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number-system-integers-rationals-l2 MCQ - Practice Questions with Answers

Solve 30 number-system-integers-rationals-l2 questions for RAS/RPSC preparation.

Practice questions

Q1A child writes 7 as 7/1. What does this show?

A 7 is a rational number.
B 7 is not an integer.
C 7 has become a fraction less than 1.
D 7/1 is invalid because the denominator is 1.
Explanation

Writing 7 as 7/1 proves it fits the rational-number form p/q. Imran should notice that the denominator is 1, not 0, so the expression is valid and keeps the same value.

Q2Which statement correctly relates whole numbers and integers?

A Every whole number is an integer.
B Every integer is a whole number.
C No whole number is an integer.
D Only negative numbers are integers.
Explanation

Whole numbers are 0 and the counting numbers. Integers extend that group by adding negative numbers. So Asha should see the integer set as larger, with every whole number already included inside it.

Q3Match the property with the example: 1. Additive identity 2. Additive inverse 3. Multiplicative identity

A 1-a x 1 = a; 2-a + 0 = a; 3-a + (-a) = 0
B 1-a + 0 = a; 2-a + (-a) = 0; 3-a x 1 = a
C 1-a + (-a) = 0; 2-a x 1 = a; 3-a + 0 = a
D 1-a/a = 1; 2-a - a = 0; 3-a + 1 = a
Explanation

The additive identity is 0 because adding it keeps a unchanged. The additive inverse gives 0, and the multiplicative identity is 1. Karan should match by meaning, not by memory of symbols.

Q4Which pair is ordered from smaller to greater?

A -2, -7
B 1/2, -1/2
C 3/2, 1
D -7, -2
Explanation

On a number line, smaller numbers are to the left. Since -7 lies left of -2, the order -7, -2 is from smaller to greater. Asha should draw the line if unsure.

Q5A teacher asks for the first four natural numbers. Which list should be accepted?

A 0, 1, 2, 3
B -1, 0, 1, 2
C 1, 2, 3, 4
D 1/2, 1, 2, 3
Explanation

Natural numbers are the counting numbers beginning at 1, so the first four are 1, 2, 3 and 4. Including 0 gives whole numbers, and including negatives or fractions moves outside this counting list.

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More questions

6Assertion: -5 is less than -2. Reason: -5 lies to the left of -2 on the number line.

ABoth are true but the reason does not explain the assertion.
BBoth are true and the reason explains the assertion.
CThe assertion is true but the reason is false.
DThe assertion is false but the reason is true.

7For integers and rational numbers, which statement about identity is correct?

A1 is the additive identity because a + 1 = a for every number a.
B0 is the additive identity and 1 is the multiplicative identity.
C0 is the multiplicative identity because a x 0 = a for every number a.
D-1 is the additive identity because it changes the sign of a number.

8How many of the following are rational numbers: -6, 0/7, 5/0, 3/4?

A1
B2
C3
D4

9What is the reciprocal of -7/5?

A7/5
B-7/-5
C5/7
D-5/7

10Which statement about integers is incorrect?

AThe sum of two integers is always an integer.
BThe product of two integers is always an integer.
CThe difference of two integers is always an integer.
DThe quotient of two integers is always an integer.

11Which operation shows that integers are not closed under ordinary division?

A7 divided by 2 equals 7/2.
B-6 divided by 3 equals -2.
C8 divided by -4 equals -2.
D0 divided by 5 equals 0.

12Statement 1: Rational numbers are closed under division by a non-zero rational number. Statement 2: 4 divided by 0 is a rational number.

ABoth statements are correct.
BOnly Statement 2 is correct.
COnly Statement 1 is correct.
DNeither statement is correct.

13On a number line, which arrangement is from left to right?

A-1/2, -2, 0, 3/4
B-2, -1/2, 0, 3/4
C-2, 0, 3/4, -1/2
D0, -1/2, -2, 3/4

14A student says, "Rational numbers are closed under division, so 3/0 is also rational." Which teacher response is most appropriate?

AAccept the answer because 3 and 0 are both integers.
BSay that all divisions of integers are integers.
CAsk the student to check the non-zero denominator condition and compare with 3 divided by 2.
DTell the student to memorize that division always breaks closure.

15For teaching the commutative property, which classroom approach is most suitable?

ACompare 3 + (-5) with (-5) + 3, then compare 3 - (-5) with (-5) - 3.
BAsk students to repeat the property name aloud ten times before solving any example.
CGive only addition examples and avoid subtraction examples.
DState that every operation on integers gives the same result after changing the order.

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