Class 7 Maths - Fractions and Decimals NCERT Solutions

Chapter 2: Fractions and Decimals (NCERT Solutions)

Exercise 2.1

Q1. Solve:
(i) 2 - (3/5)
(ii) 4 + (7/8)
(iii) (3/5) + (2/7)
(iv) (9/11) - (4/15)
(v) (7/10) + (2/5) + (3/2)
(vi) 2 (2/3) + 3 (1/2)
(vii) 8 (1/2) - 3 (5/8)

(i) 2 - 3/5
= (2×5)/5 - 3/5 = 10/5 - 3/5 = (10 - 3)/5 = 7/5 = 1 2/5

(ii) 4 + 7/8
= (4×8)/8 + 7/8 = 32/8 + 7/8 = (32 + 7)/8 = 39/8 = 4 7/8

(iii) 3/5 + 2/7
LCM of 5 and 7 is 35.
= (3×7)/35 + (2×5)/35 = 21/35 + 10/35 = (21 + 10)/35 = 31/35

(iv) 9/11 - 4/15
LCM of 11 and 15 is 165.
= (9×15)/165 - (4×11)/165 = 135/165 - 44/165 = (135 - 44)/165 = 91/165

(v) 7/10 + 2/5 + 3/2
LCM of 10, 5, and 2 is 10.
= 7/10 + (2×2)/10 + (3×5)/10 = 7/10 + 4/10 + 15/10 = (7 + 4 + 15)/10 = 26/10 = 13/5 = 2 3/5

(vi) 2 2/3 + 3 1/2
Convert to improper fractions: 8/3 + 7/2
LCM of 3 and 2 is 6.
= (8×2)/6 + (7×3)/6 = 16/6 + 21/6 = (16 + 21)/6 = 37/6 = 6 1/6

(vii) 8 1/2 - 3 5/8
Convert to improper fractions: 17/2 - 29/8
LCM of 2 and 8 is 8.
= (17×4)/8 - 29/8 = 68/8 - 29/8 = (68 - 29)/8 = 39/8 = 4 7/8

Q2. Arrange the following in descending order:
(i) 2/9, 2/3, 8/21
(ii) 1/5, 3/7, 7/10

(i) 2/9, 2/3, 8/21
LCM of denominators 9, 3, 21 is 63.
2/9 = (2×7)/63 = 14/63
2/3 = (2×21)/63 = 42/63
8/21 = (8×3)/63 = 24/63
Comparing numerators: 42 > 24 > 14
Descending order: 42/63, 24/63, 14/63
2/3, 8/21, 2/9

(ii) 1/5, 3/7, 7/10
LCM of denominators 5, 7, 10 is 70.
1/5 = (1×14)/70 = 14/70
3/7 = (3×10)/70 = 30/70
7/10 = (7×7)/70 = 49/70
Comparing numerators: 49 > 30 > 14
Descending order: 49/70, 30/70, 14/70
7/10, 3/7, 1/5

Q3. In a "magic square", the sum of the numbers in each row, in each column and along the diagonals is the same. Is this a magic square?
Row 1: 4/11, 9/11, 2/11
Row 2: 3/11, 5/11, 7/11
Row 3: 8/11, 1/11, 6/11

Sum along Row 1 = 4/11 + 9/11 + 2/11 = (4+9+2)/11 = 15/11
Sum along Row 2 = 3/11 + 5/11 + 7/11 = (3+5+7)/11 = 15/11
Sum along Row 3 = 8/11 + 1/11 + 6/11 = (8+1+6)/11 = 15/11
Sum along Col 1 = 4/11 + 3/11 + 8/11 = (4+3+8)/11 = 15/11
Sum along Col 2 = 9/11 + 5/11 + 1/11 = (9+5+1)/11 = 15/11
Sum along Col 3 = 2/11 + 7/11 + 6/11 = (2+7+6)/11 = 15/11
Sum along Diagonal 1 = 4/11 + 5/11 + 6/11 = (4+5+6)/11 = 15/11
Sum along Diagonal 2 = 2/11 + 5/11 + 8/11 = (2+5+8)/11 = 15/11

Since the sum is exactly 15/11 everywhere, Yes, it is a magic square.

Q4. A rectangular sheet of paper is 12 (1/2) cm long and 10 (2/3) cm wide. Find its perimeter.

