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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
Question 4.
Write four rational numbers equivalent to -3 7
(i) \(\frac{-3}{5}\)
(ii) \(\frac{7}{-6}\)
(iii) \(\frac{8}{9}\)
Solution:
Question 5.
Draw the number line and represent the following rational numbers on it.
Solution:
Question 6.
Find the rational numbers for the points marked on the number line.
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 \(1 \frac{3}{4}=\frac{7}{4}\)
Question 7.
Using average, write 3 rational numbers between \(\frac{14}{5}\) and \(\frac{16}{3}\)
Solution:
Question 8.
Verify that -(-x) is the same x for:
(i) x = \(\frac{11}{15}\)
(ii) x = \(\frac{-31}{45}\)
Solution:
Question 9.
Re-arrange suitable and add :
\(\frac{-3}{7}+\frac{5}{6}+\frac{4}{7}+\frac{1}{3}+\frac{13}{-6}\)
Solution:
Question 10.
What should be added to \(\frac{-8}{9}\) to get \(\frac{2}{5}\).
Solution:
Let the number to be added = x
Question 11.
Subtract \(\frac{-8}{44}\) from \(\frac{-17}{11}\)
Solution:
Question 12.
Evaluate:
(i) \(\frac{9}{2} \times \frac{-11}{3}\)
(ii) \(\frac{-7}{27} \times \frac{24}{-35}\)
Solution:
Question 13.
Divide
(i) \(\frac{-21}{5}\) by \(\frac{-7}{-10}\)
(ii) \(\frac{-3}{13}\) by -3
(iii) -2 by \(\frac{-6}{15}\)
Solution:
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:
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
Solution:
\(\frac{10}{15}<\frac{12}{15}\)
∴ \(\frac{2}{3}<\frac{4}{5}\)
Question 17.
Arrange the following rational numbers is ascending and descending order.
Solution:
Objective Type Questions
Question 18.
The number which is subtracted from \(\frac{-6}{11}\) to get \(\frac{8}{9}\) is
Solution:
(B) \(\frac{-142}{99}\)
Hint:
Let x be the number be subtracted
Question 19.
Which of the following rational numbers is the greatest?
Solution:
(A) \(\frac{-17}{24}\)
Hint:
LCM of 24, 16, 8, 32 = 8 × 2 × 3 × 2 = 96
∴ \(\frac{-17}{24}\) 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
Solution:
(D) 1
Hint:
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:
Sum of digits in the denominator = 3 + 3 = 6
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?
Solution:
(B) \(\frac{16}{-30}, \frac{-8}{15}\)
Hint:
∴ \(\frac{16}{-30}\) and \(\frac{8}{15}\) are equivalent fraction.
Question 25.
\(\frac{3}{4} \div\left(\frac{5}{8}+\frac{1}{2}\right)\) =
Solution:
(C) \(\frac{2}{3}\)
Hint:
