ncert maths class 6

ANSWERS
EXERCISE 1.1
1. (a) Ten 2. (a) 73,75,307
(b) Ten (b) 9,05,00,041
(c) Ten (c) 7,52, 21,302
(d) Ten (d) 58,423,202
(e) Ten (e) 23,30,010
3. (a) 8,75,95,762 Eight crore seventy-five lakh ninety-five thousand seven
hundred sixty two.
(b) 85,46,283 Eighty-five lakh forty-six thousand two hundred
eighty-three.
(c) 9,99,00,046 Nine crore ninety-nine lakh forty six.
(d) 9,84,32,701 Nine crore eighty-four lakh, thirty-two thousand seven
hundred one.
4. (a) 78,921,092 Seventy-eightmillion,ninehundredtwenty-onethousand,
ninety-two.
(b) 7,452,283 Seven million four hundred fifty-two thousand two
hundred eighty-three.
(c) 99,985,102 Ninety-nine million nine hundred eighty-five thousand,
one hundred two.
(d) 48,049,831 Forty-eight million forty-nine thousand eight hundred
thirty one.
EXERCISE 1.2
1. 7,707 tickets 2. 3,020 runs
3. 2,28,800 votes 4. Rs. 6,86,659; second week, Rs. 1,14,877
5. 52,965 6. 87,575 screws
7. Rs. 30,592 8. 65,124
9. 18 shirts, 1 m 30 cm 10. 177 boxes
11. 22 km 500 m 12. 180 glasses.
EXERCISE 1.3
1. (a) 1,700 (b) 500 2. (a) 5,000 ; 5,090 (b) 61,100 ; 61,130
(c) 16,000 (c) 7,800 ; 7,840
(d) 7,000 (d) 4,40,900 ; 4,40,980
3. (a) 1,20,000 (b) 1,75,00,000 (c) 7,80,000 (d) 3,00,000
EXERCISE 2.1
1. 11,000 ; 11,001 ; 11,002 2. 10,000 ; 9,999 ; 9,998
3. 0 4. 20
5. (a) 24,40,702 (b) 1,00,200 (c) 11,000,00 (d) 23,45,671
6. (a) 93 (b) 9,999 (c) 2,08,089 (e) 76,54,320

MATHEMATICS
294
7. (a) 503 is on the left of 530 ; 530 > 503
(b) 307 is on the left of 370 ; 370 > 307
(c) 56,789 is on the left of 98,765 ; 98,765 > 56,789
(d) 98,30,415 is on the left of 1,00,23,001 ; 98,30,415 < 1,00,23,001
8. (a) F (b) F (c) T (d) T (e) T (f) F (g) F (h) F (i) T (j) F
(k) F (l) T (m) F
EXERCISE 2.2
1. (a) 1,408 (b) 4,600
2. (a) 1,76,800 (b) 16,600 (c) 2,91,000 (d) 27,90,000
(e) 85,500 (f) 10,00,000
3. (a) 5,940 (b) 54,27,900 (c) 81,26,500 (d) 1,92,25,000
4. (a) 76,014 (b) 87,108 (c) 2,60,064 (d) 1,68,840
5. Rs 3,960 6. Rs 1,500
7. (i) →(c) (ii) → (a) (iii) → (b)
EXERCISE 2.3
1. (a) 2. Yes
3. Both of them will be ‘l’
4. (a) 73,528 (b) 54,42,437 (c) 20,600 (d) 5,34,375 (e) 17,640
5. 123456 × 8 + 6 = 987654
1234567 × 8 + 7 = 9876543
EXERCISE 3.1
1. (a) 1, 2, 3, 4, 6, 8, 12, 24 (b) 1, 3, 5, 15
(c) 1, 3, 7, 21 (d) 1, 3, 9, 27
(e) 1, 2, 3, 4, 6, 12 (f) 1, 2, 4, 5, 10, 20
(g) 1, 2, 3, 6, 9, 18 (h) 1, 23 (i) 1, 2, 3, 4, 6, 9, 12, 18, 36
2. (a) 5, 10, 15, 20, 25 (b) 8, 16, 24, 32, 40 (c) 9, 18, 27, 36, 45
3. (i) → (b) (ii) → (d) (iii) → (a)
(iv) → (f) (v) → (e)
4. 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
EXERCISE 3.2
1. (a) even number (b) even number
2. (a) F (b) T (c) T (d) F
(e) F (f) F (g) F (h) T
(i) F (j) T
3. 17 and 71, 37 and 73, 79 and 97
4. Prime numbers : 2, 3, 5, 7, 11, 13, 17, 19
Composite numbers : 4, 6, 8, 9, 10, 12, 14, 15, 16, 18 5. 7
6. (a) 3 + 41 (b) 5 + 31 (c) 5 + 19 (d) 5 + 13
(This could be one of the ways. There can be other ways also.)

ANSWERS
295
7. 3, 5; 5, 7 ; 11, 13
8. (a) and (c) 9. 90, 91, 92 , 93, 94, 95, 96
10. (a) 3 + 5 + 13 (b) 3 + 5 + 23
(c) 13 + 17 + 23 (d) 7 + 13 + 41
(This could be one of the ways. There can be other ways also.)
11. 2, 3 ; 2, 13; 3, 17; 7, 13; 11, 19
12. (a) prime number (b) composite number
(c) prime number, composite number (d) 2 (e) 4 (f) 2
EXERCISE 3.3
1. Number Divisible by
2 3 4 5 6 8 9 10 11
990 Yes Yes No Yes Yes No Yes Yes Yes
1586 Yes No No No No No No No No
275 No No No Yes No No No No Yes
6686 Yes No No No No No No No No
639210 Yes Yes No Yes Yes No No Yes Yes
429714 Yes Yes No No Yes No Yes No No
2856 Yes Yes Yes No Yes Yes No No No
3060 Yes Yes Yes Yes Yes No Yes Yes No
406839 No Yes No No No No No No No
2. Divisible by 4 : (a) , (b), (c), (d), (f), (g), (h), (i)
Divisible by 8 : (b), (d), (f), (h)
3. (a), (f), (g), (i) 4. (a), (b), (d), (e), (f)
5. (a) 2 and 8 (b) 0 and 9 6. (a) 8 (b) 6
EXERCISE 3.4
1. (a) 1, 2, 4 (b) 1, 5 (c) 1, 5 (d) 1, 2, 4, 8
2. (a) 1, 2, 4 (b) 1, 5
3. (a) 24, 48, 72 (b) 36, 72, 108
4. 12, 24, 36, 48, 60, 72, 84, 96
5. (a), (b), (e), (f) 6. 60 7. 1, 2, 3, 4, 6
EXERCISE 3.5
1. (a) F (b) T (c) F (d) T (e) F (f) F (g) T (h) T (i) F
2. (a) (b)

MATHEMATICS
296
3. 1 and the number itself
4. 9999, 9999 = 3 × 3 × 11 × 101
5. 10000, 10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
6. 1729 = 7 × 13 × 19
The difference of two consecutive prime factors is 6
7. (i) 2 × 3 × 4 = 24 is divisible by 6.
(ii) 5 × 6 × 7 = 210 is divisible by 6.
9. (b), (c)
10. Yes
11. No. Number 12 is divisible by both 4 and 6; but 12 is not divisible by 24.
12. 2 × 3 × 5 × 7 = 210
EXERCISE 3.6
1. (a) 6 (b) 6 (c) 6 (d) 9 (e) 12 (f) 34 (g) 35 (h) 7
(i) 9 (j) 3
2. (a) 1 (b) 2 (c) 1
3. No ; 1
EXERCISE 3.7
1. 3 kg 2. 6930 cm 3. 75 cm 4. 120
5. 960 6. 7 minutes 12 seconds past 7 a.m.
7. 31 litres 8. 95 9. 1152
10. (a) 36 (b) 60 (c) 30 (d) 60
Here, in each case LCM is a multiple of 3
Yes, in each case LCM = the product of two numbers
11. (a) 20 (b) 18 (c) 48 (d) 45
The LCM of the given numbers in each case is the larger of the two numbers.
EXERCISE 4.1
1. (a) O, B, C, D, E.
(b) Many answers are possible. Some are: DE, DO, DB, EO etc.
(c) Many answers are possible. Some are: DB, DE, OB, OE, EB etc.
(d) Many answers are possible. Some are: DE, DO, EO, OB, EB etc.
2. AB, AC, AD , BA, BC, BD , CA, CB,CD , DA, DB, DC.
3. (a) Many answers. One answer is AE .
(b) Many answers. One answer is AE .
(c) CO or OC
(d) Many answers are possible. Some are, CO, AE and AE, EF.

ANSWERS
297
4. (a) Countless (b) Only one.
6. (a) T (b) T (c) T (d) F (e) F
(f) F (g) T (h) F (i) F (j) F (k) T
EXERCISE 4.2
1. Open : (a), (c); Closed : (b), (d), (e). 4. (a) Yes (b) Yes
5. (a) (b) (c) Not possible.
EXERCISE 4.3
1. ∠ A or ∠ DAB; ∠ B or ∠ ABC; ∠ C or ∠ BCD; ∠ D or ∠ CDA
2. (a) A (b) A, C, D. (c) E, B, O, F.
EXERCISE 4.4
2. (a) ΔABC, ΔABD, ΔADC.
(b) Angles: ∠ B, ∠ C, ∠ BAC, ∠ BAD, ∠ CAD, ∠ ADB, ∠ ADC
(c) Line segments: AB, AC, BC, AD, BD, DC
(d) ΔABC, ΔABD
EXERCISE 4.5
1. The diagonals will meet in the interior of the quadrilateral.
2. (a) KL, NM and KN, ML (b) ∠ K, ∠ M and ∠ N, ∠ L
(c) KL, KN and NM, ML or KL, LM and NM, NK
(d) ∠ K, ∠ L and ∠ M, ∠ N or ∠ K, ∠ L and ∠ L, ∠ M etc.
EXERCISE 4.6
1. (a) O (b) OA, OB, OC (c) AC (d) ED
(e) O, P (f) Q (g) OAB (Shaded portion)
(h) Segment ED (Shaded portion)
2. (a) Yes (b) No
4. (a) True (b) True
EXERCISE 5.1
1. Chances of errors due to improper viewing are more.
2. Accurate measurement will be possible.
3. Yes. (because C is ‘between’A and B).
4. B lies between A and C.
5. D is the mid point of AG (because, AD = DG = 3 units).
6. AB = BC and BC = CD, therefore, AB = CD
7. The sum of the lengths of any two sides of a triangle can never be less than the length of
the third side.

MATHEMATICS
298
EXERCISE 5.2
1. (a)
2
1
(b)
1
4
(c)
1
4
(d)
3
4
(e)
3
4
(f)
3
4
2. (a) 6 (b) 8 (c) 8 (d) 2
3. (a) West (b) West (c) North (d) South
(To answer (d), it is immaterial whether we turn clockwise or anticlockwise, because one full
revolution will bring us back to the original position).
4. (a)
3
4
(b)
3
4
(c)
2
1
5. (a) 1 (b) 2 (c) 2 (d) 1 (e) 3 (f) 2
6. (a) 1 (b) 3 (c) 4 (d) 2 ( clockwise or anticlockwise).
7. (a) 9 (b) 2 (c) 7 (d) 7
(We should consider only clockwise direction here).
EXERCISE 5.3
1. (i) → (c); (ii) → (d); (iii) → (a); (iv) → (e); (v) → (b).
2. Acute : (a) and(f); Obtuse : (b); Right: (c); Straight: (e); Reflex : (d).
EXERCISE 5.4
1. (i) 90°; (ii) 180°.
2. (a) T (b) F (c) T (d) T (e) T
3. (a) Acute: 23°, 89°; (b) Obtuse: 91°, 179°.
7. (a) acute (b) obtuse (if the angle is less than 180°)
(c) straight (d) acute (e) an obtuse angle.
9. 90°, 30°, 180°
10. The view through a magnifying glass will not change the angle measure.
EXERCISE 5.5
1. (a) and (c) 2. 90°
3. One is a 30° – 60° – 90° set square; the other is a 45° – 45° – 90° set square.
The angle of measure 90° (i.e. a right angle) is common between them.
4. (a) Yes (b) Yes (c) BH, DF (d) All are true.
EXERCISE 5.6
1. (a) Scalene triangle (b) Scalene triangle (c) Equilateral triangle
(d) Right triangle (e) Isosceles right triangle (f) Acute-angled triangle
2. (i) → (e); (ii) → (g); (iii) → (a); (iv) → (f); (v) → (d);
(vi) → (c); (vii) → (b).
3. (a) Acute-angled and isosceles. (b) Right-angled and scalene.
(c) Obtuse-angled and isosceles. (d) Right-angled and isosceles.
(e) Equilateral and acute angled. (f) Obtuse-angled and scalene.
4. (b) is not possible. (Remember : The sum of the lengths of any two sides of a triangle
has to be greater than the third side.)

ANSWERS
299
EXERCISE 5.7
1. (a) T (b) T (c) T (d) T (e) F (f) F
2. (a) A rectangle with all sides equal becomes a square.
(b) A parallelogram with each angle a right angle becomes a rectangle.
(c) A rhombus with each angle a right angle becomes a square.
(d) All these are four-sided polygons made of line segments.
(e) The opposite sides of a square are parallel, so it is a parallelogram.
3. A square is a 'regular' quadrilateral
EXERCISE 5.8
1. (a) is not a closed figure and hence is not a polygon.
(b) is a polygon of six sides.
(c) and (d) are not polygons since they are not made of line segments.
2. (a) A Quadrilateral (b) A Triangle (c) A Pentagon (5-sided) (d) An Octagon
EXERCISE 5.9
1. (a) → (ii); (b) → (iv); (c) → (v); (d) → (iii); (e) → (i).
2. (a), (b) and (c) are cuboids; (d) is a cylinder; (e) is a sphere.
EXERCISE 6.1
1. (a) Decrease in weight (b) 30 km south (c) 326 A.D.
(d) Gain of Rs 700 (e) 100 m below sea level
2. (a) + 2000 (b) – 800 (c) + 200 (d) – 700
3. (a) + 5
(b) – 10
(c) + 8
(d) – 1
(e) – 6

MATHEMATICS
300
4. (a) F (b) negative integer (c) B → + 4, E → – 10
(d) E (e) D, C, B, A, O, H, G, F, E
5. (a) – 10°C, – 2°C, + 30°C, + 20°C, – 5°C
(b)
(c) Siachin (d) Ahmedabad and Delhi
6. (a) 9 (b) – 3 (c) 0 (d) 10 (e) 6 (f) 1
7. (a) – 6, – 5, – 4, – 3, – 2, – 1 (b) – 3,– 2, – 1, 0, 1, 2, 3
(c) – 14, – 13, – 12, – 11, – 10, – 9
(d) – 29, – 28, – 27, – 26, – 25, – 24
8. (a) – 19, – 18, – 17, – 16 (b) – 11, – 12, – 13, – 14
9. (a) T (b) F; – 100 is to the left of – 50 on number line
(c) F; greatest negative integer is – 1
(d) F; – 26 is smaller than – 25
10. (a) 2 (b) – 4 (c) to the left (d) to the right
EXERCISE 6.2
1. (a) 8 (b) 0 (c) – 4 (d) – 5
2. (a) 3
(b) – 6
(c) – 8
(d) 5
(e) – 6
– 6
– 11
– 7
10
– 3 – 2

ANSWERS
301
(f) 2
3. (a) 4 (b) 5 (c) 9 (d) –100 (e) – 650 (f) – 317
4. (a) – 217 (b) 0 (c) – 81 (d) 50
5. (a) 4 (b) –38
EXERCISE 6.3
1. (a) 15 (b) – 18 (c) 3 (d) – 33 (e) 35 (f) 8
2. (a) < (b) > (c) > (d) >
3. (a) 8 (b) – 13 (c) 0 (d) – 8 (e) 5
4. (a) 10 (b) 10 (c) – 105 (d) 92
EXERCISE 7.1
1. (i)
2
4
(ii)
8
9
(iii)
4
8
(iv)
1
4
(v)
3
7
(vi)
3
12
(vii)
10
10
(viii)
4
9
(ix)
4
8
(x)
1
2
3. Shaded portions do not represent the given fractions.
4.
8
24
5.
40
60
6. (a) Arya will divide each sandwich into three equal parts, and give one part of each
sandwich to each one of them.
(b)
1
3
7.
2
3
8. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12;
5
11
9. 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113;
4
12
10.
4
8
11.
3
8
,
5
8
EXERCISE 7.2
1. (a)
(b)

MATHEMATICS
302
(c)
2. (a)
2
6
3
(b)
1
2
5
(c)
3
2
7
(d)
3
5
5
(e)
1
3
6
(f)
8
3
9
3. (a)
31
4
(b)
41
7
(c)
17
6
(d)
53
5
(e)
66
7
(f)
76
9
EXERCISE 7.3
1. (a)
1 2 3 4
, , ,
2 4 6 8
; Yes (b)
4 3 2 1 6
, , , ,
12 9 6 3 15
; No
2. (a)
1
2
(b)
4
6
(c)
3
9
(d)
2
8
(e)
3
4
(i)
6
18
(ii)
4
8
(iii)
12
16
(iv)
8
12
(v)
4
16
(a), (ii); (b), (iv); (c), (i); (d), (v); (e), (iii)
3. (a) 28 (b) 16 (c) 12 (d) 20 (e) 3
4. (a)
12
20
(b)
9
15
(c)
18
30
(d)
27
45
5. (a)
9
12
(b)
3
4
6. (a) equivalent(b) not equivalent (c) not equivalent
7. (a)
4
5
(b)
5
2
(c)
6
7
(d)
3
13
(e)
1
4
8. Ramesh →
10 1
20 2
= , Sheelu →
25 1
50 2
= , Jamaal →
40 1
80 2
= . Yes
9. (i) → (d) (ii) → (e) (iii) → (a) (iv) → (c) (v) → (b)
EXERCISE 7.4
1. (a)
1 3 4 6
8 8 8 8
< < < (b)
3 4 6 8
9 9 9 9
< < <
(c)
5 2
6 6
> ,
3 0
6 6
> ,
1 6
6 6
< ,
8 5
6 6
>

ANSWERS
303
2. (a)
3 5
6 6
< (b)
1 1
7 4
< (c)
4
5
5
5
> (d)
3
5
3
7
<
4. (a)
1 1
6 3
< (b)
3 2
4 6
> (c)
2 2
3 4
> (d)
6 3
6 3
=
(e)
5 5
6 5
<
5. (a)
1 1
2 5
> (b)
2 3
4 6
= (c)
3 2
5 3
< (d)
3 2
4 8
>
(e)
3 6
5 5
< (f)
7 3
9 9
> (g)
1 2
4 8
= (h)
6 4
10 5
<
(i)
3 7
4 8
< (j)
6 4
10 5
< (k)
5 15
7 21
=
6. (a)
1
6
(b)
1
5
(c)
4
25
(d)
4
25
(e)
1
6
(f)
1
5
(g)
1
5
(h)
1
6
(i)
4
25
(j)
1
6
(k)
1
6
(l)
4
25
(a), (e), (h), (j), (k) ; (b), (f), (g) ; (c), (d), (i), (l)
7. (a) No ;
5 25 4 36 25 36
, and
9 45 5 45 45 45
= = ≠
(b) No ;
9 81 5 80 81 80
, and
16 144 9 144 144 144
= = ≠ (c) Yes ;
4 16
5 20
=
(d) No ;
1 2 2 4
and
15 30 30 30
= ≠
8. Ila has read less 9. Rohit
10. Same fraction (
4
5
) of students got first class in both the classes.
EXERCISE 7.5
1. (a) + (b) – (c) +
2. (a)
1
9
(b)
11
15
(c)
2
7
(d) 1 (e)
1
3
(f) 1 (g)
1
3
(h)
1
4
(i)
3
5
3. The complete wall.

MATHEMATICS
304
4. (a)
4 2
( )
10 5
= (b)
8
21
(c)
6
( 1)
6
= (d)
7
27
5.
2
7
EXERCISE 7.6
1. (a)
17
21
(b)
23
30
(c)
46
63
(d)
22
21
(e)
17
30
(f)
22
15
(g)
5
12
(h)
3 1
( )
6 2
= (i)
23
12
(j)
6
( 1)
6
= (k) 5
(l)
95
12
(m)
9
5
(n)
5
6
2.
23
metre
20
3. 2
5
6
4. (a)
7
8
(b)
7
10
(c)
1
3
5.
6. Length of the other piece =
5
8
metre
7. The distance walked by Nandini = )
4 2
(
10 5
= km
8. Asha’s bookshelf is more full; by
13
30
9. Rahul takes less time; by
9
20
minutes
EXERCISE 8.1
1. Hundreds Tens Ones Tenths
(100) (10) (1) (
1
10
)
(a) 0 3 1 2
(b) 1 1 0 4

