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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: