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Haryana State Board HBSE 8th Class Maths Solutions Chapter 1 Rational Numbers Ex 1.1 Textbook Exercise Questions and Answers.
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:
(i) \(\frac{2}{3} \times \frac{3}{5}+\frac{5}{2}-\frac{3}{5} \times \frac{1}{6}\)
2nd Method
3rd Method
(ii) 1st Method
\(\frac{2}{5} \times\left(\frac{-3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}\)
2nd Method
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:
\(\frac{-2}{8}\) is the additive inverse of \(\frac{2}{8}\) because
\(\frac{-6}{5}\) is the additive inverse of \(\frac{6}{5}\) because
Question 3.
Verify that – (-x) = x for
(i) x = \(\frac{11}{15}\)
(ii) x = \(-\frac{13}{17}\)
Solution:
(i) We have, x = \(\frac{11}{15}\)
The additive inverse of
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 × \(\frac{-2}{5}\)
(vi) -1
Solution:
(i) Let the multiplicative inverse of -13 be x.
∴ -13 × x = 1
(v) Let the multiplicative inverse of -1 × \(\frac{-2}{5}\) be x.
∴ -1 × \(\frac{-2}{5}\) × x = 1
⇒ x = \(\frac{1 \times 5}{-1 \times(-2)}\) = \(\frac{5}{2}\) or \(\frac{-5}{-2}\)
(vi) The multiplicative inverse of -1 is -1 because -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) 1 is the multiplicative identity. (ii) Commutativity, (iii) Multiplicative inverse.
Question 6.
Multiply \(\frac{6}{13}\) by the reciprocal of \(\frac{-7}{16}\).
Solution:
The reciprocal of \(\frac{-7}{16}\) is \(\frac{16}{-7}\)
The Product of \(\frac{6}{13}\) and \(\frac{16}{-7}\)
= \(\frac{6}{13}\) × \(\frac{16}{-7}\) = \(\frac{96}{-91}\)
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:
We know 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:
No, the multiplicative inverse of \(\frac{8}{9}\) is \(\frac{9}{8}\) or 1\(\frac{1}{8}\).
Here, -1\(\frac{1}{8}\) is negative. Therefore, \(\frac{8}{9}\) 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 = \(\frac{3}{10}\)
Here, 0.3 × 3\(\frac{1}{3}\) = \(\frac{3}{10}\) × \(\frac{10}{3}\) = 1
We say that a rational number \(\frac{c}{d}\) is called the reciprocal or multiplicative inverse of another a rational number \(\frac{a}{b}\) if \(\frac{a}{b}\) × \(\frac{c}{d}\) = 1
∴ The result will be yes.
Question 10.
Write :
(i) The rational number that does not have a reciprocal.
Solution:
Zero has no reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
Solution:
1 is equal to its reciprocal, because the reciprical of 1 is 1.
-1 is also equal to its reciprocal because the reciprocal of-1 is -1.
-1 × (-1) = 1
(iii) The Rational number that is equal to its negative.
Solution:
Its value 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 number is always a ……………..
(vi) The reciprocal of a positive rational number is ………………
Answer:
(i) no
(ii) 1.1
(iii) \(\frac{1}{-5}\)
(iv) x
(v) rational number
(vi) positive
HBSE 7th Class Maths Chapter 1 Integers
HBSE 7th Class Maths Chapter 2 Fractions and Decimals
HBSE 7th Class Maths Chapter 3 Data Handling
HBSE 7th Class Maths Chapter 4 Simple Equations
HBSE 7th Class Maths Chapter 5 Lines and Angles
HBSE 7th Class Maths Chapter 6 The Triangles and Its Properties
HBSE 7th Class Maths Chapter 7 Congruence of Triangles
HBSE 7th Class Maths Chapter 8 Comparing Quantities
HBSE 7th Class Maths Chapter 9 Rational Numbers
HBSE 7th Class Maths Chapter 10 Practical Geometry
HBSE 7th Class Maths Chapter 11 Perimeter and Area
HBSE 7th Class Maths Chapter 12 Algebraic Expressions
HBSE 7th Class Maths Chapter 13 Exponents and Powers
HBSE 7th Class Maths Chapter 14 Symmetry
HBSE 7th Class Maths Chapter 15 Visualising Solid Shapes
HBSE 7th Class Maths Chapter 1 पूर्णांक
HBSE 7th Class Maths Chapter 2 भिन्न एवं दशमलव
HBSE 7th Class Maths Chapter 3 आँकड़ो का प्रबंधन
HBSE 7th Class Maths Chapter 4 सरल समीकरण
HBSE 7th Class Maths Chapter 5 रेखा एवं कोण
HBSE 7th Class Maths Chapter 6 त्रिभुज और उसके गुण
HBSE 7th Class Maths Chapter 7 त्रिभुजों की सर्वांगसमता
HBSE 7th Class Maths Chapter 8 राशियों की तुलना
HBSE 7th Class Maths Chapter 9 परिमेय संख्याएँ
HBSE 7th Class Maths Chapter 10 प्रायोगिक ज्यामिती
HBSE 7th Class Maths Chapter 11 परिमाप और क्षेत्रफल
HBSE 7th Class Maths Chapter 12 बीजीय व्यंजक
HBSE 7th Class Maths Chapter 13 घातांक और घात
HBSE 7th Class Maths Chapter 14 सममिति
HBSE 7th Class Maths Chapter 15 ठोस आकारों का चित्रण
Haryana State Board HBSE 8th Class Maths Solutions Chapter 1 Rational Numbers InText Questions and Answers.
Try These (Textbook Page No. 4)
Question 1.
Fill in the blanks in the following table :
Answer:
Try These (Textbook Page No. 6)
Question 1.
Complete the following table :
Answer:
Try These (Textbook Page No. 9)
Question 1.
Complete the following table :
Answer:
Try These (Textbook Page No. 13)
Question 1.
Find using distributivity :
(i) \(\left\{\frac{7}{5} \times\left(\frac{-3}{12}\right)\right\}\) + \(\left\{\frac{7}{5} \times \frac{5}{12}\right\}\)
(ii) \(\left\{\frac{9}{16} \times \frac{4}{12}\right\}\) + \(\left\{\frac{9}{16} \times \frac{-3}{9}\right\}\)
Solution:
Try These (Textbook Page No. 17)
Question 1.
Write the rational number for each point labelled with a letter.
(i) 
(ii) 
Solution:
HBSE 8th Class Maths Chapter 1 Rational Numbers
HBSE 8th Class Maths Chapter 2 Linear Equations in One Variable
HBSE 8th Class Maths Chapter 3 Understanding Quadrilaterals
HBSE 8th Class Maths Chapter 4 Practical Geometry
HBSE 8th Class Maths Chapter 5 Data Handling
HBSE 8th Class Maths Chapter 6 Square and Square Roots
HBSE 8th Class Maths Chapter 7 Cube and Cube Roots
HBSE 8th Class Maths Chapter 8 Comparing Quantities
HBSE 8th Class Maths Chapter 9 Algebraic Expressions and Identities
HBSE 8th Class Maths Chapter 10 Visualizing Solid Shapes
HBSE 8th Class Maths Chapter 11 Mensuration
HBSE 8th Class Maths Chapter 12 Exponents and Powers
HBSE 8th Class Maths Chapter 13 Direct and Inverse Proportions
HBSE 8th Class Maths Chapter 14 Factorization
HBSE 8th Class Maths Chapter 15 Introduction to Graphs
HBSE 8th Class Maths Chapter 16 Playing with Numbers
HBSE 8th Class Maths Chapter 1 परिमेय संख्याएँ
HBSE 8th Class Maths Chapter 2 एक चर वाले रैखिक समीकरण
HBSE 8th Class Maths Chapter 3 चतुर्भुजों को समझना
HBSE 8th Class Maths Chapter 4 प्रायोगिक ज्यामिती
HBSE 8th Class Maths Chapter 5 आँकड़ो का प्रबंधन
HBSE 8th Class Maths Chapter 6 वर्ग और वर्गमूल
HBSE 8th Class Maths Chapter 7 घन और घनमूल
HBSE 8th Class Maths Chapter 8 राशियों की तुलना
HBSE 8th Class Maths Chapter 9 बीजीय व्यंजक एवं सर्वसमिकाएँ
HBSE 8th Class Maths Chapter 10 ठोस आकारों का चित्रण
HBSE 8th Class Maths Chapter 11 क्षेत्रमिति
HBSE 8th Class Maths Chapter 12 घातांक और घात
HBSE 8th Class Maths Chapter 13 सीधा और प्रतिलोम समानुपात
HBSE 8th Class Maths Chapter 14 गुणनखंडन
HBSE 8th Class Maths Chapter 15 आलेखों से परिचय
HBSE 8th Class Maths Chapter 16 संख्याओं के साथ खेलना