Question

CHOOSE THE CORRECT OPTION :-

1. An integer can be :-

A. Only Positive

B. Only Negative

C. Both positive and negative

D. None of the above

2. A rational number can be represented in the form of :-

A. p/q

B. p x q

C. p + q

D. p - q

3. The value of (5/4) – (8/3) is :-

A. 17/12

B. -17/12

C. 12/17

D. -12/17

4. The associative property is applicable to :-

A. Addition and subtraction

B. Multiplication and division
C. Addition and Multiplication

D. Subtraction and Division

5. The value of (-10/3) x (-15/2) x (17/19) x 0 is :-

A. 0

B. 22.66

C. 20

D. 35​

Answer 1

1. An integer can be :-

A. Only Positive

B. Only Negative

C. Both positive and negative ✔

D. None of the above

Option C: An integer can be both positive and negative. The collection of positive and negative complete numbers along with 0 is termed as integers. They are represented by the letter Z.

2. A rational number can be represented in the form of :-

A. p/q ✔

B. p x q

C. p + q

D. p - q

Option A: The definition of rational numbers state that " A number in the form p/q where p and q are integers and q ≠ 0 is known as a rational number." Henceforth we can determine that rational numbers can be represented in the form p/q.

3. The value of (5/4) – (8/3) is :-

A. 17/12

B. -17/12 ✔

C. 12/17

D. -12/17

Option B: The explanation is as follows:

The denominators are 4 and 3 and to apply the subtraction operation, we must equivalize the denominators through LCM:

LCM of 3 and 4 = 3 x 4 = 12

$\sf{\longrightarrow\:\dfrac{5}{4}\times\dfrac{3}{3}=\dfrac{15}{12}}$

$\sf{\longrightarrow\:\dfrac{8}{3}\times\dfrac{4}{4}=\dfrac{32}{12}}$

Therefore:

$\sf{\longrightarrow\:\dfrac{15}{12}-\dfrac{32}{12}}$

$\sf{\longrightarrow\:\dfrac{15-32}{12}}$

$\bf{\longrightarrow\:\dfrac{-17}{12}}$

4. The associative property is applicable to :-

A. Addition and subtraction

B. Multiplication and division

C. Addition and Multiplication ✔

D. Subtraction and Division

Option C: The associative property states that while applying the operations of addition and multiplication, the way in which the addends or multiplicands are grouped doesn't affect the result.

5. The value of (-10/3) x (-15/2) x (17/19) x 0 is :-

A. 0 ✔

B. 22.66

C. 20

D. 35​

Option A: Any number multiplied to 0 is 0 itself. Therefore the answer here is 0 too.

Answer 2

$\huge\bf{Answer :}$

$\sf\underbrace{Choose \: the \: correct \: option \: :-}$

1. An integer can be :-

A. Only Positive

B. Only Negative

C. $\sf\underline\red{Both \: negative \: and \: positive}$ ✓

D. None of the above

• Going according to the definition of integers, integers are the set of both the numbers which are considered as positive, as well as negative.
• For example, 2 can also be considered as an integer, and -5 can also be called as integer.
• O is also included in the counting of Integers.
• Hence, C.Both positive and negative is the correct option.

2. A rational number can be represented in the form of :-

A. $\sf\underline\red{p/q}$ ✓

B. p × q

C. p + q

D. p - q

• Since we're talking about rational numbers, these number can be depicted in the form of p/q, where p and q represents natural numbers, and talking about natural numbers, these number starts from 1, and 0 is not included, and q should not be 0 ( q ≠ 0 ).
• For example, take the rational number, 2/3. So, it can be represented in the form of p/q where, p = 2 and q = 3, and p and q are real numbers, and q is a non-zero.
• Hence, A. p/q is the correct option.

3. The value of (5/4) – (8/3) is :-

A. 17/12

B. $\sf\underline\red{-17/12}$ ✓

C. 12/17

D. -12/17

• Value of (5/4) – (8/3) :-

Step 1 ) Taking LCM of the denominator of both rational numbers, i.e 4 and 3.

⠀⠀⠀⠀⠀⠀⠀⠀⠀L•C•M ( 4 and 3 ) = 12 ( 4 × 3 )

Step 2 ) Making the denominator equal to the 12 by making suitable calculations.

$\longrightarrow$ $\sf \dfrac{5}{4} \times \dfrac{3}{3} = \dfrac{15}{12}$

$\longrightarrow$ $\sf \dfrac{8}{3} \times \dfrac{4}{4} = \dfrac{32}{12}$

Step 3 ) Subtraction both the numerators of the new fractions taking 32 as common.

$\longrightarrow$ $\sf \dfrac{15}{12} - \dfrac{32}{12}$

$\longrightarrow$ $\sf \dfrac{15 \: - \: 32}{12}$

$\longrightarrow$ $\bf\sf \dfrac{ - 17}{32}$, $\text{Ans}$

• Hence, B. -17/12 is the correct option.

4. The associative property is applicable to :-

A. Addition and subtraction

B. Multiplication and division

C. $\sf\underline\red{Addition \: and \: Multiplication}$ ✓

D. Subtraction and Division

• The associative property means that while we're doing calculation of sum and multiplication, exchanging or re-arranging the order of calculation will not affect the answer.
• Hence, C. Addition and Multiplication is the correct option.

5. The value of (-10/3) x (-15/2) x (17/19)x0 is :-

A. $\sf\underline\red{0}$ ✓

B. 22.66

C. 20

D. 35

• In this question, we don't need to perform lengthy and time consuming calculations. The answer is itself given in the question.
• Anything which is multiplied or divided with the 0, will give 0 as the result.
• Hence, A. 0 is the correct option.