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

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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.
$$\frac{-3}{7}+\frac{5}{6}+\frac{4}{7}+\frac{1}{3}+\frac{13}{-6}$$
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: