Class 7 maths Rational numbers

Express (-192/108) as a rational number with numerator:

(i) 64

• 72/-25

• 64/-36

• 64/33

• 28/-36

Answer explanation

Given (-192/108)

To get numerator 64 we have to divide both numerator and denominator by -3

Then we get, (-192/108) ÷ (-3/-3)

= (64/-36)

Therefore (-192/108) as a rational number with numerator 64 is (64/-36)

Express each of the following rational numbers to the lowest form:

(i) (4/22)

• 1/11

• 2/10

• 6/55

• 2/11

Answer explanation

Given (4/22)

We know that HCF of 4 and 22 is 2

By dividing the given number by its HCF we get

(4 ÷ 2/22 ÷ 2) = (2/11)

Therefore (2/11) is the simplest form of the given number

Express each of the following rational numbers to the lowest form:

(i) (132/-428)

• 85/-36

• 33/-107

• 22/-55

• 87/-64

Answer explanation

Given (132/-428)

We know that HCF of 132 and 428 is 4

By dividing the given number by its HCF we get

(132 ÷ 4/-428 ÷ 4) = (33/-107)

Therefore (33/-107) is the simplest form of the given number

Fill in the blanks:

(i) (-5/7) = (…/35) = (…/49)

• -71/53

• -61/22

• -35/49

• 44/52

Answer explanation

Given (-5/7) = (…/35) = (…/49)

Here (-5/7) × (5/5) = (-25/35)

And also (-5/7) × (7/7) = (-35/49)

(ii) (-4/-9) = (8/18) = (12/27)

Write each of the following rational numbers in the standard form:

(i) (2/10)

• 8/5

• 5/3

• 2/4

• 1/5

Answer explanation

Given (2/10)

We know that HCF of 2 and 10 is 2

Now dividing the numerator and denominator by HCF i.e. 2, we get:

(2/10) ÷ (2/2) = (1/5)

Therefore (1/5) is the standard form of given number

In each of the following pairs represent a pair of equivalent rational numbers, find the values of x.

(i) (2/3) and (5/x)

• 25/2

• 16/3

• 15/2

• 22/5

Answer explanation

Given (2/3) and (5/x)

Also given that they are equivalent rational number so (2/3) = (5/x)

x = (5 × 3)/2

x = (15/2)

In each of the following pairs represent a pair of equivalent rational numbers, find the values of x.

(13/6) and (-65/x)

• 82

• -30

• 22

• 37

Answer explanation

Given (13/6) and (-65/x)

Also given that they are equivalent rational number so (13/6) = (-65/x)

x = 6/13 x (- 65)

x = 6 x (-5)

x = -30

(i)  A number which can be expressed in the form p/q, where p and q are integers and q is not equal to zero, is called a ………..

• Rational number

• Irrational Number

  If the integers p and q have no common divisor other than 1 and q is positive, then the rational number (p/q) is said to be in the ….

• Negative integer

• Standard form

• Irrational number

• positive integer

Two rational numbers are said to be equal, if they have the same …. form

• Standard form

• Non standard form