Rational Numbers Test

Result

Rational Numbers Test - 4

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Question 1
1 / -0

Integers are closed under all fundamental mathematical operations except

A
Multiplication

B
Subtraction

C
Division

D
Both (b) and (c)

Solution

Integers are closed under addition, subtraction and multiplication but not under division.
Question 2
1 / -0

Reciprocal of any natural number lies between

A
0 and -1

B
1 and infinity

C
100 and 1000

D
0 and 1

Solution

A natural number is always equal to or greater than 1.

The reciprocal of a number which is greater than 1 is always less than 1.

Moreover, all natural numbers are positive and reciprocal of a positive number is always positive.

Therefore, the reciprocal of any natural number lies between 0 and 1.
Question 3
1 / -0

(3 - 5) is not a natural number. This shows that

A
natural numbers are not closed under subtraction

B
subtraction is not defined for natural numbers

C
natural numbers are not associative for subtraction

D
natural numbers are not commutative for subtraction

Solution

3 - 5 = -2

-2 is not a natural number.

This shows that natural numbers are not closed under subtraction.
Question 4
1 / -0

In the representation of rational numbers, the number line extends

A
indefinitely to the left side of zero

B
idnefinitely on both sides of 0

C
indefinitely to the right side of 1

D
indefinitely to the right side of zero

Solution

Since, rational numbers include whole numbers, natural numbers and integers, representation of rational numbers on number lines extends indefinitely on both sides of 0.
Question 5
1 / -0

While representing an integer, the number line extends

A
indefinitely to the left side of 0 only

B
indefinitely to the right side of 0 only

C
indefinitely to the right side of 1 only

D
indefinitely on both sides of 0

Solution

Integers constitute both positive and negative numbers; hence the number line extends indefinitely on both sides of zero.