OPERATIONS ON RATIONAL NUMBERS WORKSHEET

(1)  Fill in the blanks:

(i) −19/5 lies between the integers __________ and __________.

(ii) The rational number that is represented by 0.44 is __________.

(iii)  The standard form of + 58/(-78) is _________

(iv)  The value of (-5/12) + (7/15)  =  

(v)  The value of 

is                Solution

(2)  Say True or False:

(i) 0 is the smallest rational number.

(ii) There are an unlimited number of rational numbers between 0 and 1.

(iii) The rational number which does not have a reciprocal is 0.

(iv) The only rational number which is its own reciprocal is –1.

(v) The rational numbers that are equal to their additive inverses are 0 and–1.            Solution

(3)  List five rational numbers between

(i) –2 and 0

(ii)  -1/2 and 3/5

(iii)  0.25 and 0.35

(iv) –1.2 and -2.3              Solution

(4)  Write four rational numbers equivalent to

(i) −3/5              (ii)  -7/6         (iii)  8/9

Solution

(5)  Draw the number line and represent the following rational numbers on it

(i)  9/4   (ii)  -8/3   (iii)  -17/(-5)   (iv)  -15/4

Solution

Find the rational numbers for the question marks marked on the number line.

(i)  

(ii) 

(iii)  

Solution

(7)  Using average, write 3 rational numbers between (14/5) and (16/3)         Solution

(8)  Verify that −(−x) is the same x for:

(i)  x  =  11/15

(ii)  x  =  -31/45              Solution

(8)  Re-arrange suitably and add :

(9)  What should be added to -8/9 to get 2/5 ?  Solution

(10)  Subtract -8/44 from -17/11           Solution

(11)  Evaluate:

(i)  (9/2) x (-11/3)

(ii)  (-7/27) x (24/(-35))

Solution

(12)  Divide

(i) (-21/5) by (-7/-10)

(ii) (-3/13) by (-3)

(iii) -2 by -6/15 

Solution

(13)  Simplify (2/5 + 3/2) ÷ (3/10) as a rational number and show that it is between 6 and 7.    Solution

(14)  Write five rational numbers which are less than –2.

Solution

(15)  Compare the following pairs of rational numbers.

(i)  −11/5, -21/8

(ii)  3/(-4) , -1/2

(iii)   2/3, 4/5             Solution

(16)  Arrange the following rational numbers in ascending and descending order.

(i)  -5/12, -11/8, -15/24, -7/(-9), 12/36

(ii)  -17/10, -7/5, 0, -2/4, -19/20

Solution

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