CBSE Class 8 Mathematics Rational Numbers Assignment Set 11

Question. Define rational number. Give at least 5 examples of such numbers.
Answer: A number which can be written in the form \( \frac{p}{q} \), where \( q \neq 0 \) and \( p, q \in I \) (integers). Examples of such numbers are: \( \frac{2}{3}, \frac{3}{2}, \frac{1}{7}, \frac{5}{1}, \frac{1}{2}, \frac{3}{4} \).

Question. Are \( \frac{0}{1}, \frac{0}{-1}, \frac{-0}{1}, 5, 0 \) a rational number. Is there any number which is not a rational number?
Answer: Yes. Yes, any number with a denominator of 0 is not a rational number (e.g., \( \frac{1}{0} \) is not a rational number).

Question. Is every whole number a rational number? Is the converse also true?
Answer: Yes. No, the converse is not true (a rational number may or may not be a whole number).

Question. What is the difference between a fraction and a rational number? Explain with the help of an example.
Answer: Fractions represent parts of a whole and are positive, e.g., \( \frac{1}{2}, \frac{1}{4}, \frac{3}{8} \), etc. Rational numbers include both positive and negative fractions as well as integers, e.g., \( -\frac{1}{2}, -\frac{1}{4}, -\frac{3}{8}, \frac{1}{2}, \frac{1}{4}, \frac{3}{8} \), etc.

Question. Represent \( \frac{1}{2}, \frac{3}{4} \) on the number line.
Answer: To represent these numbers, draw a number line and mark points for 0 and 1. Since both \( \frac{1}{2} \) and \( \frac{3}{4} \) lie between 0 and 1, divide the interval between 0 and 1 into 4 equal segments. The second mark from 0 represents \( \frac{2}{4} = \frac{1}{2} \), and the third mark represents \( \frac{3}{4} \).

Question. Define equivalent rational numbers with the help of example. Are \( \frac{2}{5} \) and \( \frac{4}{10} \) equivalent rational numbers?
Answer: Equivalent rational numbers are numbers that represent the same value when simplified, e.g., \( \frac{1}{2}, \frac{2}{4}, \frac{3}{6} \), etc. Yes, \( \frac{2}{5} \) and \( \frac{4}{10} \) are equivalent rational numbers.

Question. Reduce the following rational numbers into lowest form if possible.
(i) \( \frac{12}{16} \)
(ii) \( \frac{17}{79} \)
(iii) \( \frac{-24}{48} \)
(iv) \( \frac{-60}{-84} \)
(v) \( \frac{12}{36} \)
(vi) \( \frac{11}{13} \)
(vii) \( -\frac{5}{10} \)
(viii) \( -\frac{33}{11} \)
Answer:
(i) \( \frac{3}{4} \)
(ii) \( \frac{17}{79} \)
(iii) \( -\frac{1}{2} \)
(iv) \( \frac{5}{7} \)
(v) \( \frac{1}{3} \)
(vi) \( \frac{11}{13} \)
(vii) \( -\frac{1}{2} \)
(viii) \( -3 \)

Question. Express \( \frac{1}{4} \) as a rational number with denominator as
(i) 20
(ii) -80
(iii) -24.
Answer:
(i) \( \frac{5}{20} \)
(ii) \( \frac{-20}{-80} \)
(iii) \( \frac{-6}{-24} \)

Question. Write \( \frac{2}{5} \) in an equivalent form so that the numerator is
(i) -56
(ii) 154
(iii) 10.
Answer:
(i) \( \frac{-56}{-140} \)
(ii) \( \frac{154}{385} \)
(iii) \( \frac{10}{25} \)

Question. Fill the gap
(i) \( \frac{2}{3} = \frac{\text{___}}{135} \)
(ii) \( \frac{\text{___}}{4} = \frac{90}{120} \)
(iii) \( \frac{5}{\text{___}} = \frac{90}{216} \)
(iv) \( \frac{9}{16} = \frac{90}{\text{___}} \)
Answer:
(i) 90
(ii) 3
(iii) 12
(iv) 160

Question. In each of the following, find an equivalent form of the rational number having a common denominator
(i) \( \frac{5}{6} \) and \( \frac{7}{9} \)
(ii) \( \frac{2}{3}, \frac{5}{6} \) and \( \frac{7}{12} \)
(iii) \( \frac{5}{7}, \frac{3}{8}, \frac{9}{14} \) and \( \frac{20}{21} \)
Answer:
(i) \( \frac{15}{18} \) & \( \frac{14}{18} \)
(ii) \( \frac{8}{12}, \frac{10}{12}, \frac{7}{12} \)
(iii) \( \frac{120}{168}, \frac{63}{168}, \frac{108}{168}, \frac{160}{168} \)

Question. Write the following rational number in standard form
(i) \( \frac{-144}{-504} \)
(ii) \( \frac{140}{490} \)
(iii) \( \frac{240}{-840} \)
(iv) \( \frac{132}{330} \)
Answer:
(i) \( \frac{2}{7} \)
(ii) \( \frac{2}{7} \)
(iii) \( -\frac{2}{7} \)
(iv) \( \frac{2}{5} \)

Question. Compare the following rational number.
(i) \( \frac{21}{15} \) and \( \frac{19}{27} \)
(ii) \( \frac{-15}{22} \) and \( \frac{-34}{29} \)
Answer:
(i) \( \frac{21}{15} > \frac{19}{27} \)
(ii) \( \frac{-15}{22} > \frac{-34}{29} \)

Question. Find the absolute value of the following numbers.
(i) \( -\frac{5}{7} \)
(ii) \( \frac{-5}{-7} \)
(iii) \( -\left(\frac{2}{3}\right) \)
Answer:
(i) \( \frac{5}{7} \)
(ii) \( \frac{5}{7} \)
(iii) \( \frac{2}{3} \)

Question. Simplify \( -\left|-\frac{2}{3}\right| + \left|-\frac{1}{3}\right| + \left|-\left(-\frac{2}{3}\right)\right| - \left|-\frac{1}{3}\right| \)
Answer: 0