Length (L) = 12 1/2 = 25/2 cm.
Breadth (B) = 10 2/3 = 32/3 cm.
Perimeter = 2 × (L + B)
= 2 × (25/2 + 32/3)
LCM of 2 and 3 is 6.
= 2 × [ (25×3)/6 + (32×2)/6 ]
= 2 × [ 75/6 + 64/6 ]
= 2 × (139 / 6)
= 139 / 3 = 46 1/3 cm

Q5. Find the perimeters of:
(i) ▵ABE
(ii) the rectangle BCDE in this figure. Whose perimeter is greater?
[Given: AB = 5/2 cm, AE = 3 (3/5) cm, BE = 2 (3/4) cm, ED = 7/6 cm]

(i) Perimeter of ▵ABE:
Sides: AB = 5/2, BE = 2 3/4 = 11/4, AE = 3 3/5 = 18/5.
Perimeter = 5/2 + 11/4 + 18/5
LCM of 2, 4, 5 is 20.
= (5×10)/20 + (11×5)/20 + (18×4)/20
= 50/20 + 55/20 + 72/20 = (50+55+72)/20 = 177/20 cm = 8 17/20 cm.

(ii) Perimeter of rectangle BCDE:
Length BE = 2 3/4 = 11/4 cm.
Breadth ED = 7/6 cm.
Perimeter = 2 × (L + B) = 2 × (11/4 + 7/6)
LCM of 4 and 6 is 12.
= 2 × [(11×3)/12 + (7×2)/12] = 2 × [33/12 + 14/12]
= 2 × (47/12) = 47/6 cm = 7 5/6 cm.

Comparing:
▵ABE perimeter = 177/20 = (177×3)/60 = 531/60 cm.
Rectangle BCDE perimeter = 47/6 = (47×10)/60 = 470/60 cm.
Since 531 > 470, the perimeter of ▵ABE is greater.

Q6. Salil wants to put a picture in a frame. The picture is 7 (3/5) cm wide. To fit in the frame the picture cannot be more than 7 (3/10) cm wide. How much should the picture be trimmed?

Width of picture = 7 3/5 = 38/5 cm.
Required width = 7 3/10 = 73/10 cm.
Trim amount = (Width of picture) - (Required width)
= 38/5 - 73/10
LCM of 5 and 10 is 10.
= (38×2)/10 - 73/10 = 76/10 - 73/10 = 3/10 cm.
The picture should be trimmed by 3/10 cm.

Q7. Ritu ate 3/5 part of an apple and the remaining apple was eaten by her brother Somu. How much part of the apple did Somu eat? Who had the larger share? By how much?

Part of apple Ritu ate = 3/5.
Total apple = 1.
Part of apple Somu ate = 1 - 3/5 = 5/5 - 3/5 = 2/5.
Comparing: 3/5 (Ritu) > 2/5 (Somu). So, Ritu had the larger share.
Difference = 3/5 - 2/5 = 1/5.
Ritu's share is larger by 1/5 part.

Q8. Michael finished colouring a picture in 7/12 hour. Vaibhav finished colouring the same picture in 3/4 hour. Who worked longer? By what fraction was it longer?

Time taken by Michael = 7/12 hour.
Time taken by Vaibhav = 3/4 hour.
To compare, make denominators same. 3/4 = (3×3) / (4×3) = 9/12 hour.
Since 9/12 > 7/12, Vaibhav worked longer.
Difference = 9/12 - 7/12 = 2/12 = 1/6 hour.
Vaibhav worked longer by 1/6 hour.

Exercise 2.2

Q1. Multiply and reduce to lowest form and convert into a mixed fraction:
(i) 7 × 3/5
(ii) 4 × 1/3
(iii) 2 × 6/7
(iv) 5 × 2/9
(v) 2/3 × 4
(vi) 5/2 × 6
(vii) 11 × 4/7
(viii) 20 × 4/5
(ix) 13 × 1/3
(x) 15 × 3/5

(i) 7 × 3/5 = 21/5 = 4 1/5

(ii) 4 × 1/3 = 4/3 = 1 1/3

(iii) 2 × 6/7 = 12/7 = 1 5/7

(iv) 5 × 2/9 = 10/9 = 1 1/9

(v) 2/3 × 4 = 8/3 = 2 2/3

(vi) 5/2 × 6 = 30/2 = 15 = 15

(vii) 11 × 4/7 = 44/7 = 6 2/7

(viii) 20 × 4/5 = 80/5 = 16 = 16

(ix) 13 × 1/3 = 13/3 = 4 1/3

(x) 15 × 3/5 = 45/5 = 9 = 9

Q2. Find:
(a) 1/2 of (i) 24 (ii) 46
(b) 2/3 of (i) 18 (ii) 27
(c) 3/4 of (i) 16 (ii) 36
(d) 4/5 of (i) 20 (ii) 35

(a)
(i) 1/2 of 24 = 1/2 × 24 = 12.
(ii) 1/2 of 46 = 1/2 × 46 = 23.

(b)
(i) 2/3 of 18 = 2/3 × 18 = 2 × 6 = 12.
(ii) 2/3 of 27 = 2/3 × 27 = 2 × 9 = 18.

(c)
(i) 3/4 of 16 = 3/4 × 16 = 3 × 4 = 12.
(ii) 3/4 of 36 = 3/4 × 36 = 3 × 9 = 27.

(d)
(i) 4/5 of 20 = 4/5 × 20 = 4 × 4 = 16.
(ii) 4/5 of 35 = 4/5 × 35 = 4 × 7 = 28.

Q3. Multiply and express as a mixed fraction:
(a) 3 × 5 1/5
(b) 5 × 6 3/4
(c) 7 × 2 1/4
(d) 4 × 6 1/3
(e) 3 1/4 × 6
(f) 3 2/5 × 8

(a) 3 × 26/5 = 78/5 = 15 3/5

(b) 5 × 27/4 = 135/4 = 33 3/4

(c) 7 × 9/4 = 63/4 = 15 3/4

(d) 4 × 19/3 = 76/3 = 25 1/3

(e) 13/4 × 6 = (13×6)/4 = 78/4 = 39/2 = 19 1/2

(f) 17/5 × 8 = 136/5 = 27 1/5

Q4. Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 litres of water. Vidya consumed 2/5 of the water. Pratap consumed the remaining water.
(i) How much water did Vidya drink?
(ii) What fraction of the total quantity of water did Pratap drink?

(i) Total water = 5 litres.
Water drunk by Vidya = 2/5 of 5 litres = (2/5)×5 = 2 litres.

(ii) Total fraction of water = 1.
Fraction of water consumed by Vidya = 2/5.
Fraction of water consumed by Pratap = 1 - 2/5 = 5/5 - 2/5 = 3/5.

Exercise 2.3

Q1. Find:
(i) 12 ÷ 3/4
(ii) 14 ÷ 5/6
(iii) 8 ÷ 7/3
(iv) 4 ÷ 8/3
(v) 3 ÷ 2 1/3
(vi) 5 ÷ 3 4/7

(i) 12 ÷ 3/4 = 12 × 4/3 = 4 × 4 = 16

(ii) 14 ÷ 5/6 = 14 × 6/5 = 84/5 = 16 4/5

(iii) 8 ÷ 7/3 = 8 × 3/7 = 24/7 = 3 3/7

(iv) 4 ÷ 8/3 = 4 × 3/8 = 3/2 = 1 1/2

(v) 3 ÷ 7/3 = 3 × 3/7 = 9/7 = 1 2/7

(vi) 5 ÷ 25/7 = 5 × 7/25 = 7/5 = 1 2/5

Q2. Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.
(i) 3/7
(ii) 5/8
(iii) 9/7
(iv) 6/5
(v) 12/7
(vi) 1/8
(vii) 1/11

(i) Reciprocal of 3/7 is 7/3. It is an Improper Fraction.

(ii) Reciprocal of 5/8 is 8/5. It is an Improper Fraction.

(iii) Reciprocal of 9/7 is 7/9. It is a Proper Fraction.

(iv) Reciprocal of 6/5 is 5/6. It is a Proper Fraction.

(v) Reciprocal of 12/7 is 7/12. It is a Proper Fraction.

(vi) Reciprocal of 1/8 is 8/1 = 8. It is a Whole Number.

(vii) Reciprocal of 1/11 is 11/1 = 11. It is a Whole Number.

Q3. Find:
(i) 7/3 ÷ 2
(ii) 4/9 ÷ 5
(iii) 6/13 ÷ 7
(iv) 4 1/3 ÷ 3
(v) 3 1/2 ÷ 4
(vi) 4 3/7 ÷ 7

(i) 7/3 ÷ 2/1 = 7/3 × 1/2 = 7/6 = 1 1/6

(ii) 4/9 ÷ 5/1 = 4/9 × 1/5 = 4/45

(iii) 6/13 ÷ 7/1 = 6/13 × 1/7 = 6/91

(iv) 13/3 ÷ 3/1 = 13/3 × 1/3 = 13/9 = 1 4/9

(v) 7/2 ÷ 4/1 = 7/2 × 1/4 = 7/8

(vi) 31/7 ÷ 7/1 = 31/7 × 1/7 = 31/49

Q4. Find:
(i) 2/5 ÷ 1/2
(ii) 4/9 ÷ 2/3
(iii) 3/7 ÷ 8/7
(iv) 2 1/3 ÷ 3/5
(v) 3 1/2 ÷ 8/3
(vi) 2/5 ÷ 1 1/2
(vii) 3 1/5 ÷ 1 2/3
(viii) 2 1/5 ÷ 1 1/5

(i) 2/5 ÷ 1/2 = 2/5 × 2/1 = 4/5

(ii) 4/9 ÷ 2/3 = 4/9 × 3/2 = 12/18 = 2/3

(iii) 3/7 ÷ 8/7 = 3/7 × 7/8 = 3/8

(iv) 7/3 ÷ 3/5 = 7/3 × 5/3 = 35/9 = 3 8/9

(v) 7/2 ÷ 8/3 = 7/2 × 3/8 = 21/16 = 1 5/16

(vi) 2/5 ÷ 3/2 = 2/5 × 2/3 = 4/15

(vii) 16/5 ÷ 5/3 = 16/5 × 3/5 = 48/25 = 1 23/25

(viii) 11/5 ÷ 6/5 = 11/5 × 5/6 = 11/6 = 1 5/6

Exercise 2.4

Q1. Find:
(i) 0.2 × 6
(ii) 8 × 4.6
(iii) 2.71 × 5
(iv) 20.1 × 4
(v) 0.05 × 7
(vi) 211.02 × 4
(vii) 2 × 0.86

(i) 0.2 × 6 = 2/10 × 6 = 12/10 = 1.2

(ii) 8 × 4.6 = 8 × 46/10 = 368/10 = 36.8

(iii) 2.71 × 5 = 271/100 × 5 = 1355/100 = 13.55

(iv) 20.1 × 4 = 201/10 × 4 = 804/10 = 80.4

(v) 0.05 × 7 = 5/100 × 7 = 35/100 = 0.35

(vi) 211.02 × 4 = 21102/100 × 4 = 84408/100 = 844.08

(vii) 2 × 0.86 = 2 × 86/100 = 172/100 = 1.72

Q2. Find the area of rectangle whose length is 5.7 cm and breadth is 3 cm.

Length = 5.7 cm, Breadth = 3 cm.
Area of Rectangle = Length × Breadth
= 5.7 × 3
= 57/10 × 3 = 171/10 = 17.1 cm²

Q3. Find:
(i) 1.3 × 10
(ii) 36.8 × 10
(iii) 153.7 × 10
(iv) 168.07 × 10
(v) 31.1 × 100
(vi) 156.1 × 100
(vii) 3.62 × 100
(viii) 43.07 × 100
(ix) 0.5 × 10
(x) 0.08 × 10
(xi) 0.9 × 100
(xii) 0.03 × 1000

(i) 1.3 × 10 = 13

(ii) 36.8 × 10 = 368

(iii) 153.7 × 10 = 1537

(iv) 168.07 × 10 = 1680.7

(v) 31.1 × 100 = 3110

(vi) 156.1 × 100 = 15610

(vii) 3.62 × 100 = 362

(viii) 43.07 × 100 = 4307

(ix) 0.5 × 10 = 5

(x) 0.08 × 10 = 0.8

(xi) 0.9 × 100 = 90

(xii) 0.03 × 1000 = 30

Q4. A two-wheeler covers a distance of 55.3 km in one litre of petrol. How much distance will it cover in 10 litres of petrol?

Distance covered in 1 litre = 55.3 km.
Distance covered in 10 litres = 55.3 × 10
= 553 km

Q5. Find:
(i) 2.5 × 0.3
(ii) 0.1 × 51.7
(iii) 0.2 × 316.8
(iv) 1.3 × 3.1
(v) 0.5 × 0.05
(vi) 11.2 × 0.15
(vii) 1.07 × 0.02
(viii) 10.05 × 1.05
(ix) 101.01 × 0.01
(x) 100.01 × 1.1

(i) 2.5 × 0.3 = 25/10 × 3/10 = 75/100 = 0.75

(ii) 0.1 × 51.7 = 1/10 × 517/10 = 517/100 = 5.17

(iii) 0.2 × 316.8 = 2/10 × 3168/10 = 6336/100 = 63.36

(iv) 1.3 × 3.1 = 13/10 × 31/10 = 403/100 = 4.03

(v) 0.5 × 0.05 = 5/10 × 5/100 = 25/1000 = 0.025

(vi) 11.2 × 0.15 = 112/10 × 15/100 = 1680/1000 = 1.68

(vii) 1.07 × 0.02 = 107/100 × 2/100 = 214/10000 = 0.0214

(viii) 10.05 × 1.05 = 1005/100 × 105/100 = 105525/10000 = 10.5525

(ix) 101.01 × 0.01 = 10101/100 × 1/100 = 10101/10000 = 1.0101

(x) 100.01 × 1.1 = 10001/100 × 11/10 = 110011/1000 = 110.011

Exercise 2.5

Q1. Find:
(i) 0.4 ÷ 2
(ii) 0.35 ÷ 5
(iii) 2.48 ÷ 4
(iv) 65.4 ÷ 6
(v) 651.2 ÷ 4
(vi) 14.49 ÷ 7
(vii) 3.96 ÷ 4
(viii) 0.80 ÷ 5

(i) 0.4 ÷ 2 = 4/10 × 1/2 = 2/10 = 0.2

(ii) 0.35 ÷ 5 = 35/100 × 1/5 = 7/100 = 0.07

(iii) 2.48 ÷ 4 = 248/100 × 1/4 = 62/100 = 0.62

(iv) 65.4 ÷ 6 = 654/10 × 1/6 = 109/10 = 10.9

(v) 651.2 ÷ 4 = 6512/10 × 1/4 = 1628/10 = 162.8

(vi) 14.49 ÷ 7 = 1449/100 × 1/7 = 207/100 = 2.07

(vii) 3.96 ÷ 4 = 396/100 × 1/4 = 99/100 = 0.99

(viii) 0.80 ÷ 5 = 80/100 × 1/5 = 16/100 = 0.16

Q2. Find:
(i) 4.8 ÷ 10
(ii) 52.5 ÷ 10
(iii) 0.7 ÷ 10
(iv) 33.1 ÷ 10
(v) 272.23 ÷ 10
(vi) 0.56 ÷ 10
(vii) 3.97 ÷ 10

Shift decimal one place to left.
(i) 4.8 ÷ 10 = 0.48
(ii) 52.5 ÷ 10 = 5.25
(iii) 0.7 ÷ 10 = 0.07
(iv) 33.1 ÷ 10 = 3.31
(v) 272.23 ÷ 10 = 27.223
(vi) 0.56 ÷ 10 = 0.056
(vii) 3.97 ÷ 10 = 0.397

Q3. Find:
(i) 2.7 ÷ 100
(ii) 0.3 ÷ 100
(iii) 0.78 ÷ 100
(iv) 432.6 ÷ 100
(v) 23.6 ÷ 100
(vi) 98.53 ÷ 100

Shift decimal two places to left.
(i) 2.7 ÷ 100 = 0.027
(ii) 0.3 ÷ 100 = 0.003
(iii) 0.78 ÷ 100 = 0.0078
(iv) 432.6 ÷ 100 = 4.326
(v) 23.6 ÷ 100 = 0.236
(vi) 98.53 ÷ 100 = 0.9853

Q4. Find:
(i) 7.9 ÷ 1000
(ii) 26.3 ÷ 1000
(iii) 38.53 ÷ 1000
(iv) 128.9 ÷ 1000
(v) 0.5 ÷ 1000

Shift decimal three places to left.
(i) 7.9 ÷ 1000 = 0.0079
(ii) 26.3 ÷ 1000 = 0.0263
(iii) 38.53 ÷ 1000 = 0.03853
(iv) 128.9 ÷ 1000 = 0.1289
(v) 0.5 ÷ 1000 = 0.0005

Q5. Find:
(i) 7 ÷ 3.5
(ii) 36 ÷ 0.2
(iii) 3.25 ÷ 0.5
(iv) 30.94 ÷ 0.7
(v) 0.5 ÷ 0.25
(vi) 7.75 ÷ 0.25
(vii) 76.5 ÷ 0.15
(viii) 37.8 ÷ 1.4
(ix) 2.73 ÷ 1.3

(i) 7 ÷ 3.5 = 7 ÷ 35/10 = 7 × 10/35 = 70/35 = 2

(ii) 36 ÷ 0.2 = 36 ÷ 2/10 = 36 × 10/2 = 360/2 = 180

(iii) 3.25 ÷ 0.5 = 325/100 ÷ 5/10 = 325/100 × 10/5 = 325/50 = 6.5

(iv) 30.94 ÷ 0.7 = 3094/100 ÷ 7/10 = 3094/100 × 10/7 = 3094/70 = 44.2

(v) 0.5 ÷ 0.25 = 5/10 ÷ 25/100 = 5/10 × 100/25 = 500/250 = 2

(vi) 7.75 ÷ 0.25 = 775/100 ÷ 25/100 = 775/100 × 100/25 = 775/25 = 31

(vii) 76.5 ÷ 0.15 = 765/10 ÷ 15/100 = 765/10 × 100/15 = 7650/15 = 510

(viii) 37.8 ÷ 1.4 = 378/10 ÷ 14/10 = 378/10 × 10/14 = 378/14 = 27

(ix) 2.73 ÷ 1.3 = 273/100 ÷ 13/10 = 273/100 × 10/13 = 273/130 = 2.1

Q6. A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much distance will it cover in one litre of petrol?

Distance covered in 2.4 litres = 43.2 km.
Distance in 1 litre = 43.2 ÷ 2.4
= 432/10 ÷ 24/10
= 432/10 × 10/24 = 432/24 = 18 km.

Class 7 Maths - Fractions and Decimals Practice

Chapter 2: Fractions and Decimals (Practice Questions)

RD Sharma / Extra Practice

Q1. Evaluate: 2 1/5 × 1 1/4 × 3 1/3

= 11/5 × 5/4 × 10/3
= (11 × 5 × 10) / (5 × 4 × 3)
= 550 / 60 = 55 / 6 = 9 1/6

Q2. Simplify: 5 1/6 ÷ 9/2

= 31/6 ÷ 9/2
= 31/6 × 2/9
= 62/54 = 31/27 = 1 4/27

Q3. A rope of length 9 3/4 m is cut into 6 pieces of equal length. Find the length of each piece.

Total length = 9 3/4 = 39/4 m.
Length of one piece = 39/4 ÷ 6
= 39/4 × 1/6 = 39/24 = 13/8 = 1 5/8 m.

Q4. By what number should 1 1/2 be multiplied to get 4 1/2?

Let the number be x.
(3/2) × x = 9/2
x = (9/2) ÷ (3/2) = 9/2 × 2/3 = 18/6 = 3.

Q5. The product of two fractions is 9 3/5. If one of the fractions is 9 3/7, find the other.

Product = 9 3/5 = 48/5.
One fraction = 9 3/7 = 66/7.
Other fraction = 48/5 ÷ 66/7 = 48/5 × 7/66
= 336/330 = 112/110 = 56/55 = 1 1/55.

Q6. Simplify: 0.008 × 0.2

= 8/1000 × 2/10 = 16/10000 = 0.0016

Q7. Evaluate: 1.07 × 0.02 × 100

= 1.07 × (0.02 × 100) = 1.07 × 2 = 2.14

Q8. Divide 0.12 by 0.003

= 0.12 / 0.003 = (12/100) / (3/1000)
= (12/100) × (1000/3) = 120 / 3 = 40

Q9. Evaluate: (2.5 × 2.5) - (0.5 × 0.5)

= 6.25 - 0.25 = 6.0 (or 6)

Q10. Find the cost of 4.5 metres of cloth if 1 metre costs Rs. 42.50.

Total Cost = 4.5 × 42.50
= 45/10 × 425/10 = 19125/100 = Rs. 191.25

Q11. The thickness of 12 sheets of paper is 2.16 mm. Find the thickness of 1 sheet.

Thickness = 2.16 / 12
= 216 / 1200 = 18 / 100 = 0.18 mm

Q12. What number should be added to 3.189 to get 7?

Let the number be x.
3.189 + x = 7.000
x = 7.000 - 3.189 = 3.811

Q13. The side of an equilateral triangle is 3.5 cm. Find its perimeter.

Perimeter = 3 × side
= 3 × 3.5 = 10.5 cm

Q14. Simplify: 15.6 \div 0.3 + 0.4

= (156/10 ÷ 3/10) + 0.4
= (156/10 × 10/3) + 0.4
= 52 + 0.4 = 52.4

Q15. Write 5 / 1000 in decimal notation.

= 0.005

Q16. Find the area of a square whose side is 2.5 m.

Area = side × side
= 2.5 × 2.5 = 6.25 m²

Q17. Which is greater: 0.5 or 0.05?

Convert to equivalent fractions: 0.50 and 0.05.
Since 50 > 5, 0.5 is greater.

Q18. Evaluate: (1/2 + 1/3) ÷ (1/4 - 1/6)

Numerator: (3+2)/6 = 5/6
Denominator: (3-2)/12 = 1/12
Result = (5/6) ÷ (1/12) = 5/6 × 12/1 = 60/6 = 10

Q19. Find 3/4 of a day in hours.

1 day = 24 hours.
3/4 × 24 = 3 × 6 = 18 hours.

Q20. Convert 12.05 to a mixed fraction in simplest form.

12.05 = 12 + 0.05 = 12 + 5/100
Reduce 5/100 = 1/20.
So, 12.05 = 12 1/20.

Class 7 Maths - Fractions and Decimals Summary

Chapter 2: Fractions and Decimals (Concepts & Summary)

1. Types of Fractions

Proper Fraction: A fraction representing a part of a whole (numerator < denominator). Example: 3/4.
Improper Fraction: A fraction where the numerator is greater than or equal to the denominator. Example: 7/4.
Mixed Fraction: A combination of a whole and a proper fraction. Example: 1 3/4.
Equivalent Fractions: Fractions that represent the same part of a whole. Example: 1/2 = 2/4 = 3/6.

2. Multiplication of Fractions

To multiply a fraction by a whole number, multiply the numerator by the whole number. Example: 2 × (3/5) = 6/5.
To multiply a fraction by a fraction, multiply the numerators together and denominators together.
(Fraction 1) × (Fraction 2) = (Product of Numerators) / (Product of Denominators)
The product of two proper fractions is less than each of the fractions.
The product of two improper fractions is greater than each of the fractions.
The part operator 'of' represents multiplication. Example: 1/2 of 10 = (1/2) × 10 = 5.

3. Division of Fractions

Reciprocal of a fraction: It is obtained by interchanging the numerator and the denominator. The product of a fraction and its reciprocal is always 1. Example: The reciprocal of 5/9 is 9/5.
To divide a whole number by a fraction, multiply the whole number by the reciprocal of the fraction. Example: 3 ÷ (1/2) = 3 × 2/1 = 6.
To divide a fraction by a fraction, multiply the first fraction by the reciprocal of the second fraction. Example: (2/3) ÷ (5/7) = (2/3) × (7/5) = 14/15.

4. Operations with Decimals

Multiplication of Decimals: Multiply them as whole numbers. Place the decimal point in the product such that the number of decimal places in the product is equal to the sum of the decimal places in the given decimals.
Multiplying by 10, 100, 1000: Move the decimal point to the right by as many places as there are zeros over 1.
Example: 1.23 × 100 = 123.
Division of Decimals by Whole Numbers: Divide as whole numbers. Place the decimal point directly above the decimal point in the dividend.
Dividing by 10, 100, 1000: Move the decimal point to the left by as many places as there are zeros over 1.
Example: 43.5 ÷ 10 = 4.35.
Division of Decimal by a Decimal: Shift the decimal point to the right by equal number of places in both, to make the divisor a whole number, then divide. Example: 2.4 ÷ 0.2 = 24 ÷ 2 = 12.

📱 Practice MCQs for this topic inside our App