Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 1 Rational Numbers Ex 1.1

Students can Download Maths Chapter 1 Rational Numbers Ex 1.1 Questions and Answers, Notes Pdf, Samacheer Kalvi 8th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.
Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 1 Rational Numbers Ex 1.1

Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 1 Rational Numbers Ex 1.1

Question 1.
Fill in the blanks:
(i) \(\frac{-19}{5}\) lies between the integers _____ and _____
(ii) The rational number that is represented by 0.44 is ______.
(iii) The standard form of \(\frac{+58}{-78}\) is _____.
(iv) The value of \(\frac{-5}{12}+\frac{7}{15}\) = ______
(v) The value of \(\left(\frac{-15}{23}\right) \div\left(\frac{+30}{-46}\right)\) is ______
Solution:
(i) -4 and -3
(ii) \(\frac{11}{25}\)
(iii) \(\frac{-29}{39}\)
(iv) \(\frac{1}{20}\)
(v) 1

Question 2.
Say True or False.
(i) 0 is the smallest rational number.
(ii) There are an unlimited rationals between 0 and 1.
(iii) The rational number that does not have a reciprocal is 0.
(iv) The only rational number which is its own reciprocal is -1.
(v) The rational numbers that are equal to their additive inverses are 0 and -1.
Solution:
(i) False
(ii) True
(iii) True
(iv) False
(v) False

Question 3.
List five rational numbers between 2 and 0
(i) -2 and 0
(ii) \(\frac{-1}{2}\) and \(\frac{3}{5}\)
(iii) 0.25 and 0.35
(iv) -1.2 and -2.3
Solution:
(i) -2 and 0
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 1
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 2

Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 1 Rational Numbers Ex 1.1

Question 4.
Write four rational numbers equivalent to -3 7
(i) \(\frac{-3}{5}\)
(ii) \(\frac{7}{-6}\)
(iii) \(\frac{8}{9}\)
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 3
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 4
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 5

Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 1 Rational Numbers Ex 1.1

Question 5.
Draw the number line and represent the following rational numbers on it.
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 6
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 7
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 8

Question 6.
Find the rational numbers for the points marked on the number line.
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 9
Solution:
(i) The number lies between -3 and -4. The unit part between -3 and -4 is divided into 3 equal parts and the second part is asked.
∴ The required number is \(-3 \frac{2}{3}=-\frac{11}{3}\).
(ii) The required number lies between 0 and -1. The unit part between 0 and -1 is divided into 5 equal parts, and the second part is taken.
∴The required number is \(-\frac{2}{5}\)
(iii) The required number lies between 1 and 2. The unit part between 1 and 2 is divided into 4 equal parts and the third part is taken.
∴ The required number is \(1 \frac{3}{4}=\frac{7}{4}\)

Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 1 Rational Numbers Ex 1.1

Question 7.
Using average, write 3 rational numbers between \(\frac{14}{5}\) and \(\frac{16}{3}\)
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 10
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 11
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 12

Question 8.
Verify that -(-x) is the same x for:
(i) x = \(\frac{11}{15}\)
(ii) x = \(\frac{-31}{45}\)
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 13
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 14

Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 1 Rational Numbers Ex 1.1

Question 9.
Re-arrange suitable and add :
\(\frac{-3}{7}+\frac{5}{6}+\frac{4}{7}+\frac{1}{3}+\frac{13}{-6}\)
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 15

Question 10.
What should be added to \(\frac{-8}{9}\) to get \(\frac{2}{5}\).
Solution:
Let the number to be added = x
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 16

Question 11.
Subtract \(\frac{-8}{44}\) from \(\frac{-17}{11}\)
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 17

Question 12.
Evaluate:
(i) \(\frac{9}{2} \times \frac{-11}{3}\)
(ii) \(\frac{-7}{27} \times \frac{24}{-35}\)
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 19

Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 1 Rational Numbers Ex 1.1

Question 13.
Divide
(i) \(\frac{-21}{5}\) by \(\frac{-7}{-10}\)
(ii) \(\frac{-3}{13}\) by -3
(iii) -2 by \(\frac{-6}{15}\)
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 18

Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 1 Rational Numbers Ex 1.1

Question 14.
Simplify \(\left(\frac{2}{5}+\frac{3}{2}\right)+\frac{3}{10}\) as a rational number and show that it is between 6 and 7.
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 19

Question 15.
Write the five rational numbers which are less than -2.
Solution:
All the integers are rational numbers
∴ Rational numbers less than -2 are -10, -15, -20, -25, -30

Question 16.
Compare the following pairs of rational numbers
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 21
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 22
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 23
\(\frac{10}{15}<\frac{12}{15}\)
∴ \(\frac{2}{3}<\frac{4}{5}\)

Question 17.
Arrange the following rational numbers is ascending and descending order.
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 24
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 25
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 26
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 27
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 28

Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 1 Rational Numbers Ex 1.1

Objective Type Questions

Question 18.
The number which is subtracted from \(\frac{-6}{11}\) to get \(\frac{8}{9}\) is
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 29
Solution:
(B) \(\frac{-142}{99}\)
Hint:
Let x be the number be subtracted
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 31

Question 19.
Which of the following rational numbers is the greatest?
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 30
Solution:
(A) \(\frac{-17}{24}\)
Hint:
LCM of 24, 16, 8, 32 = 8 × 2 × 3 × 2 = 96
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 32
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 33
∴ \(\frac{-17}{24}\) is the greatest number.

Question 20.
\(\frac{-5}{4}\) is a rational number which lies between
(A) 0 and \(\frac{-5}{4}\)
(B) -1 and 0
(C) -1 and -2
(D) -4 and -5
Solution:
(C) -1 and -2
Hint:
\(\frac{-5}{4}\) = \(-1 \frac{1}{4}\)
∴ \(\frac{-5}{4}\) lies between -1 and -2.

Question 21.
The standard form of \(\frac{3}{4}+\frac{5}{6}+\left(\frac{-7}{12}\right)\) is
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 34
Solution:
(D) 1
Hint:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 35

Question 22.
The sum of the digits of the denominator in the simplest form of \(\frac{112}{528}\)
(A) 4
(B) 5
(C) 6
(D) 7
Solution:
(C) 6
Hint:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 36
Sum of digits in the denominator = 3 + 3 = 6

Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 1 Rational Numbers Ex 1.1

Question 23.
The rational number (numbers) which has (have) additive inverses is (are)
(A) 7
(B) \(\frac{-5}{7}\)
(C) 0
(D) all of these
Solution:
(D) all of these
Hint:
Additive inverse of 7 is -7
Additive inverse of \(\frac{-5}{7}\) is \(\frac{-5}{7}\)
Additive inverse of 0 is 0.

Question 24.
Which of the following pairs is equivalent?
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 37
Solution:
(B) \(\frac{16}{-30}, \frac{-8}{15}\)
Hint:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 38
∴ \(\frac{16}{-30}\) and \(\frac{8}{15}\) are equivalent fraction.

Question 25.
\(\frac{3}{4} \div\left(\frac{5}{8}+\frac{1}{2}\right)\) =
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 39
Solution:
(C) \(\frac{2}{3}\)
Hint:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.1 40

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