ANSWERS
305
2. Hundreds Tens Ones Tenths
(100) (10) (1) (
1
10
)
(a) 0 1 9 4
(b) 0 0 0 3
(c) 0 1 0 6
(d) 2 0 5 9
3. (a) 0.7 (b) 20.9 (c) 14.6 (d) 102.0 (e) 600.8
4. (a) 0.5 (b) 3.7 (c) 265.1 (d) 70.8 (e) 8.8
(f) 4.2 (g) 1.5 (h) 0.4 (i) 2.4 (j) 3.6
(k) 4.5
5. (a)
6 3
,
10 5
(b)
25 5
,
10 2
(c) 1, 1 (d)
38 19
,
10 5
(e)
137 137
,
10 10
(f)
212 106
,
10 5
(g)
64 32
,
10 5
6. (a) 0.2cm (b) 3.0 cm (c) 11.6 cm (d) 4.2 cm
(e) 16.2 cm (f) 8.3 cm
7. (a) 0 and 1; 1 (b) 5 and 6; 5 (c) 2 and 3; 3 (d) 6 and 7; 6
(e) 9 and 10; 9 (f) 4 and 5; 5
8.
9. A, 0.8 cm; B, 1.3 cm; C, 2.2 cm; D, 2.9 cm
10. (a) 9.5 cm (b) 6.5 cm
EXERCISE 8.2
1. Ones Tenths Hundredths Number
(a) 0 2 6 0.26
(b) 1 3 8 1.38
(c) 1 2 8 1.28
2. (a) 3.25 (b) 102.63 (c) 30.025 (d) 211.902 (e) 12.241
3. Hundreds Tens Ones Tenths Hundredths Thousandths
(a) 0 0 0 2 9 0
(b) 0 0 2 0 8 0
(c) 0 1 9 6 0 0
(d) 1 4 8 3 2 0
(e) 2 0 0 8 1 2

MATHEMATICS
306
4. (a) 29.41 (b) 137.05 (c) 0.764 (d) 23.206 (e) 725.09
5. (a) Zero point zero three (b) One point two zero
(c) One hundred eight point five six (d) Ten point zero seven
(e) Zero point zero three two (f) Five point zero zero eight
6. (a) 0 and 0.1 (b) 0.4 and 0.5 (c) 0.1 and 0.2
(d) 0.6 and 0.7 (e) 0.9 and 1.0 (f) 0.5 and 0.6
7. (a)
3
5
(b)
1
20
(c)
3
4
(d)
9
50
(e)
1
4
(f)
1
8
(g)
33
500
EXERCISE 8.3
1. (a) 0.4 (b) 0.07 (c) 3 (d) 0.5 (e) 1.23
(f) 0.19 (g) both are same (h) 1.490 (i) both are same (j) 5.64
EXERCISE 8.4
1. (a) Re 0.05 (b) Re 0.75 (c) Re 0.20 (d) Rs 50.90 (e) Rs 7.25
2. (a) 0.15 m (b) 0.06 m (c) 2.45 m (d) 9.07 m (e) 4.19 m
3. (a) 0.5 cm (b) 6.0 cm (c) 16.4 cm (d) 9.8 cm (e) 9.3 cm
4. (a) 0.008 km (b) 0.088 km (c) 8.888 km (d) 70.005 km
5. (a) 0.002 kg (b) 0.1 kg (c) 3.750 kg (d) 5.008 kg (e) 26.05 kg
EXERCISE 8.5
1. (a) 38.587 (b) 29.432 (c) 27.63 (d) 38.355 (e) 13.175 (f) 343.89
2. Rs 68.35 3. Rs 26.30 4. 5.25 m
5. 3.042 km 6. 22.775 km 7. 18.270 kg
EXERCISE 8.6
1. (a) Rs 2.50 (b) 47.46 m (c) Rs 3.04 (d) 3.155 km (e) 1.793 kg
2. (a) 3.476 (b) 5.78 (c) 11.71 (d) 1.753
3. Rs 14.35 4. Rs 6.75 5. 15.55 m
6. 9.850 km 7. 4.425 kg
EXERCISE 9.1
1. Marks Tally marks Number of students
1 | | 2
2 | | | 3
3 | | | 3
4 | | | | | | 7
5 | | | | | 6
6 | | | | | | 7
7 | | | | 5
8 | | | | 4
9 | | | 3

ANSWERS
307
(a) 12 (b) 8
2. Sweets Tally marks Number of students
Ladoo |||| |||| | 11
Barfi ||| 3
Jalebi |||| || 7
Rasgulla |||| |||| 9
30
(b) Ladoo
3. Numbers Tally marks How many times?
1 |||| || 7
2 |||| | 6
3 |||| 5
4 |||| 4
5 |||| |||| | 11
6 |||| || 7
(a) 4 (b) 5 (c) 1 and 6
4. (i) Village D (ii) Village C (iii) 3 (iv) 28
5. (a) VIII (b) No (c) 12
6. (a) Number of bulbs sold on Monday are 12. Similarly, number of bulbs sold on
other days can be found.
(b) Maximum number of bulbs were sold on Sunday.
(c) Same number of bulbs were sold. On Wednesday and Saturday.
(d) Then minimum number of bulbs were sold on Wednesday and Saturday.
(e) The total number of bulbs sold in the given week were 86.
7. (a) Martin (b) 700 (c) Anwar, Martin, Ranjit Singh
EXERCISE 9.2
1.
(a) 6 (b) Village B (c) Village C

MATHEMATICS
308
2.
A (a) 6 (b) 5 complete and 1 incomplete
B Second
EXERCISE 9.3
1. (a) 2002 (b) 1998
2. (a) This bar graph shows the number of shirts sold from Monday to Saturday
(b) 1 unit = 5 shirts (c) Saturday, 60
(d) Tuesday (e) 35
3. (a) This bar graph shows the marks obtained by Aziz in different subjects.
(b) Hindi (c) Social Studies
(d) Hindi – 80, English – 60, Mathematics – 70, Science – 50 and Social Studies – 40.
EXERCISE 9.4
1.
Reading story books.
1 Unit length = 5 students

ANSWERS
309
2.
3.
1 Unit length = 100 bicycles
1 Unit length = 5 books
Days

MATHEMATICS
310
(a) 2002 (b) 1999
4.
(a) 30 – 44, 45 – 59
(b) 1 lakh 20 thousand
EXERCISE 10.1
1. (a) 12 cm (b) 133 cm (c) 60 cm (d) 15 cm (e) 15 cm
(f) 52 cm 2. 100 cm or 1 m 3. 7.5 m 4. 106 cm
5. 9.6 km 6. (a) 12 cm (b) 27 cm (c) 22 cm
7. 39 cm 8. 48 m 9. 5 m 10. 20 cm
11. (a) 7.5 cm (b) 10 cm (c) 5 cm 12. 10 cm
13. Rs 20,000 14. Rs 7200 15. Bulbul
16. (a) 100 cm (b) 100 cm (c) 100 cm (d) 100 cm
All the figures have same perimeter.
17. (a) 6 m (b) 10 m (c) Cross has greater perimeter
EXERCISE 10.2
1. (a) 9 sq units (b) 5 sq units (c) 4 sq units (d) 8 sq units (e) 10 sq units
(f) 4 sq units (g) 6 sq units (h) 5 sq units (i) 9 sq units (j) 4 sq units
(k) 5 sq units (l) 8 sq units (m) 14 sq units (n) 18 sq units
EXERCISE 10.3
1. (a) 12 sq cm (b) 252 sq cm (c) 6 sq km (d) 1.40 sq m
2. (a) 100 sq cm (b) 196 sq cm (c) 25 sq m
1 Unit length = 20 thousand
Age group
Numberofthousands

ANSWERS
311
3. (c) largest area (b) smallest area
4. 6 m 5. Rs 8000 6. 3 sq m 7. 14 sq m
8. 11 sq m 9. 15 sq m
10. (a) 28 sq cm (b) 9 sq cm
11. (a) 40 sq cm (b) 245 sq cm (c) 9 sq cm
12. (a) 240 tiles (b) 42 tiles
EXERCISE 11.1
1. (a) 2n (b) 3n (c) 3n (d) 2n (e) 5n
(f) 5n (g) 6n
2. (a) and (d); The number of matchsticks required in each of them is 2
3. 5n 4. 50b 5. 5s
6. t km 7. 8r, 64, 80 8. (x – 4) years 9. l + 5
10. 2x + 10
11. (a) 3x + 1, x = number of squares
(b) 2x + 1, x = number of triangles
EXERCISE 11.2
1. 3l 2. 6l 3. 12l 4. d = 2r
5. (a + b) + c = a + (b + c)
EXERCISE 11.3
2. (c), (d)
3. (a) Addition, subtraction, addition, subtraction
(b) Multiplication, division, multiplication
(c) Multiplication and addition, multiplication and subtraction
(d) Multiplication, multiplication and addition, multiplication and subtraction
4. (a) p + 7 (b) p – 7 (c) 7 p (d)
7
p
(e) – m – 7 (f) – 5p (g)
–
5
p
(h) – 5 p
5. (a) 2m + 11 (b) 2m – 11 (c) 5y + 3 (d) 5y – 3
(e) – 8y (f) – 8 y + 5 (g) 16 – 5y (h) – 5y + 16
6. (a) t + 4, t – 4, 4t,
4
t
,
4
t
, 4 – t, 4 + t (b) 2y + 7, 2y – 7, 7y + 2, ....., ......,
EXERCISE 11.4
1. (a) (i) y + 5 (ii) y – 3 (iii) 6y (iv) 6y – 2 (v) 3y + 5
(b) (3b – 4) metres (c) length = 5h cm, breadth = 5h – 10 cm
(d) s + 8, s – 7, 4s – 10 (e) (5v + 20) km
2. (a) A book costs three times the cost of a notebook.
(b) Tony’s box contains 8 times the marbles on the table.

