CBSE Class 7 Mathematics Rational Numbers Assignment Set 08

Question. Multiply \( 4 \) by \( \frac{3}{32} \)
Answer: \( \frac{3}{8} \)

Question. Multiply \( -3\frac{4}{17} \) and \( \frac{-85}{33} \) and express the result as a mixed fraction.
Answer: \( 8\frac{1}{3} \)

Question. Simplify \( \frac{11}{18} \times \frac{12}{33} \times \frac{-6}{25} \)
Answer: \( \frac{-4}{75} \)

Question. Simplify \( \left( \frac{-3}{8} \times 1\frac{5}{6} \right) - \left( \frac{2}{3} - \frac{-3}{4} \right) \)
Answer: \( -2\frac{5}{48} \)

Question. Verify that : \( \frac{-3}{16} \times \frac{8}{21} = \frac{8}{21} \times \frac{-3}{16} \)
Answer:
L.H.S. = \( \frac{-3}{16} \times \frac{8}{21} = -\frac{1}{14} \)
R.H.S. = \( \frac{8}{21} \times \frac{-3}{16} = -\frac{1}{14} \)
Since L.H.S. = R.H.S., the given equation is verified.

Question. Verify that : \( \left(\frac{5}{7} \times \frac{12}{13}\right) \times \frac{7}{18} = \frac{5}{7} \times \left(\frac{12}{13} \times \frac{7}{18}\right) \)
Answer:
L.H.S. = \( \left(\frac{5}{7} \times \frac{12}{13}\right) \times \frac{7}{18} = \frac{10}{39} \)
R.H.S. = \( \frac{5}{7} \times \left(\frac{12}{13} \times \frac{7}{18}\right) = \frac{10}{39} \)
Since L.H.S. = R.H.S., the given equation is verified.

Question. Find multiplicative inverse (reciprocal) of
(i) \( \frac{-7}{24} \)
(ii) \( \frac{0}{5} \)
(iii) \( -2 \)
Answer:
(i) \( -\frac{24}{7} \)
(ii) does not exist
(iii) \( -\frac{1}{2} \)

Question. Simplify: \( (-3) \times \left( \frac{-10}{9} \right) \times \left( \frac{18}{-5} \right) \times \left( \frac{1}{-6} \right) \)
Answer: \( 2 \)

Question. The Product of two numbers is \( \frac{-28}{27} \). If one of them is \( -\frac{9}{4} \). Find the other.
Answer: \( \frac{112}{243} \)

Question. By what rational number should we multiply \( \frac{-15}{56} \) to get \( \frac{-3}{28} \)
Answer: \( \frac{2}{5} \)

Question. Multiply the sum of \( \frac{2}{5} \) and \( \frac{4}{15} \) by the sum of \( \frac{3}{7} \) and \( -\frac{2}{21} \).
Answer: \( \frac{2}{9} \)

Question. Multiply the difference of \( \frac{-3}{11} \) and \( \frac{7}{22} \) by the product of \( \frac{4}{7} \) and \( -\frac{14}{9} \).
Answer: \( \frac{52}{99} \)

Question. Find the cost of \( 2\frac{1}{3} \) metres of cloth at the rate of Rs \( 16\frac{2}{3} \) per metre.
Answer: Rs \( 38\frac{8}{9} \)

Question. Which two numbers product is \( \frac{3}{10} \)?
Answer: \( \frac{3}{2} \text{ and } \frac{1}{5} \) and many more

Question. The Speed of Car is \( 45\frac{1}{2} \text{ km} \) per hour. Find the distance covered in \( 2\frac{1}{2} \text{ hr.} \)
Answer: \( 113\frac{3}{4} \text{ km} \)