# Practice Worksheet on Rational numbers

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**1) Represent the following rational numbers on the number line:**

a)-3/4 b) 31/-6 c) -1/2 d) ¾

**2) Write the following rational numbers in the standard form:**

a) 5/15 b) -24/40 c) 33/-77 d) -45/-105

**3) Compare the following rational numbers:**

1) -9/27, 6/-18 2) -5/7, 10/-6

3) 3/-8, -15/40 4) -11/7, 33/21

**4) Arrange the following rational numbers in the descending order:**

1) 2/-3, -4/9, -5/12, 7/-18

2) 3/-4, -5/12, -7/16, 9/-24

**5) Arrange the following rational numbers in the ascending order:**

1) 2/5, 1/3, 3/4, 1/6 2) 5/6, 7/8, 11/12, 3/10

**6) Fill in the blanks by the correct symbol >, = or < :**

1) | 3/4| ---------| ½| 2) |-1/2| ----- | -3/4 |

**7) Add:**1) 3/7 and -9/7, 2) 5/9 and 7/-9

3) 2/5, 5/-9 and -6/15

**8) Simplify:**1) -2 + ( 3 / 8 ) + ( - 1 / 5 ) , 2) (2/3) + ( -7/11) + (-1/4 )

**9) Verify that a + b = b + a**by taking (1) a = -7/5, b = 2/7

(2) a = -1 , b = -2/3

**10) Verify that (a+b)+c.=a+(b+c)**by taking

(1) a = -2 , b = -2/3 , c = -3/4

(2) a = -12, b = -9/11, c = 7/-12

**11) Simplify the following:**

1) (2/3) + (-4/5) + I + (-2/3) + (-11/5)

2)(5/8) + (-8/9) + 0 + (-13/3) + (17/24)

**12) Subtract :**1) (-3/4) from (1/2) 2) (5/8) from (-3/14)

**13) What should be added to (-7/20) to get (-2/5)?**

**14) The sum of two rational numbers is (-3/7). If one of the number is (-5/8) find the other.**

**15) The sum of two rational numbers is (-5/8). If one of the number is (-6/11), find the other number.**

**16) To which number should (2/3) be added to give (-11/4)?**

**17) From which number should (-11/4) be subtracted to give (-11/4)?**

**18) Find the product of :**

1) 5/9, -2/5 2) -5, -3/15

**19) Multiply, and give the product in the standard form:**

1) -6/25 by 50/24 2) 3/11 by 22

3) 21/5 by -15/21 4) -36 by -5/9

**20) Verify the property a x b = b x a by taking :**

1) a = (-12/7), b = (-21/5) 2) a = 0 , b = (-13/3)

**21) Verify the property a x ( b x c ) = (a x b) x c by taking**

1) a = (7/5), b = (-9/4), c = (1/2)

2) a = 1, b = (-13/5), c = (3/5)

**22) Verify the property ax(b+c)=(axb)+(axc) by taking:**

1) a = (1/3), b = 0, c = (-7/6)

2) a = -2, b = (9/5), c = (-2/15)

**23) Verify ( x x y )**

^{-1}= x^{-1}x y^{-1}1) x = 1/2, y = 1/3 2) x = -3/4 y=-1/8

**24) Verify that | x + y | ≤ | x| + | y |**by taking x= 13/4 and y= 3/2

**25) Verify that | x + y | = | x| + | y |**by taking x = 1/2 and y = -1/4

**26) The product of two rational numbers is 6. If one of them is 8, find the other number.**

**27) By what number should (-6/11) be multiplied to get (-32/11)?**

**28) Find the rational number between:**

1) 3 and 4 2) -7 and -6

**29) Find three rational numbers between:**

1) -5 and 8 2) ( -1/3 ) and (1/2)

**30) State whether true or false:**(practice worksheet on rational numbers)

1) Absolute value of a rational number is either positive or 0.

2) There are countless rational numbers with absolute value less than 5.

3) The absolute value of 0 is 0.

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