16
−
(
8
−
3
)
and
(
16
−
8
)
−
3
(16-8) - 3
(
16
−
8
)
−
3
(c)
27
−
(
18
+
4
)
27-(18+4)
27
−
(
18
+
4
)
and
27
+
(
−
18
−
4
)
27+(-18-4)
27
+
(
−
18
−
4
)
Q4
Figure it Out 5
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
319+537, 319-537, -537+319, 537-319
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
87+46-109, 87+46-109, 87+46-109, 87-46+109, 87 -(46+109), (87-46)+109
87
+
46
−
109
,
87
+
46
−
109
,
87
+
46
−
109
,
87
−
46
+
109
,
87
−
(
46
+
109
)
,
(
87
−
46
)
+
109
Q5
Figure it Out 5
Add brackets at appropriate places in the expressions such that they lead to the values indicated.
(a)
34
−
9
+
12
=
13
34-9+12=13
34
−
9
+
12
=
13
(b)
56
−
14
−
8
=
34
56-14-8=34
56
−
14
−
8
=
34
(c)
−
22
−
12
+
10
+
22
=
−
22
-22-12+10+22=-22
−
22
−
12
+
10
+
22
=
−
22
Q6
Figure it Out 5
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
+
423+
423
+
__
=
419
+
=419+
=
419
+
__
(b)
207
−
68
=
210
−
207-68=210-
207
−
68
=
210
−
__
Q7
Figure it Out 5
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
2-3+5=4
2
−
3
+
5
=
4
and
3
−
(
5
−
2
)
=
0
3-(5-2) =0
3
−
(
5
−
2
)
=
0
.
Q8
Figure it Out 5
Whenever Jasoda has to subtract 9 from a number, she subtracts 10 and adds 1 to it. For example,
36
−
9
=
26
+
1
36-9=26+1
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.
Q9
Figure it Out 5
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
)
73-(14+1)
73
−
(
14
+
1
)
b) 73-(14-1)
(c)
73
+
(
−
14
+
1
)
73+(-14+1)
73
+
(
−
14
+
1
)
d)
73
+
(
−
14
−
1
)
73+(-14-1)
73
+
(
−
14
−
1
)
Q1
Figure it Out 6
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
3 \times(6+7)=3 \times 6+3 \times 7
3
×
(
6
+
7
)
=
3
×
6
+
3
×
7
(b)
(
8
+
3
)
×
4
=
8
×
4
+
3
×
4
(8+3) \times 4=8 \times 4+3 \times 4
(
8
+
3
)
×
4
=
8
×
4
+
3
×
4
(c)
3
×
(
5
+
8
)
=
3
×
5
3 \times(5+8)=3 \times 5
3
×
(
5
+
8
)
=
3
×
5
☐
3
×
3 \times
3
×
______
(d)
(
9
+
2
)
×
4
=
9
×
4
(9+2) \times 4=9 \times 4
(
9
+
2
)
×
4
=
9
×
4
☐
2
×
2 \times
2
×
______
(e)
3
×
(
3 \times(
3
×
(
______
+
4
)
=
3
×
+4)=3 \times
+
4
)
=
3
×
______
+
3
×
4
+3 \times 4
+
3
×
4
(f)
(
(
(
______
+
6
)
×
4
=
13
×
4
+
+6) \times 4=13 \times 4+
+
6
)
×
4
=
13
×
4
+
______
×
4
\times 4
×
4
(g)
3
×
(
3 \times(
3
×
(
______
+
+
+
______
)
=
3
×
5
+
3
×
2
) =3 \times 5+3 \times 2
)
=
3
×
5
+
3
×
2
(h)
(
(
(
______
+
+
+
______
)
×
) \times
)
×
______
=
2
×
4
+
3
×
4
=2 \times 4+3 \times 4
=
2
×
4
+
3
×
4
(i)
5
×
(
9
−
2
)
=
5
×
9
−
5
×
5 \times(9-2)=5 \times 9-5 \times
5
×
(
9
−
2
)
=
5
×
9
−
5
×
______
(j)
(
5
−
2
)
×
7
=
5
×
7
−
2
×
(5-2) \times 7=5 \times 7-2 \times
(
5
−
2
)
×
7
=
5
×
7
−
2
×
______
(k)
5
×
(
8
−
3
)
=
5
×
8
5 \times(8-3)=5 \times 8
5
×
(
8
−
3
)
=
5
×
8
☐
5
×
5 \times
5
×
______
(l)
(
8
−
3
)
×
7
=
8
×
7
(8-3) \times 7=8 \times 7
(
8
−
3
)
×
7
=
8
×
7
☐
3
×
7
3 \times 7
3
×
7
(m)
5
×
(
12
−
5 \times(12-
5
×
(
12
−
______
)
=
5
×
) = 5 \times
)
=
5
×
______ ☐
5
×
5 \times
5
×
______
(n)
(
15
−
(15-
(
15
−
______
)
×
7
=
) \times 7=
)
×
7
=
______ ☐
6
×
7
6 \times 7
6
×
7
(o)
5
×
(
5 \times(
5
×
(
______
−
-
−
______
)
=
5
×
9
−
5
×
4
) =5 \times 9-5 \times 4
)
=
5
×
9
−
5
×
4
(p)
(
(
(
______
−
-
−
______
)
×
) \times
)
×
______
=
17
×
7
−
9
×
7
=17 \times 7-9 \times 7
=
17
×
7
−
9
×
7
Q2
Figure it Out 6
In the boxes below, fill '<', '>', 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
(8-3) \times 29
(
8
−
3
)
×
29
☐
(
3
−
8
)
×
29
(3-8) \times 29
(
3
−
8
)
×
29
(b)
15
+
9
×
18
15+9 \times 18
15
+
9
×
18
☐
(
15
+
9
)
×
18
(15+9) \times 18
(
15
+
9
)
×
18
(c)
23
×
(
17
−
9
)
23 \times(17-9)
23
×
(
17
−
9
)
☐
23
×
17
+
23
×
9
23 \times 17+23 \times 9
23
×
17
+
23
×
9
(d)
(
34
−
28
)
×
42
(34-28) \times 42
(
34
−
28
)
×
42
☐
34
×
42
−
28
×
42
34 \times 42-28 \times 42
34
×
42
−
28
×
42
Q3
Figure it Out 6
Here is one way to make 14: ______
2
‾
×
(
\underline{2} \times(
2
×
(
______ 1
+
+
+
______ 6 ) = 14. Are there other ways of getting 14? Fill them out below:
(a)
______ × ( ______ + ______ ) = 14
(b)
______ × ( ______ + ______ ) = 14
(c)
______ × ( ______ + ______ ) = 14
(d)
______ × ( ______ + ______ ) = 14
Q4
Figure it Out 6
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.
Q1
Figure it Out 7
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 a 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 amount 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?
Q2
Figure it Out 7
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
5 \times 2 \times 8
5
×
2
×
8
(b)
(
7
−
2
)
×
8
(7-2) \times 8
(
7
−
2
)
×
8
(c)
8
×
7
8 \times 7
8
×
7
(d)
7
×
2
×
8
7 \times 2 \times 8
7
×
2
×
8
(e)
7
×
5
−
2
7 \times 5-2
7
×
5
−
2
(f)
(
7
+
2
)
×
8
(7+2) \times 8
(
7
+
2
)
×
8
(g)
7
×
8
−
2
×
8
7 \times 8-2 \times 8
7
×
8
−
2
×
8
(h)
(
7
−
5
)
×
8
(7-5) \times 8
(
7
−
5
)
×
8
Q3
Figure it Out 7
Find different ways of evaluating the following expressions:
(a)
1
−
2
+
3
−
4
+
5
−
6
+
7
−
8
+
9
−
10
1-2+3-4+5-6+7-8+9-10
1
−
2
+
3
−
4
+
5
−
6
+
7
−
8
+
9
−
10
(b)
1
−
1
+
1
−
1
+
1
−
1
+
1
−
1
+
1
−
1
1-1+1-1+1-1+1-1+1-1
1
−
1
+
1
−
1
+
1
−
1
+
1
−
1
+
1
−
1
Q4
Figure it Out 7
Compare the following pairs of expressions using '<', '>', or '=' or by reasoning.
(a)
49
−
7
+
8
49-7+8
49
−
7
+
8
vs
49
−
7
+
8
49-7+8
49
−
7
+
8
(b)
83
×
42
−
18
83 \times 42-18
83
×
42
−
18
vs
83
×
40
−
18
83 \times 40-18
83
×
40
−
18
(c)
145
−
17
×
8
145-17 \times 8
145
−
17
×
8
vs
145
−
17
×
6
145-17 \times 6
145
−
17
×
6
(d)
23
×
48
−
35
23 \times 48-35
23
×
48
−
35
vs
23
×
(
48
−
35
)
23 \times(48-35)
23
×
(
48
−
35
)
(e)
(
16
−
11
)
×
12
(16-11) \times 12
(
16
−
11
)
×
12
vs
−
11
×
12
+
16
×
12
-11 \times 12+16 \times 12
−
11
×
12
+
16
×
12
(f)
(
76
−
53
)
×
88
(76-53) \times 88
(
76
−
53
)
×
88
vs
88
×
(
53
−
76
)
88 \times(53-76)
88
×
(
53
−
76
)
(g)
25
×
(
42
+
16
)
25 \times(42+16)
25
×
(
42
+
16
)
vs
25
×
(
43
+
15
)
25 \times(43+15)
25
×
(
43
+
15
)
(h)
36
×
(
28
−
16
)
36 \times(28-16)
36
×
(
28
−
16
)
vs
35
×
(
27
−
15
)
35 \times(27-15)
35
×
(
27
−
15
)
Q5
Figure it Out 7
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
84-38-12
84
−
38
−
12
(ii)
84
−
(
37
+
12
)
84-(37+12)
84
−
(
37
+
12
)
(iii)
83
−
38
−
13
83-38-13
83
−
38
−
13
(iv)
−
37
+
83
−
12
-37+83-12
−
37
+
83
−
12
(b)
93
+
37
×
44
+
76
93+37 \times 44+76
93
+
37
×
44
+
76
(i)
37
+
93
×
44
+
76
37+93 \times 44+76
37
+
93
×
44
+
76
(ii)
93
+
37
×
76
+
44
93+37 \times 76+44
93
+
37
×
76
+
44
(iii)
(
93
+
37
)
×
(
44
+
76
)
(93+37) \times(44+76)
(
93
+
37
)
×
(
44
+
76
)
(iv)
37
×
44
+
93
+
76
37 \times 44+93+76
37
×
44
+
93
+
76
Q6
Figure it Out 7
Choose a number and create ten different expressions having that value.
More from this chapter
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