Tamilnadu State Board New Syllabus Samacheer Kalvi 8th Maths Guide Pdf Chapter 1 Numbers Ex 1.1 Textbook Questions and Answers, Notes.

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

Question 1.
Fill in the blanks:
(i) $$\frac{-19}{5}$$ lies between the integers _________ and _________ .
Answer:
-4 and -3

(ii) The decimal form of the rational number $$\frac{15}{-4}$$ is _________ .
Answer:
-3.75

(iii) The rational numbers $$\frac{-8}{3}$$ and $$\frac{8}{3}$$ are equidistant from _________.
Answer:
0

(iv) The next rational number in the sequence $$\frac{-15}{24}, \frac{20}{-32}, \frac{-25}{40}$$ is _________.
Answer:
$$\frac{30}{-48}$$

(v) The standard form of $$\frac{58}{-78}$$ is _________.
Answer:
$$\frac{-29}{39}$$

Question 2.
Say True or False
(i) 0 is the smallest rational number.
Answer:
False

(ii) $$\frac{-4}{5}$$ lies to the left of $$\frac{-3}{4}$$.
Answer:
True

(iii) $$\frac{-19}{5}$$ is greater than $$\frac{15}{-4}$$.
Answer:
False

(iv) The average of two rational numbers lies between them.
Answer:
True

(v) There are an unlimited number of rational numbers between 10 and 11.
Answer:
True

Question 3.
Find the rational numbers represented by each of the question marks marked on the following number lines.
(i)

Answer:
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)

Answer:
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)

Answer:
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 4.
The points S, Y, N, C, R, A, T, I and O on the number line are such that CN=NY=YS and RA=AT=TI=IO. Find the rational numbers represented by the letters Y, N, A, T and I.

Answer:

Question 5.
Draw a number line and represent the following rational numbers on it.
(i) $$\frac{9}{4}$$
(ii) $$\frac{-8}{3}$$
(iii) $$\frac{-17}{-5}$$
(iv) $$\frac{15}{-4}$$
Answer:
(i) $$\frac{9}{4}$$
$$\frac{9}{4}=2 \frac{1}{4}$$
∴ $$\frac{9}{4}$$ lies between 2 and 3

(ii) $$\frac{-8}{3}$$
$$\frac{-8}{3}=-2 \frac{2}{3}$$
$$-2 \frac{2}{3}$$ lies between -2 and 3

(iii) $$\frac{-17}{-5}$$
$$\frac{-17}{-5}=3 \frac{2}{5}$$
$$3 \frac{2}{5}$$ lies between 3 and 4 in the number line.

(iv) $$\frac{15}{-4}$$
$$\frac{15}{-4}=-3 \frac{3}{4}$$
$$-3 \frac{3}{4}$$ lies between -3 and -4

Question 6.
Write the decimal form of the following rational numbers.
(i) $$\frac{1}{11}$$
(ii) $$\frac{13}{4}$$
(iii) $$\frac{-18}{7}$$
(iv) $$1 \frac{2}{5}$$
(v) $$-3 \frac{1}{2}$$
Answer:
(i) $$\frac{1}{11}$$
$$\frac{1}{11}$$ = 0.0909….

(ii) $$\frac{13}{4}$$
$$\frac{13}{4}$$ = 3.25

(iii) $$\frac{-18}{7}$$
$$\frac{-18}{7}$$ = -2.571428571428….

(iv) $$1 \frac{2}{5}$$
$$1 \frac{2}{5}=\frac{7}{5}$$ = 1.4

(v) $$-3 \frac{1}{2}$$
$$-3 \frac{1}{2}=-\frac{7}{2}=-3.5$$

Question 7.
List any five rational numbers between the given rational numbers.
(i) 2 and 0
(ii) $$\frac{-1}{2}$$ and $$\frac{3}{5}$$
(iii) $$\frac{1}{4}$$ and $$\frac{7}{20}$$
(iv) $$\frac{-6}{4}$$ and $$\frac{-23}{10}$$
Answer:
(i) 2 and 0
i.e., $$\frac{-2}{1}$$ and $$\frac{0}{1}$$

∴ Five rational number between $$\frac { -20 }{ 10 }$$ (= -2) and $$\frac { 0 }{ 10 }$$ (= 0) are

(ii) $$\frac{-1}{2}$$ and $$\frac{3}{5}$$
LCM of 2 and 5 = 2 × 5 = 10

∴ Five rational number between

(iii) $$\frac{1}{4}$$ and $$\frac{7}{20}$$

∴ Five rational number between

(iv) $$\frac{-6}{4}$$ and $$\frac{-23}{10}$$

∴ Five rational number between

Question 8.
Use the method of averages to write 2 rational numbers between $$\frac{14}{5}$$ and $$\frac{16}{3}$$
Answer:
The average of a and b is $$\frac { 1 }{ 2 }$$(a + b)

Question 9.
Compare the following pairs of rational numbers.
(i) $$\frac{-11}{5}, \frac{-21}{8}$$
(ii) $$\frac{3}{-4}, \frac{-1}{2}$$
(iii) $$\frac{2}{3}, \frac{4}{5}$$
Answer:
(i) $$\frac{-11}{5}, \frac{-21}{8}$$
LCM of 5, 8 is 40

(ii) $$\frac{3}{-4}, \frac{-1}{2}$$
LCM of 4 and 2 = 4

(iii) $$\frac{2}{3}, \frac{4}{5}$$
LCM of 3 and 5 is 15.

Question 10.
Arrange the following rational numbers in ascending and descending order.
(i) $$\frac{-5}{12}, \frac{-11}{8}, \frac{-15}{24}, \frac{-7}{-9}, \frac{12}{36}$$
(ii) $$\frac{-17}{10}, \frac{-7}{5}, 0, \frac{-2}{4}, \frac{-19}{20}$$
Answer:
(i) $$\frac{-5}{12}, \frac{-11}{8}, \frac{-15}{24}, \frac{-7}{-9}, \frac{12}{36}$$
LCM of 12, 8, 24, 9, 36 is 4 × 3 × 2 × 3 = 72

Now comparing the numerators – 30, – 99, -45, 56, 24 we get 56 > 24 > – 30 > – 45 > – 99

(ii) $$\frac{-17}{10}, \frac{-7}{5}, 0, \frac{-2}{4}, \frac{-19}{20}$$
LCM of 10, 5, 4, 20 is 5 × 2 × 2 = 20

Negative numbers are less than zero.
∴ Arranging the numerators we get
– 34 < – 28 < – 19 < – 10 < 0

Objective Type Questions:

Question 11.
The number which is subtracted from $$\frac{-6}{11}$$ to get $$\frac{8}{9}$$ is _________ .
(A) $$\frac{34}{99}$$
(B) $$\frac{-142}{99}$$
(C) $$\frac{142}{99}$$
(D) $$\frac{-34}{99}$$
Answer:
(B) $$\frac{-142}{99}$$
Hint:
Let x be the number to be subtracted
$$\frac{-6}{11}-x$$ = $$\frac{8}{9}$$
$$\frac{-6}{11}-\frac{8}{9}$$ = x

Question 12.
Which of the following pairs is equivalent?
(A) $$\frac{-20}{12}, \frac{5}{3}$$
(B) $$\frac{16}{-30}, \frac{-8}{15}$$
(C) $$\frac{-18}{36}, \frac{-20}{44}$$
(D) $$\frac{7}{-5}, \frac{-5}{7}$$
Answer:
(B) $$\frac{16}{-30}, \frac{-8}{15}$$
Hint:

∴ $$\frac{16}{-30}$$ and $$\frac{-8}{15}$$

Question 13.
$$\frac{-5}{4}$$ 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
Answer:
(C) -1 and -2
Hint:
$$\frac{-5}{4}$$ = -1 $$\frac{1}{4}$$
∴ $$\frac{-5}{4}$$ lies between -1 and -2.

Question 14.
Which of the following rational numbers is the greatest?
(A) $$\frac{-17}{24}$$
(B) $$\frac{-13}{16}$$
(C) $$\frac{7}{-8}$$
(D) $$\frac{-31}{32}$$
Answer:
(A) $$\frac{-17}{24}$$
Hint:
LCM of 24, 16, 8, 32 = 8 × 2 × 3 × 2 = 96

∴ $$\frac{-17}{24}$$ is the greatest number

Question 15.
The sum of the digits of the denominator in the simplest form of is $$\frac{112}{528}$$ is _________ .
(A) 4
(B) 5
(C) 6
(D )7
Answer:
(C) 6
Hint:

Sum of digits in the denominator = 3 + 3 = 6