Rational numbers class 8 worksheet

In this page we have Rational numbers class 8 worksheet. We have given True and false questions, Multiple choice questions, Subjective questions based on properties of the rational numbers . Hope you like them and do not forget to like , social share and comment at the end of the page.

Question 1
Find the value of a
1. $\frac {1}{7} - \frac {5}{16 } = a$
2. $\frac {3}{13} - a =\frac { 20}{143}$
3. $a - \frac {1}{11 } = \frac {29}{165}$
4. $\frac {1}{3} - \frac {5}{13 } = a$
5. $\frac {5}{18} \times \frac {1}{4 } =a$
6. $\frac {5}{19} \times a =\frac { 5}{209}$
7. $a \times \frac {1}{5 } = \frac {1}{7}$

1. $\frac {-19}{112}$
2. $\frac {1}{11 }$
3. $\frac {4}{15}$
4. $\frac {-2}{39}$
5. $\frac { 5}{72}$
6. $\frac { 1}{11 }$
7. $\frac {5}{7}$

Question 2
Evaluate below expression
1. $\frac {1}{19} \times \frac {2}{9 }$
2. $\frac {2}{19} - \frac {1}{10 }$
3. $\frac {4}{13} \times \frac {1}{11 }$
4. $\frac { 3}{76} \div \frac {3}{8 }$
5. $\frac {2}{9} - \frac {5}{11 } =$
6. $\frac {4}{13} \times \frac {5}{16 } - \frac {5}{52}$
7. $\frac {1}{3} \times \frac {5}{11 } + \frac {5}{33}$
8. $\frac {1}{16} \times \frac {2}{19 } \div \frac { 1}{152}$
9. $\frac {1}{18} \times \frac {1}{5 } - \frac {1}{90}$
10. $\frac {3}{11} \times \frac {1}{9 }$
11. $\frac {1}{4} - \frac {1}{3 } - \frac {-1}{12}$
12. $\frac {4}{7} - \frac {4}{11 } + \frac {16}{77}$
13. $\frac {1}{19} - \frac {1}{15 } - \frac {-4}{285}$

1. $\frac {2}{171}$
2. $\frac { 1}{190}$
3. $\frac {4}{143}$
4. $\frac {2}{19}$
5. $\frac {-23}{99}$
6. 0
7. $\frac {10}{33}$
8. 1
9. 0
10. $\frac {1}{33}$
11. 0
12. $\frac {32}{77}$
13. 0

Question 3
Find the additive inverse of each of the following:
1. $\frac {1}{2}$
2. $\frac {-2}{7}$
3. $\frac {-1}{11}$
4. 12
5. $\frac {-3}{10}$

(i) $\frac {1}{2}$
Additive inverse = $\frac {-1}{2}$
(ii) $\frac {-2}{7}$
Additive inverse = $\frac {2}{7}$
(iii) $\frac {-1}{11}$
Additive inverse = $\frac {1}{11}$
(iv)12
(v)$\frac {-3}{10}$
Additive inverse=$\frac {3}{10}$

Question 4
True or False Statement
1. Every rational number has a reciprocal
2. 3/2 lies between 1 and 2
3. The negative of 1 is 1 itself.
4. For all rational numbers a and b, a – b = b – a.
5. -1/2 is smaller than -2

(i) false as 0 does not have reciprocal
(ii) True
(iii) False
(iv) false
(v)false

Question 5
Find the multiplicative inverse of the following.
1. $\frac {-12}{11}$
2. $\frac {-1}{9}$
3. $\frac {2}{3}$
4. $\frac {-1}{2} \times \frac {-2}{5}$
5. $\frac {-1}{8} \times \frac {-8}{7}$
6. -11

1. $\frac {-12}{11}$
Multiplicative inverse =>$\frac {-11}{12}$
2. $\frac {-1}{9}$
Multiplicative inverse =$\frac {-9}{1}=-9$
3. $\frac {2}{3}$
Multiplicative inverse =$\frac {3}{2}$
4. $\frac {-1}{2} \times \frac {-2}{5} =\frac {1}{5}$
Multiplicative inverse =$5$
5. $\frac {-1}{8} \times \frac {-8}{7} = \frac {1}{7}$
Multiplicative inverse =7
6. -11
Multiplicative inverse =-1/11

Multiple Choice Questions

Question 6
if a and b are positive numbers and a > b, then which of the is true?
(a) -a > -b
(b) 1/a > 1/b
(c) 1/b > 1/a
(d) -1/b > -1/a
Question 7
Which of the following is a rational number between 2/3 and 4/5?
(a) 1/2
(b) 1
(c) 2
(d) 41/60
Question 8
Multiplicative inverse of a negative rational number is
(a) a positive rational number.
(b) a negative rational number.
(c) 0
(d) 1
Question 9
which of the following is false?
(a) 9/6 lies between 1 and 2
(b) The multiplicative inverse of 3/4 is 4/3
(c) The reciprocal of 2/5 is 45/10
(d) None of the above
Question 10
The multiplicative inverse of $-1 \frac {2}{9}$ is
(a) -10/9
(b) -11/9
(c) -9/11
(d) 9/11
Question 11
The sum of the additive inverse and multiplicative inverse of 2 is
(a) 3/2
(b) -3/2
(d) 1/2
(d) 1
Question 12
The product of the additive inverse and multiplicative inverse of -1/2 is
(a) 1
(b) 2
(d) -1
(d) 0

6. (c)
7. (d)
8. (b)
9. (d)
10. (d)
11. (b)
12 (d)

Subjective Type Questions

Question 13
Ram have a rope of 50 metres long and he cut the pieces of equal size from equal. If the length of the one of the piece is 5/3, how many pieces did he cut?

Total Number of pieces = Total Length/Lenght of one piece = $\frac {50}{\frac {5}{3}}= 50 \times \frac {3}{5} = 30$

Question 14
Write the following rational numbers in the descending order.
8/7,-9/8 ,-3/2 ,0 , 1/2, 2/5

LCM of 7,8,2,5=280$Equilvalent Fractions will be 360/280, -315/280, -420/280,0, 140/280, 118/280 So Descending order will be 360/280,140/280,118/280, 0, -315/280, -420/280 or 8/7,1/2,2/5,0,-9/8,-3/2 Question 15 A and B receives the same amount of Salary. Here are expenditures by each of them (i) If the amount left is gone to saving, what fraction of salary are A and B Saving? (ii) If the Salary is Rs 60000, what is the saving in Rupees Answer (i) Saving for A =$1 - \frac {1}{3} - \frac {1}{4} - \frac {1}{5} = \frac { 60 - 20 -15 -12}{60}=\frac {13}{60}$Saving for B =$1 - \frac {1}{3} - \frac {1}{5} - \frac {2}{5} = \frac { 15 - 5 -3 -6}{60}=\frac {1}{15}$(ii) Saving in Rs for A =$ \frac {13}{60} \times 60000=13000$Saving in Rs for B =$ \frac {1}{15} \times 60000=4000\$

Summary

This Rational numbers class 8 worksheet is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feebback on the mail.