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Ramesh covered distance by bus = 4(1/4) km or (17/4) km. 

Ramesh walked to school = (3/4) km 

∴ Total distance covered by Ramesh 

= ((17/4) + (3/4)) Km 

= (17 + 3)/4 Km 

= (20/4) Km = 5 Km

Dolly get part of cake = 1/5

Teenu get part of cake = 1/7

∵ Fractions 1/5 and 1/7 are unit fractions. 

∴ Fractions with smaller denominator will be greater. 

Thus, Dolly got more cake than Teenu, because fraction 1/5 is greater than fraction 1/7.

Reena ate part of fruit = 3/5

Kamal ate part of fruit = 2/5

∴ They both ate total fruit = (3/5) + (2/5) = 5/5 = 1

Sunita got part of mango = 1/4

Marry got part of mango = 1/4

∴ Total parts of mango they both got = (1/4) + (1/4) 

= (1 + 1)/4 = 2/4 = 1/2 

Thus, they together got 1/2 part of mango.

Sum of the numbers in each row: 

i. 22 + 12 + 18 + 87 = 139 

ii. 88 + 17 + 9 + 25 = 139 

iii. 10 + 24 + 89 + 16 = 139 

iv. 19 + 86 + 23 + 11 = 139

Sum of the numbers along the diagonals: 

i. 22 + 17 + 89 + 11 = 139 

ii. 87 + 9 + 24 + 19 = 139

Sum of the numbers in each column: 

i. 22 + 88 + 10 + 19 = 139 

ii. 12 + 17 + 24 + 86 = 139 

iii. 18 + 9 + 89 + 23 = 139 

iv. 87 + 25 + 16 + 11 = 139

∴ We observe that the sum of the numbers in each of the rows, the columns and along each diagonal remains the same every time. The numbers in the first row 22 – 12 – 1887 is the birth date of Srinivasa Ramanujan.

2/3 of 27 is 18.

= 2/3 × 27

= 2 × 9

= 18

False.

Consider the proper fraction 5/8.

Then, reciprocal of 5/8 = 8/5.

Therefore the obtained fraction is improper fraction.

False.

The reciprocal of 4/7 is 7/4.

False.

2/3 of 8 = (2/3) × 8

1 metre 40 centimetres + 60 centimetres = 1.40 metres + 0.60 metres

[ 100 centimetres = 1 metre]

= 2.00 metres

Since, 2.6 > 2.00

∴ 2.6 metres is greater.

False 

As 0.2 × 0.3 = 0.06

Out of 0, 1, 2, 3, 4, 5 ➝ 1, 2, 3, 4 and 5 are the natural numbers.

∴ The fraction that represents the number of natural numbers to the total numbers = 5/6 and the whole numbers are 0,1, 2, 3, 4 and 5.

∴ The fraction that represents the number of whole numbers to the total numbers = 6/6

Natural numbers from 2 to 12 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, & 12

Prime numbers among these are 2, 3, 5, & 11

Therefore, out of 11 numbers, 5 are prime numbers. It represents a fraction 5/11

There are 4 circle, out of 8, having X’s in them,

Therefore it represents a fraction 4/8.

Dress dyed so far = 20

Total dress = 30

Fraction = 20/30 = 2/3

Total CDs Kristin had on her birthday 3 + 5 = 8

Out of 8 CDs, She bought 3 CDs and also got 5 CDs as gifts

Therefore, she bought and received CDs as gifts in a fraction of 3/8 and 5/8 respectively.

(a) 3/5 = ..../20

3 × 20 = 5 × ....

3 × 2 × 2 × 5 = 5 × ...

12 = ...

Hence, the required fraction is 12/20

(b) 3/5 = 9/...

3 × ... = 5 × 9

3 × ... = 5 × 3 × 3

.... = 15

Hence, the required fraction is 9/15

(c) 3/5 = .../30

3 × 30 = 5 × .....

3 × 2 × 3 × 5 = – 5 × ...

18 = ......

Hence, the required fraction is 18/30

(d) 3/5 = 27/.....

3 × ... = 5 × 27

3 × .... = 5 × 3 × 3 × 3

Hence, the required fraction is 27/45

(a) 2/5 = two-fifth

(b) 3/4 =  three-fourth

(c) 7/10 = seven-tenth

(d) 11/12 = eleven-twelveth

(e) 2/3 = two-third

(f) 4/5 = four-fifth

(g) 5/8 =  five-eight

(h) 3/7 = three-seventh

(i) 5/6 = five-sixth

(j) 7/9 = seven-nineth

(a)  36/48 = 9/....

36 × .... = 48 × 9

3 × 3 × 2 × 2 × ... = 2 × 2 × 2 × 2 × 3 × 3 × 3

.... = 12

Hence, the required fraction 9/12

(b) 36/48 = .../4

36 × 4 = 48 × .....

