True False With Reason

Question 12 Marks

State whether the following statement are true or false. Give reason for your answer.
Every rational number is a whole number.

Answer

False.
Explanation:
As rational numbers are of the form $\frac{\text{p}}{\text{q}}$ where $\text{q}\neq0.$ Whole numbers are natural numbers together with a zero.
For example, $\frac{5}{7}$ is a rational number but not a whole number.

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Question 22 Marks

State whether the following statement are true or false. Give reason for your answer.
Every rational number is an integer.

Answer

False.
Explanation:
As rational numbers are of the form $\frac{\text{p}}{\text{q}}$ where $\text{q}\neq0.$ Integers are negative and positive numbers which are not in $\frac{\text{p}}{\text{q}}$ form.
For example, $\frac{1}{2}$ is a rational number but not an integer.

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Question 32 Marks

State whether the following statement are true or false. Give reason for your answer.
Every integer is a whole number.

Answer

False.
Explanation:
Whole numbers are natural numbers together with a zero whereas integers include negative numbers also.

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Question 42 Marks

State whether the given statement is true of false.
The sum of two irrational numbers is irrational.

Answer

False. Explanation:$\big(2+\sqrt{3}\big)+\big(2-\sqrt{3}\big)=4$
Here, 4 is a rational number.

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Question 52 Marks

State whether the given statement is true of false.
The product of a nonzero rational number and an irrational number is a rational number.

Answer

False. Explanation:$(4)\times\sqrt{5}=4\sqrt{5}$
Here, $4\sqrt{5}$ is an irrational number.

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Question 62 Marks

State whether the given statement is true of false.$\pi$ is irrational and $\frac{22}{7}$ is rational.

Answer

True.

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Question 72 Marks

State whether the given statement is true of false.
The product of two rational numbers is rational.

Answer

True.

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Question 82 Marks

State whether the following statement are true or false. Give reason for your answer.
Every integer is a rational number.

Answer

True.
Explanation:
As rational numbers are of the form $\frac{\text{p}}{\text{q}}$ where $\text{q}\neq0.$ All integers can be represented in the form $\frac{\text{p}}{\text{q}}$ where $\text{q}\neq0.$

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Question 92 Marks

State whether the given statement is true of false.
Every real number is either rational or irrational.

Answer

True.

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Question 102 Marks

State whether the given statement is true of false.
The sum of a rational number and an irrational number is irrational.

Answer

True.

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Question 112 Marks

State whether the given statement is true of false.
The product of two irrational number is irrational.

Answer

False. Explanation:$\sqrt{3}\times\sqrt{3}=3$
Here, 3 is a rational number.

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Question 122 Marks

State whether the following statement are true or false. Give reason for your answer.
Every whole number is a natural number.

Answer

False.
Explanation:
As whole numbers contain natural numbers and 0 whereas natural numbers only contain the counting numbers except 0.

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Question 132 Marks

State whether the following statement are true or false. Give reason for your answer.
Every natural number is a whole number.

Answer

True.
Explanation:
since natural numbers are counting numbers i.e N = 1, 2,...
Whole numbers are natural numbers together with 0. i.e W = 0, 1, 2,...
So, every natural number is a whole number.

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Question 142 Marks

State whether the given statement is true of false.
The sum of two rational numbers is rational.

Answer

True.

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Question 152 Marks

State whether the given statement is true of false.
Every real number is rational.

Answer

False.
Explanation:
Real numbers can be divided into rational and irrational numbers.

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