Rational Numbers - Worksheets

CBSE Worksheet 01
Class 08 - Mathematics (Rational Numbers)

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General Instructions: All questions are compulsory. Q.1 to Q.2 carries one mark each. Q.3 to Q.7 carries two marks each. Q.8 and Q.9 carries three marks each. Q.10 to Q.12 carries four marks each.

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1. Represent 74$\frac{7}{4}$on the number line.
2. Write five rational numbers greater than –2.
3. State True or False
   1. When we multiply a rational number with 1 we get same number.
   2. A rational number is always a whole number.
   3. All the whole numbers are rational numbers.
   4. All the integers are rational numbers.
4. Fill in the blanks
   1. Zero has ________ reciprocal.
   2. The product of a rational no. and its inverse is ________.
   3. The numbers 5 and -5 are their own ________.
   4. The number _______ is not the reciprocal of any number.
5. Match the columns

   Column A	Column B
   i. The multiplicative inverse of 1711$1\frac{7}{11}$	a. Not defined
   ii. The reciprocal of -1	b. −1711$-1\frac{7}{11}$
   iii. The reciprocal of 0	c. -1
   iv. Negative of 1711$1\frac{7}{11}$	d. 1118$\frac{11}{18}$

6. Represent 34$\frac{3}{4}$ on the number line.
7. Arrange in ascending order
   25,13,−34,16$\frac{2}{5},\frac{1}{3},\frac{-3}{4},\frac{1}{6}$
8. Which is greater?
   1. 9−13$\frac{9}{-13}$ and 7−12$\frac{7}{-12}$
   2. −89$\frac{-8}{9}$ and −910$\frac{-9}{10}$
9. using appropriate properties find : 25×(−37)−16×32+114×25$\frac{2}{5}\times \left(-\frac{3}{7}\right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$.
10. Compare
    1. −125$\frac{-12}{5}$ and -3
    2. −23$\frac{-2}{3}$ and 5−8$\frac{5}{-8}$
    3. 4−5$\frac{4}{-5}$ and −710$\frac{-7}{10}$
11. What should be subtracted from (34−23)$\left(\frac{3}{4}-\frac{2}{3}\right)$ to get −16$\frac{-1}{6}$?
12. Find the multiplicative inverse of ∞$\mathrm{\infty }$.

CBSE Worksheet 01
Class 08 - Mathematics (Rational Numbers)
Solution

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1. 74=134$\frac{7}{4}=1\frac{3}{4}$
   
2. Five rational numbers greater than –2 are :
   −32,−1,−12,0,12$\frac{-3}{2},-1,\frac{-1}{2},0,\frac{1}{2}$
3. 1. True
   2. False , it is not necessary that every rational number is whole number.
   3. True
   4. True
4. 1. Zero
   2. One
   3. Reciprocals
   4. Zero
5. 1. - d
   2. - c
   3. - a
   4. - b
6. Divide the number line into 4 equal parts starting from 04,14$\frac{0}{4},\frac{1}{4}$,....... 44$\frac{4}{4}$ on the right side of number line. Bold mark 34$\frac{3}{4}$ as asked in the question  and mark it as any alphabet like A.
   
7. LCM of 5, 3, 4 and 6 is 60.
   So, (12,20,−15,10)60$\frac{(12,20,-15,10)}{60}$
   Ascending order: −1560,1060,1260,2060$\frac{-15}{60},\frac{10}{60},\frac{12}{60},\frac{20}{60}$
   −34,16,25,13$\frac{-3}{4},\frac{1}{6},\frac{2}{5},\frac{1}{3}$.
8. 1. (9×(−1)(−13×(−1))=(−913)$\frac{(9\times (-1)}{(-13\times (-1))}=\left(\frac{-9}{13}\right)$ and (7×(−1))(−12×(−1))=(−712)$\frac{(7\times (-1))}{(-12\times (-1))}=\left(\frac{-7}{12}\right)$
      LCM of 13 and 12 is 156
      (−108,−91)156$\frac{(-108,-91)}{156}$
      −108156<−91156$\frac{-108}{156}<\frac{-91}{156}$
      Hence, −712$\frac{-7}{12}$ is greater
   2. LCM of 9 and 10 is 90.
      (−80,−81)90$\frac{(-80,-81)}{90}$
      −8190<−8090$\frac{-81}{90}<\frac{-80}{90}$
      Hence, −89$\frac{-8}{9}$ is greater.
9. 25×(−37)−16×32+14×25$\frac{2}{5}\times \left(-\frac{3}{7}\right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{4}\times \frac{2}{5}$
   =25×(−37)−16×32+25×114$=\frac{2}{5}\times \left(-\frac{3}{7}\right)-\frac{1}{6}\times \frac{3}{2}+\frac{2}{5}\times \frac{1}{14}$ . . . . [By commutativity]
   =25×(−37)+25×114−16×32$=\frac{2}{5}\times \left(-\frac{3}{7}\right)+\frac{2}{5}\times \frac{1}{14}-\frac{1}{6}\times \frac{3}{2}$ . . . . [By associativity]
   =25×{(−37)+114}−16×32$=\frac{2}{5}\times \left\{\left(-\frac{3}{7}\right)+\frac{1}{14}\right\}-\frac{1}{6}\times \frac{3}{2}$ . . . . [ By distributivity ]
   =25×{(−6)+114}−16×32$=\frac{2}{5}\times \left\{\frac{(-6)+1}{14}\right\}-\frac{1}{6}\times \frac{3}{2}$
   =25×{−514}−16×32=−17−14$=\frac{2}{5}\times \left\{\frac{-5}{14}\right\}-\frac{1}{6}\times \frac{3}{2}=\frac{-1}{7}-\frac{1}{4}$
   =−4−728=−1128$=\frac{-4-7}{28}=\frac{-11}{28}$
10. 1. LCM of 5 and 1 is 5
       (−12,−15)5$\frac{(-12,-15)}{5}$
       i.e −125>−−155$\frac{-12}{5}>-\frac{-15}{5}$
       Hence, −125>−3$\frac{-12}{5}>-3$    
    2. LCM of 3 and 8 is 24
       (−16,−15)24$\frac{(-16,-15)}{24}$
       i.e. −1624<−1524$\frac{-16}{24}<\frac{-15}{24}$
       Hence, −23<−58$\frac{-2}{3}<\frac{-5}{8}$
    3. LCM of 5 and 10 is 10
       (−8,−7)10$\frac{(-8,-7)}{10}$
       i.e. −810<−710$\frac{-8}{10}<\frac{-7}{10}$
       Hence, −45<−710$\frac{-4}{5}<\frac{-7}{10}$
11. Let the number to be subtracted be x
    (34−23)−x=−16$\left(\frac{3}{4}-\frac{2}{3}\right)-x=\frac{-1}{6}$
    [(9−8)12]−x=−16$\left[\frac{\left(9-8\right)}{12}\right]-x=\frac{-1}{6}$
    112+16=x$\frac{1}{12}+\frac{1}{6}=x$
    x=(1+2)12$x=\frac{(1+2)}{12}$
    x=312$x=\frac{3}{12}$
    x=14$x=\frac{1}{4}$
12. ∞$\mathrm{\infty }$ is the symbol used for undefined.
    ∞$\mathrm{\infty }$ =10$=\frac{1}{0}$
    Because, any non zero number divided by zero is undefined or infinity.
    To get reciprocal of 10$\frac{1}{0}$, zero becomes the numerator and 1 becomes the denominator i.e. 01$\frac{0}{1}$.
    Hence, zero divided by any non-zero number is zero.
    Therefore, the multiplicative inverse of ∞$\mathrm{\infty }$ is 0.