# Practice Worksheet on Rational numbers

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Practice worksheet on rational numbers is for 7th grade.

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.