MATHEMATICS
312
(c) Total number of students in the school is 20 times that of our class.
(d) Jaggu’s uncle is 4 times older than Jaggu and Jaggu’s aunt is 3 years younger than
his uncle.
(e) The total number of dots is 5 times the number of rows.
EXERCISE 11.5
1. (a) an equation with variable x (e) an equation with variable x
(f) an equation with variable x (h) an equation with variable n
(j) an equation with variable p (k) an equation with variable y
(o) an equation with variable x
2. (a) No (b) Yes (c) No (d) No
(e) No (f) Yes (g) No (h) No
(i) Yes (j) Yes (k) No (l) No
(m) No (n) No (o) No (p) No (q) Yes
3. (a) 12 (b) 8 (c) 10 (d) 14
(e) 4 (f) – 2
4. (a) 6 (b) 7 (c) 12 (d) 10
5. (i) 22 (ii) 16 (iii) 17 (iv) 11
EXERCISE 12.1
1. (a) 4 : 3 (b) 4 : 7
2. (a) 1 : 2 (b) 2 : 5
3. (a) 3 : 2 (b) 2 : 7 (c) 2 : 7
4. 3 : 4 5. 5, 12, 25, Yes
6. (a) 3 : 4 (b) 14 : 9 (c) 3 : 11 (d) 2 : 3
7. (a) 1 : 3 (b) 4 : 15 (c) 11 : 20 (d) 1 : 4
8. (a) 3 : 1 (b) 1 : 2
9. 17 : 550
10. (a) 115 : 216 (b) 101 : 115 (c) 101 : 216
11. (a) 3 : 1 (b) 16 : 15 (c) 5 : 12
12. 15 : 7 13. 20 ; 100 14. 12 and 8 15. 20 and 16
16. (a) 3 : 1 (b) 10 : 3 (c) 13 : 6 (d) 15 : 1
EXERCISE 12.2
1. (a) Yes (b) No (c) No (d) No
(e) Yes (f) Yes
2. (a) T (b) T (c) F (d) T
(e) F (f) T
3. (a) T (b) T (c) T (d) T (e) F
4. (a) Yes, Middle Terms – 1 m, Rs 40; Extreme Terms – 25 cm, Rs 160
(b) Yes, Middle Terms – 65 litres, 6 bottles; Extreme Terms – 39 litres,

ANSWERS
313
10 bottles
(c) No.
(d) Yes, Middle Terms – 2.5 litres, Rs 4 ; Extreme Terms – 200 ml, Rs 50
EXERCISE 12.3
1. Rs 210 2. Rs 4500 3. 644 mm
4. (a) Rs 48.80 (b) 10 kg
5. 5 degrees 6. Rs 30, 000 7. 10 bananas 8. 5 kg
9. 300 litres 10. Manish 11. Anup
EXERCISE 13.1
1. Four examples are the blackboard, the table top, a pair of scissors, the computer
disc etc.
2. The line l2
3. Except (c) all others are symmetric.
EXERCISE 13.2
1. (a) 4 (b) 4 (c) 4 (d) 1
(e) 6 (f) 4 (g) 0 (h) 0 (i) 3
3. Number of lines of symmetry are :
Equilateral triangle – 3; Square – 4; Rectangle – 2; Isosceles triangle – 1;
Rhombus – 2; Circle – countless.
4. (a) Yes; an isosceles triangle. (b) No.
(c) Yes; an equilateral triangle. (d) Yes; a scalene triangle.
7. (a) A,H,I,M,O,T,U,V,W,X,Y (b) B, C, D, E, H, I, K, O, X
(c) F, G, J, L, N, P, Q, R, S, Z
EXERCISE 13.3
1. Number of lines of symmetry to be marked :
(a) 4 (b) 1 (c) 2 (d) 2
(e) 1 (f) 2

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