Question

aModern School Barakhamba Road, Delhi

Summer Vacation Assignment(20-21)

Class: S3                                                                                                Subject: Mathematics

Chapter: Rational Numbers

1.      Choose the correct option:

i.    A number of the form    is said to be a rational number if:

a.         p and q are integers.

b.        p and q are integers and q ¹ 0 


c.         p and q are integers and p ¹ 0 


d.        p and q are integers and p ¹ 0 also q ¹ 0. 


ii.   Which of the following is not true?


a. +    =    +                                    b.    –    =    –     

c.   ´    =    ´                                    d.   ¸    =    ¸  

iii. In the standard form of a rational number, the common factor of numerator and denominator is always: 


a.      0          b.  1          c.  –2          d.  2

iv. The additive inverse of  
is:

a.            b.          c.             d.  

v.  Which of the following is equivalent to  

a.     
        b.           c.             d.   

vi.      Multiplicative inverse of a negative rational number is

a.    a positive rational number.                                     c. 0

b.    a negative rational number. 0                                 d. 1

c.   In the standard form of a rational number, the denominator is always:

a.         0                                 c. 1

b.        a negative integer      d.  a positive integer 

d.     Which number line correctly represents the rational numbers  ?

a.         

b.      

c.         

d.      

e.      The multiplicative inverse of 3  is:

a.     – 3            b. 5            c.            d. – 

 

f.          Which property is illustrated by the relation:

+ 0 = 0 +   where p and q are integers and q ¹ 0.

a.      Commutative property of rational numbers under addition

b.     Associative property of rational numbers under addition

c.      Multiplicative identity of rational number

d.     Additive identity of rational numbers

2.      State the property that justifies each of the following statements.

a.      +  =  +    [ ____________________________________________________]

b.    1 ´  =     [ ____________________________________________________]     

c.         =         [ ________________________________________]           

d.       =   +   [ ______________________________________]  

e.       +   =       [ ____________________________________________________]                                      

f.        ´  =   ´  ´  [ ______________________________________________]

g.       –  ]=  [ ] +  [ ]  [ _____________________________________]         

h.       + 0 =         [ ____________________________________________________]

3.      Given that  and  are two rational numbers with different denominators and both of them are in standard form. To compare these rational numbers we say that:

a.        <  , if p x s < r x q

 

b.      = , if ______= ______

 

c.      __ > __, if p x s > r x q

4.      Write the following  as rational numbers in their standard form:

a.     35% = ______________________________________

b.     1.2 =   ______________________________________

c.        = ______________________________________

d.     240 ÷ (- 840)  =  ______________________________________

e.      115 : 207 = ______________________________________

5.      Write:

a)       The rational numbers that are equal to their reciprocals. [ _______________ ]

b)      The rational number that does not have a reciprocal. 
[ _______________ ]

c)      The rational number that is equal to its negative. 
[ _______________ ]

6.      Write a rational number exactly halfway between:

a.      and    [ _____________ ] 

b.      and       [ _____________ ] 

c.     and  [ _____________ ] 

d.      and     [ _____________ ]  

7.      Read the passage given carefully to answer the questions following it:

·     While expressing a fraction in the decimal form when we perform division we notice that the division is complete after a certain number of steps when we get the remainder zero. The quotient obtained as decimal is called the Terminating Decimal. Such a decimal has a finite number of digits after the decimal point.

When we express 17/8 in the decimal form we get:  Save

 

 

 

 

 

 

 

 

                     

 

 Since, the remainder is zero. Therefore, the quotient 2.125 is a terminating decimal.

e.g.  = 0.5,  = 0.2,   = 0.25,   = 0.125

·     While expressing a fraction in the decimal form, if the division process does not end i.e. we do not get the remainder equal to zero; then such quotient obtained as decimal is known as Non-Terminating Decimal. In some cases, a digit or a block of digits repeats itself in the decimal part. Such decimals are called Non-Terminating repeating decimals.

e.g. When we express 5/3 in decimal form we get:

 

Save
















      

        Therefore, 1.666... is a non-terminating repeating decimal.

      e.g.  = 0.333…,  = 0.666…,  = 0.142857142857142857…

·     In some non-terminating decimals the digits in decimal part do not repeat in a pattern. Such decimals are called Non-Terminating non repeating decimals.

e.g. 3.141592…, 0.343443444…

·     A fraction is a terminating decimal if factors of its denominators are only 2’s or 5’s or both.

 

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Answer 1

Answer:

this is a very long question but is not posibal