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