RATIONAL NUMBER

 

Worksheet 1

Rational Numbers (Class 7 ICSE)

Section A: Multiple Choice Questions (MCQs)

1. Which of the following is a rational number?

   • a) $\sqrt{2}$
   • b) $\frac{3}{5}$
   • c) $\pi$
     
   • d) $\sqrt{3}$

2. Which of the following is not a rational number?

   • a) $\frac{7}{8}$
   • b) $-\frac{3}{4}$
   • c) $0.6$
     
   • d) $\sqrt{5}$

3. The number 0.75 can be written as:

   • a) $\frac{3}{5}$
   • b) $\frac{7}{10}$
   • c) $\frac{3}{4}$
   • d) $\frac{4}{3}$

4. Which of the following is the reciprocal of $\frac{4}{7}$?

   • a) $\frac{7}{4}$
   • b) $\frac{3}{4}$
   • c) $\frac{4}{3}$
   • d) $\frac{1}{4}$

Section B: True/False

5. A rational number can be expressed as a fraction where the denominator is zero. (True/False)

6. Every integer is a rational number. (True/False)

7. The decimal form of a rational number always terminates. (True/False)

Section C: Short Answer Questions

8. Convert $0.8$ into a rational number.

9. Is $\frac{0}{5}$ a rational number? Justify your answer.

10. Express $\frac{7}{9}+\frac{5}{9}$ as a rational number.

11. Find the value of $\frac{-5}{6}\times \frac{3}{2}$
    

Section D: Long Answer Questions

12. Simplify the following expression:
    $\frac{3}{5}-\frac{2}{3}$

13. Represent the following on the number line:
    $-\frac{4}{3}$, $\frac{2}{5}$, $\frac{1}{2}$, $\frac{-1}{4}$

14. If $x$ is a rational number such that $x+\frac{1}{3}=\frac{5}{6}$, find the value of $x$
    

15. Write 5 rational numbers between $\frac{2}{3}$ and $\frac{3}{4}$.

Section E: Applications

16. A recipe requires $\frac{3}{4}$ cup of sugar. If a baker wants to make half the quantity, how much sugar should he use?

17. The perimeter of a rectangle is $\frac{5}{3}$ meters. If the length of the rectangle is $\frac{2}{3}$ meters, find the width of the rectangle.

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Answers Key

Section A:

1. b) $\frac{3}{5}$
2. d) $\sqrt{5}$
3. c) $\frac{3}{4}$
4. a) $\frac{7}{4}$

Section B:

5. False (Denominator cannot be zero)
6. True (Integers are rational numbers with denominator 1)
7. False (A rational number's decimal form can terminate or repeat)

Section C:

8. $\mathrm{<br>}\frac{4}{5}$
9. No, because dividing by zero is undefined.
10. $\frac{\mathrm{<br>}}{}\frac{4}{3}$
11. $\frac{-5}{4}$

Section D:

12. $\frac{\mathrm{<br>}}{}\frac{-1}{15}$
13. (Graph points on a number line between -1 and 1 based on the given fractions.)
14. $\mathrm{<br>}\frac{1}{2}$
15. (List fractions between $\frac{2}{3}$ and $\frac{3}{4}$ such as $\frac{5}{7}$, $\frac{4}{6}$, etc.)

Section E:

16. $\frac{\mathrm{<br>}}{}\frac{8}{}$ cup of sugar.
17. Width $\frac{3}{}$ meters.

Worksheet 2

Rational Numbers (Class 7 ICSE)

Section A: Fill in the Blanks

1. The rational number $\frac{a}{b}$ is defined if $b \neq \_\_\_\_\_$
   
2. The reciprocal of $-\frac{5}{7}$ is ____
3. $\frac{-4}{5}+\frac{4}{5}=\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{.}$
4. The decimal form of $\frac{1}{8}$is _____.
5. A rational number between $\frac{1}{3}$ and $\frac{2}{3}$ is _____.

Section B: Match the Following

Column A	Column B
1. $\frac{4}{6}$ in simplest form	a) $\frac{-7}{6}$
2. Reciprocal of $\frac{2}{9}$	b) $\frac{-1}{6}$
3. $\frac{-3}{2} + \frac{-2}{3}$	c) $\frac{2}{3}$
4. $\frac{-1}{3} \times \frac{1}{2}$	d) $\frac{9}{2}$
5. $\frac{-14}{12}$ simplified	e) $\frac{-7}{6}$

Section C: Solve the Following

6. Add: $\frac{5}{8} + \frac{-3}{8}$
   
7. Subtract: $\frac{-7}{9} - \frac{-2}{3}$
   
8. Multiply: $\frac{-4}{5} \times \frac{10}{3}$
   
9. Divide: $\frac{15}{16} \div \frac{-5}{4}$
   
10. Find 5 rational numbers greater than $-1$ but less than $0$.

Section D: Word Problems

11. A farmer divides his land into three parts. The first part is $\frac{2}{5}$of the total land, the second part is $\frac{1}{4}$, and the rest is for grazing. What fraction of the land is for grazing?

12. A tank is $\frac{3}{7}$ full of water. If $\frac{2}{7}$ of the tank is emptied, what fraction of the tank is still filled?

13. A car covers $\frac{3}{4}$ of a journey in 3 hours. What fraction of the journey does it cover in 1 hour?

14. The sum of two rational numbers is $\frac{4}{9}$. If one of the numbers is $-\frac{2}{9}$, find the other number.

15. Arrange the following rational numbers in ascending order:
    $-\frac{5}{6}, \frac{1}{3}, -\frac{2}{3}, \frac{2}{5}$
    

Section E: True/False

16. The product of two negative rational numbers is positive.
17. Zero is the smallest rational number.
18. Every fraction is a rational number.
19. Rational numbers are closed under subtraction.
20. The sum of $\frac{-1}{4}$ and $\frac{1}{4}$ is $\frac{-2}{4}$
    

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Answer Key

Section A:

1. 0
2. $-\frac{7}{5}$
3. 0
4. 0.125
5. $\frac{1}{2}$

Section B:

1. c) $\frac{2}{3}$
2. d) $\frac{9}{2}$
3. a) $\frac{-7}{6}$
4. b) $\frac{-1}{6}$
5. e) $\frac{-7}{6}$

Section C:

6. $\frac{2}{8} = \frac{1}{4}$
7. $\frac{-7}{9} - \frac{-6}{9} = \frac{-1}{9}$
8. $\frac{-40}{15} = \frac{-8}{3}$
9. $\frac{15}{16} \div \frac{-5}{4} = \frac{15}{16} \times \frac{-4}{5} = \frac{-60}{80} = \frac{-3}{4}$
10. Examples: $-\frac{9}{10}, -\frac{4}{5}, -\frac{3}{4}, -\frac{7}{8}, -\frac{1}{2}$

Section D:

11. Grazing land: $1 - \left(\frac{2}{5} + \frac{1}{4}\right) = 1 - \frac{13}{20} = \frac{7}{20}$
12. Water remaining: $\frac{3}{7} - \frac{2}{7} = \frac{1}{7}$
13. Distance per hour: $\frac{3}{4} \div 3 = \frac{1}{4}$
14. Second number: $\frac{4}{9} - \left(-\frac{2}{9}\right) = \frac{6}{9} = \frac{2}{3}$
15. Ascending order: $-\frac{5}{6}, -\frac{2}{3}, \frac{1}{3}, \frac{2}{5}$
    

Section E:

16. True
17. False
18. True
19. True
20. False