Chapter 1: Rational Numbers

Solution:-

Zero has no reciprocal.

The reciprocal of 0 = 1/0

= Undefined

Solution:-

The numbers 1 and -1 are their own reciprocal.

Reciprocal of 1 = 1/1 = 1

Reciprocal of -1 = 1/-1 = -1

Solution:-

If y be the reciprocal of x, then the reciprocal of y² in terms of x will be x².

From the question, (1/x) = y

Then,

Reciprocal of y² = 1/y²

Substitute (1/x) in the place of y,

= 1/ (1/x)²

= x²/1

= x²

Solution:-

= (2 × -4)/ (5 × 9)

= -8/45

Reciprocal = -45/8

Hence, the reciprocal of (2/5) × (-4/5) is -45/8.

Solution:-

Let us assume the missing number be x

Then,

= 1 / (213 × 657) = (1/213) × (x)

X = 213/ (213/657)

X = 1/657

X = 657^-1

So, (213 × 657)^-1 = 213^-1 × 657^-1

Solution:-

The negative of 1 is -1.

Solution:-

For rational numbers (a/b), (c/d) and (e/f) we have (a/b) × ((c/d) + (e/f)) = ((a/b) × (c/d)) + ((a/b) × (e/f))

Solution:-

-5/7 is more than -3.

Solution:-

There are infinitely many rational numbers between any two rational numbers.

Solution:-

The rational numbers 1/3 and -1/3 are on the opposite sides of zero on the number line.