CBSE · NCERT · Class 8 Maths · Chapter 1

NCERT Solutions: Class 8 Maths Chapter 1 - Rational Numbers

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Chapter-wise NCERT intext questions and exercise answers for Rational Numbers, grounded in the official textbook.

Questions are taken verbatim from the NCERT textbook; answers were grounded against the chapter's content during generation. Items needing review are marked.
Sections in this chapter
Exercise 1.1 8
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1Exercise 1.18 questions
Q.1Name the property under multiplication used in: (i) $-\dfrac{4}{5}\times1=1\times-\dfrac{4}{5}=-\dfrac{4}{5}$ (ii) $-\dfrac{13}{17}\times-\dfrac{2}{7}=-\dfrac{2}{7}\times-\dfrac{13}{17}$ (iii) $-\dfrac{19}{29}\times1=1\times-\dfrac{19}{29}=-\dfrac{19}{29}$.v
Solution

Multiplication by 1 leaves a rational number unchanged. Interchanging two rational factors without changing the product is the commutative property.

Answer:

(i) Multiplicative identity. (ii) Commutative property of multiplication. (iii) Multiplicative identity.

Q.2Tell what property allows you to compute $\dfrac{1}{3}\times\left(6\times\dfrac{4}{3}\right)$ as $\left(\dfrac{1}{3}\times6\right)\times\dfrac{4}{3}$.v
Solution

Only the grouping of the three factors changes; their order is unchanged.

Answer:

Associative property of multiplication of rational numbers.

Q.3The product of two rational numbers is always a ___.v
Solution

Rational numbers are closed under multiplication.

Answer:

The product of two rational numbers is always a rational number.

Q.4The reciprocal of a positive rational number is ___.v
Solution

If $\dfrac{a}{b}>0$, then $\dfrac{b}{a}>0$.

Answer:

The reciprocal of a positive rational number is positive.

Q.5The reciprocal of a negative rational number is ___.v
Solution

Changing a rational number to its reciprocal does not change its sign.

Answer:

The reciprocal of a negative rational number is negative.

Q.6Zero has ___ reciprocal.v
Solution

A reciprocal of 0 would require division by 0, which is not defined.

Answer:

Zero has no reciprocal.

Q.7The numbers ___ and ___ are their own reciprocals.v
Solution

$1/1=1$ and $1/(-1)=-1$.

Answer:

$1$ and $-1$ are their own reciprocals.

Q.8Find five rational numbers between $-1$ and $0$.v
Solution

Write $-1=-\dfrac{6}{6}$ and $0=0$. Fractions with denominator 6 between them give the required numbers.

Answer:

One set is $-\dfrac{5}{6},-\dfrac{4}{6},-\dfrac{3}{6},-\dfrac{2}{6},-\dfrac{1}{6}$.