Using appropriate properties Find:

(i)

(ii)

(i)

(ii)

Write the additive inverse of each of the following:

(i)

(ii)

(iii)

(iv)

(v)

(i)

(ii)

(iii)

(iv)

(v)

Verify that –(–x) = x for.

(i)

(ii)

(i)

The additive inverse of

The equality

represents that the additive inverse of

or it can be said that

The additive inverse of

The equality

represents that the additive inverse of

or it can be said that

(ii)

The additive inverse of

This equality represents that

the additive inverse of

i.e., –(–x)=x

The additive inverse of

This equality represents that

the additive inverse of

i.e., –(–x)=x

Find the multiplicative inverse of the following.

(i) -13

(ii)

(iii)

(iv)

(v)

(vi) -1

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Name the property under multiplication used in each of the following:

(i)

(ii)

(iii)

(i)

1 is the multiplicative identity.

1 is the multiplicative identity.

(ii) Commutativity

(iii) Multiplicative inverse

Multiply by the reciprocal of

Tell what property allows you to compute

Associativity

Is the multiplicative inverse of Why or why not?

If it is the multiplicative inverse, then the product should be 1.

However, here, the product is not 1 as

Is 0.3 the multiplicative inverse of Why or why not?

Here, the product is 1. Hence, 0.3 is the multiplicative inverse of

Write:-

(i) The rational number that does not have a reciprocal.

(ii) The rational numbers that are equal to their reciprocals.

(iii) The rational number that is equal to its negative.

(i) 0 is a rational number but its reciprocal is not defined.

(ii) 1 and –1are the rational numbers that are equal to their reciprocals.

(iii) 0 is the rational number that is equal to its negative.

Fill in the blanks.

(i) Zero has _________ reciprocal.

(ii) The numbers _________ and _________ are their own reciprocals.

(iii) The reciprocal of –5 is _________.

(iv) Reciprocal of where x ≠ 0 is _________.

(v) The product of two rational numbers is always a _________.

(vi) The reciprocal of a positive rational number is _________.

(i) Zero has no reciprocal.

(ii) The numbers 1, and –1 are their own reciprocals.

(iii) The reciprocal of –5 is

(iv) The reciprocal of where x ≠ 0 is x.

(v) Rational number

(vi) Positive Rational number

Represent these numbers on the number line:

(i)

(ii)

(i) can be represented on the number line as follows.

(ii) can be represented on the number line as follows.

Represent on the number line.

can be represented on the number line as follows.

Write five rational numbers which are smaller than 2.

2 can be represented as

Therefore, five rational numbers smaller than 2 are:

Find ten rational numbers between

can be represented as respectively.

Therefore, ten rational numbers between are

Find five rational numbers between

(i)

(ii)

(iii)

(i) can be represented as respectively.

Therefore, five rational numbers between are

(ii) can be represented as respectively Therefore, five rational numbers

between are:

between are:

(iii) can be represented as respectively.

Therefore, five rational numbers between and

Write five rational numbers greater than –2.

–2 can be represented as

Therefore, five rational numbers greater than –2 are

Find ten rational numbers between

can be represented as

Therefore, ten rational numbers between are

NCERT SOLUTIONS FOR RATIONAL NUMBERS