3 × 3 × 2 × 2 × 1 = 2 × 2 × 2 × 2 × 3 × .....

3 = ....

Hence, the required fraction is 3/4

(i) 4/7

(ii) 2/9

(iii) 7/10

(a) The denominator of the fraction 1/8 is 8

(b) The numerator of the fraction 2/5 is 2

(c) 3 is the denominator of fraction 1/3​​​​​

(d) 1 is the numerater of the fraction 1/5

(e) In a fraction, the denominator is written below the numerator separated by a line.

1/2 x 5/8

= (1 x 5)/(2 x 8)

= 5/16

(i) By interchanging 1/2 × 5/8 we get 5/8 × 1/2

5/8 × 1/2 = (5 x 1)/ (8 x 2) = 5/16 which is same as the product we get in Example 32 by multiplying 1 2 and 5 8 . This means that interchanging the fractions does not affect the answer. 

(ii) By observing the 3 products given in the solution of Example 32, we come to know that the value of the fractions in the products are as follows 

(a) The product of two fractions whose value is less than 1 i.e. the proper fractions is less than each of the fractions that are multiplied. 

(b) The product of a proper and an improper fraction is less than the improper fractions and greater than the proper fraction. 

(c) The product of two improper fractions is greater than each of the two fractions.

1/3 x 7/5

= (1 x 7)/(3 x 5)

= 7/15

4/3 x 5/2

= (4 x 5)/(3 x 2)

= 20/6

= 10/3

Quantity of water in the first beaker = 1 full

Quantity of water in the second beaker = 1/4

Quantity of water in the third beaker = 3/4

Quantity of water in the fourth beaker = 1/2

Ascending order 1/4 < 1/2 < 3/4 < 1

i. 3

ii. 36

iii. 3

iv. 7

v. 8, 18

vi. 12, 6

vii. 9, 16, 20, 24

viii. 15, 20, 35, 36, 55

(i) Total number of equal parts = 3

Shaded parts = 2

Fraction representing the shaded portion = 2/3

(ii) Total number of equal parts = 4

Shaded parts = 3

Fraction representing the shaded parts = 3/4

(iii) Total number of equal parts = 5

Shaded parts = 4

Fraction representing the shaded parts = 4/5

The numerator may be any one of!, 2, 3,4, 5, 6, 7, 8, 9 and the denominator may be any one of 1, 2,3,4, 5,6, 7,8,9. Sum of numerator and denominator is a multiple of 3.

∴ Possible proper fractions are 1/2,1/5,1/8,2/4,2/7,3/6,3/9,4/5,4/8,5/7,6/9

Also given the product of numerator and denominator is a multiple of 4.

∴ Possible fractions are 1/8,2/4,4/5,4/8

Total number of dots = 24

Number of dots in the triangle = 6

∴ Fraction represents the dots in the triangle = 6/24

i. \(\frac{3}{30},\frac{20}{30}\)

ii. \(\frac{15}{35},\frac{28}{35}\)

iii. \(\frac{5}{15},\frac{9}{15}\)

iv. \(\frac{5}{20},\frac{8}{20}\)

Given, numerator of an equivalent fraction = 15

Equivalent fraction of 3/5 = (3×5)/(5×5) = 15/25

Painted portion of the wall = 3/8

Of which the yellow colour painted = 1/3

Yellow colour in the entire wall = 1/3 of 3/8

= 1/3 x 3/8 

= 1/8

1/8 of the wall is painted yellow.

Here the denominators, of both fractions are same.

Also 7 > 6 So 7/10 > 6/10

We know that if the numerators are same in two fractions, the fraction with smaller denominator is greater.

∴ 1/3 > 1/5

∴ Mala got more marks.

Correct option is B) A rational number is in the form of p/q, q≠0

Given length of rectangular sheet of paper is 12 (1/2) i.e. (25/2)

Breadth of rectangular sheet of paper is 10 (2/3) i.e. (32/3)

But we know that perimeter of rectangle = 2 (length + breadth)

Perimeter of rectangular sheet = 2 [(25/2) + (32/3)]

LCM of 2 and 3 is 6, by taking this and simplifying we get

Perimeter = 2[(25 × 3)/6 + (32 × 2)/6]

= 2[(75/6) + (64/6)]

= 2(139/6)

= (139/3)

= 46 (1/3) cm

(ii) Parts of fractions is 2

(iii) Improper fraction is 6/5

It is shown from the diagram that fraction 1/5 is smaller than fraction 1/3, because 1/3 is a part of 3 parts of a unit, and 1/5 is a part of 5 parts of a unit.

(i) Smaller fraction is 7/9

(ii) Bigger fraction is 6/7

Even numbers 1 to 15 = 2, 4, 6, 8, 10, 12, 14. 

Total even numbers = 7 

Hence, fraction = 7/15

There are 60 minutes in a hour. Therefore 40, minutes of an hour represent 40/60.