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## Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 1 Rational Numbers Intext Questions

Exercise 1.1

Try This (Textbook Page No. 6)

Question 1.

Is the number \(\frac{7}{-5}\) a fraction or a rational number ? Why?

Solution:

\(\frac{7}{-5}\) is a rational number

Because of rational number is a rational number which is of the form \(\frac{p}{q}\) , q ≠ 0 and p and q are integers.

But fraction is part of a whole.

Question 2.

Write any 6 rational numbers of your choice.

Solution:

0, \(\frac{-1}{2}\), \(\frac{1}{2}\), \(\frac{3}{4}\), \(\frac{6}{7}\), -5, 6

Try This (Textbook Page No. 7)

Question 1.

Explain why the following statements are true?

(i) 0.8 = \(\frac{4}{5}\)

(ii) 1.4 > \(\frac{1}{4}\)

(iii) 0.74 < \(\frac{3}{4}\) (iv) 0.4 > 0.386

(v) 0.096 < 0.24

(vi) 1.128 = 0.1280

Solution:

(vi) 0.128 = \(\frac{128}{1000}=\frac{1280}{10000}\)

0.1280 = \(\frac{1280}{10000}\)

∴ Both are equal. i.e., 0.128 = 0.1280

Try This (Textbook Page No. 9)

Question 1.

Which of the pairs are equivalent rational numbers?

Solution:

Question 2.

Find the standard form of

(i) \(\frac{36}{-96}\)

(ii) \(\frac{-56}{-72}\)

(iii) \(\frac{27}{18}\)

Solution:

Question 3.

Mark the following rational numbers on a number line.

(i) \(\frac{-2}{3}\)

(ii) \(\frac{-8}{-5}\)

(iii) \(\frac{5}{-4}\)

Solution:

(i) \(\frac{-2}{3}\) lies between 0 and -1.

The unit part between 0 and -1 is divided into 3 equal parts and second part is taken.

(ii) \(\frac{-8}{-5}=1 \frac{3}{5}\)

\(1 \frac{3}{5}\) lies between 1 and 2. The unit part between 1 and 2 is divided into 5 equal parts and the third part is taken.

(iii) \(\frac{5}{-4}=-\frac{5}{4}=-1 \frac{1}{4}\)

\(-1 \frac{1}{4}\) lies between -1 and The unit part between -1 and -2 is divided into four equal parts and the first part is taken.

Try This (Textbook Page No. 15)

Question 1.

Are there any rational numbers between \(\frac{-7}{11}\) and \(\frac{6}{-11}\) ?

Solution:

Try This (Textbook Page No. 19)

Question 1.

Divide: (i) 5 by \(\frac{-7}{3}\)

(ii) \(\frac{-7}{3}\) by 5

Solution:

Exercise 1.2

Try This (Textbook Page No. 25)

Question 1.

The closure property on integers holds for subtraction and not for division. What about rational numbers? Verify.

Solution:

Let 0 and \(\frac{1}{2}\) be two rational numbers 0 – \(\frac{1}{2}\) = \(\frac{1}{2}\) is a rational number

∴ Closure property for subtraction holds for rational numbers.

But consider the two rational number \(\frac{5}{2}\) and 0.

\(\frac{5}{2} \div 0=\frac{5}{2 \times 0}=\frac{5}{0}\)

Here denominator = 0 and it is not a rational number.

∴ Closure property is not true for division of rational numbers.

Question 2.

Check whether \(\frac{3}{5}-\frac{7}{8}=\frac{7}{8}-\frac{3}{5}\)

Solution:

∴ Subtraction of rational numbers is not commutative

Question 3.

Is \(\frac{3}{5} \div \frac{7}{8}=\frac{7}{8} \div \frac{5}{3}\)? So, what do you conclude?

Solution:

∴ Commutative property not hold good for division of rational numbers.

Try This (Textbook Page No. 26)

Question 1.

Check whether the associative property holds for subtraction and division.

Solution:

Consider the rational numbers \(\frac{2}{3}\), \(\frac{1}{2}\) and \(\frac{3}{4}\)

∴ Associative property does not hold for division of rational numbers

Question 2.

Observe that

Use your reasoning skills, to find the sum of the first 7 numbers in the pattern given above.

Solution: