You can Download KSEEB Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 Questions and Answers to help you to revise the complete syllabus.
KSEEB Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1
Question 1.
Using appropriate properties find:
(i) \(-\frac{2}{3} \times \frac{3}{5}+\frac{5}{2}-\frac{3}{5} \times \frac{1}{6}\)
(ii) \(\frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}\)
Solution:
Question 2.
Write the additive inverse of each of the following:
(i) \(\frac{2}{8}\)
(ii) \(\frac{-5}{9}\)
(iii) \(\frac{-6}{-5}\)
(iv) \(\frac{2}{-9}\)
(v) \(\frac{19}{-6}\)
Solution:
(i) The additive inverse of \(\frac{2}{8}\) is \(\frac{-2}{8}\).
(ii) The additive inverse of \(\frac{-5}{9}\) is \(-\left(\frac{-5}{9}\right)\) = \(\frac{5}{9}\)
(iii) \(\frac{-6}{-5}=\frac{6}{5}\)
∴ The additive inverse of \(\frac{6}{5}\) is \(\frac{-6}{5}\).
(iv) \(\frac{2}{-9}=\frac{-2}{9}\)
∴ The additive inverse of \(\frac{-2}{9}\) is \(\frac{2}{9}\).
(v) \(\frac{19}{-6}=\frac{-19}{6}\)
∴ The additive inverse of \(\frac{-19}{6}\) is \(\frac{19}{6}\).
Question 3.
Verify that -(-x) = x for:
(i) x = \(\frac{11}{15}\)
(ii) x = \(-\frac{13}{17}\)
Solution:
Question 4.
Find the multiplicative inverse of the following:
(i) -13
(ii) \(\frac{-13}{19}\)
(iii) \(\frac{1}{5}\)
(iv) \(\frac{-5}{8} \times \frac{-3}{7}\)
(v) \(-1 \times \frac{-2}{5}\)
(vi) -1
Solution:
(i) The multiplicative inverse of -13 is \(\frac{1}{-13}\).
(ii) The multiplicative inverse of \(\frac{-13}{19}\) is \(\frac{1}{\frac{-13}{19}}=\frac{19}{-13}\).
(iii) The multiplicative inverse of \(\frac{1}{5}\) is 5.
(iv) The multiplicative inverse of \(\frac{-5}{8} \times \frac{-3}{7}=\frac{15}{56}\) is \(\frac{56}{15}\).
(v) The multiplicative inverse of \(-1 \times \frac{-2}{5}=\frac{2}{5}\) is \(\frac{5}{2}\).
(vi) The multiplicative inverse of -1 is \(\frac{1}{-1}\) = -1.
Question 5.
Name the property under multiplication used in each of the following:
(i) \(\frac{-4}{5} \times 1=1 \times \frac{-4}{5}=-\frac{4}{5}\)
(ii) \(-\frac{13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17}\)
(iii) \(\frac{-19}{29} \times \frac{29}{-19}=1\)
Solution:
(i) Multiplicative inverse.
(ii) Commutative.
(iii) 1, is the multiplicative identity.
Question 6.
Multiply \(\frac{6}{13}\) by the reciprocal of \(\frac{-7}{16}\)
Solution:
The reciprocal of \(\frac{-7}{16}\) is \(\frac{16}{-7}=\frac{6}{13} \times \frac{16}{-7}=\frac{96}{-91}\)
Question 7.
Tell what property allows you to compute \(\frac{1}{3} \times\left(6 \times \frac{4}{3}\right)\) as \(\left(\frac{1}{3} \times 6\right) \times \frac{4}{3}\)
Solution:
For any three rational numbers a, b and c
a × (b × c) = (a × b) × c
The multiplication is associative for rational numbers.
Question 8.
Is \(\frac{8}{9}\) the multiplicative inverse of \(-1 \frac{1}{8}\)? Why or why not?
Solution:
Multiplicative inverse of \(\frac{8}{9}\) is \(\frac{9}{8}\) or \(1 \frac{1}{8}\)
But, here \(-1 \frac{1}{8}\) is negative.
∴ \(\frac{8}{9}\) is not multiplicative inverse of \(-1 \frac{1}{8}\).
Question 9.
Is 0.3 the multiplicative inverse of \(3 \frac{1}{3}\)? Why or why not?
Solution:
0.3 = \(\frac{3}{10}\)
Multiplicative inverse of \(\frac{3}{10}\) is \(\frac{10}{3}\) = \(3 \frac{1}{3}\)
Hence, 0.3 is multiplicative inverse of \(3 \frac{1}{3}\)
Since \(\frac{3}{10} \times \frac{10}{3}=1\)
If product of a number and its multiplicative inverse is 1.
Question 10.
Write:
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.
Solution:
(i) Zero is the rational number, that does not have reciprocal.
(ii) 1 is such a rational number, which is equal to its reciprocal. (-1) is also such a rational number.
(iii) 0 is a number which is equal to its negative.
Question 11.
Fill in the blanks:
(i) Zero has ________ reciprocal.
(ii) The numbers _________ and ________ are their own reciprocals.
(iii) The reciprocal of -5 is ________
(iv) Reciprocal of \(\frac{1}{x}\), where x ≠ 0 is ________
(v) The product of two rational numbers is always a ________
(vi) The reciprocal of a positive rational number is ________
Solution:
(i) No
(ii) 1, -1
(iii) \(\frac{-1}{5}\)
(iv) x
(v) Rational number
(vi) Positive