Rational Numbers Test

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Rational Numbers Test - 22

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Weekly Quiz Competition

Question 1
1 / -0

............ is the additive inverse of $\dfrac {-3}{11}.$

A
$\dfrac {-3}{11}$

B
$\dfrac {11}{3}$

C
$-1$

D
$\dfrac {3}{11}$

Solution

In mathematics, the additive inverse of a number is the number that, when added to a, yields zero.

This number is also known as the opposite (number), sign change, and negation.

For a real number, it reverses its sign: the opposite to a positive number is negative, and the opposite to a negative number is positive.

The given rational number is $\dfrac {-3}{11}$ and its negative is $-\left (\dfrac {-3}{11}\right ) = \dfrac {3}{11}$ . Thus, the additive inverse of $\dfrac {-3}{11}$ is $\dfrac {3}{11}$ .
Question 2
1 / -0

The additive inverse of $\dfrac {2}{7}$ is ..........

A
$\dfrac {2}{7}$

B
$\dfrac {-2}{7}$

C
$\dfrac {7}{2}$

D
$\dfrac {-7}{2}$

Solution

The additive inverse of a number $a$ is the number that, when added to $a$ , yields zero.

If $a$ is an integer, then its negative $(-a)$ is called the additive inverse of $a$ .

The given rational number is $\dfrac {2}{7}$ and its negative is $\dfrac {-2}{7}$ .

Thus, the additive inverse of $\dfrac {2}{7}$ is $\dfrac {-2}{7}$ .
Question 3
1 / -0

There are ....... rational number which when multiplied by $0$ , gives product as $1.$

A
$0$

B
$2$

C
$4$

D
infinite

Solution

There are no rational numbers which when multiplied by $0$ gives product as $1$ because the product of $0$ and any number is always $0.$
Question 4
1 / -0

$1$ is the multiplicative identity for ........

A
whole numbers

B
integers

C
rational numbers

D
all of the above

Solution

${\textbf{Step - 1: Defining Multiplicative identity}}$

${\text{Multiplicative identity is a number which when multiplied by another number gives}}$

   ${\text{the another number again as result}}{\text{.}}$

   ${\text{For example, if x }} \times {\text{ y = x then y is multiplicative identity of x}}$

${\textbf{Step - 2: Identifying multiplicative identity}}$

   ${\text{We know that, any number multiplied by 1 gives the number itself}}{\text{.}}$

   $\Rightarrow {\text{ 1 is the multiplicative identity for any real number}}$

${\textbf{Hence correct option is (D) all of the above}}$
Question 5
1 / -0

$\dfrac {3x}{y}\times 1 = ..........$ is stated by multiplicative identity property.

A
$3x$

B
$y$

C
$\dfrac {3x}{y}$

D
$1$

Solution

The multiplicative identity property states that when we multiply a number by $1,$ then the product is the number itself.
So, $\dfrac {3x}{y} \times 1 = \dfrac {3x}{y}$ .
Question 6
1 / -0

Find using additive inverse property, what should be added to $\dfrac {-1}{3}$ , so that the sum is zero ?

A
$\dfrac {-1}{3}$

B
$\dfrac {1}{3}$

C
$1$

D
$0$

Solution

We know that the sum of a rational number and its additive inverse is zero.

Since the given rational number is $\dfrac {-1}{3}$ , its negative is $-\left (\dfrac {-1}{3}\right ) = \dfrac {1}{3}$

Now, $\dfrac {-1}{3} + \dfrac {1}{3} = 0$ . Hence, $\dfrac {1}{3}$ should be added to $\dfrac {-1}{3}$ to get the sum as $0$ .
Question 7
1 / -0

The product of ........... and any rational number is the rational number itself.

A
$1$

B
$-1$

C
$0$

D
the given rational number

Solution

The product of $1$ and any rational number is the rational number itself because $1$ is the multiplicative identity for rational numbers.

Ex: $\dfrac 3 2$ when multiplied by $1$ gives $\dfrac 3 2$ itself, which is a rational number.
Question 8
1 / -0

Which of the following number lines, represents rational numbers?

A

B

C

D
All of the above
Question 9
1 / -0

Which of the following rational number does not have a reciprocal?

A
$1$

B
$-1$

C
$0$

D
none

Solution

If we try to find the reciprocal of 0 then, we get the result which is not defined.
As, $\dfrac{1}{0}=$ Not a number
So, we can say that $0$ does not have a reciprocal.
Question 10
1 / -0

There exists ....... number of rational numbers between $\dfrac {2}{5}$ and $\dfrac {4}{5}.$

A
$0$

B
$1$

C
$5$

D
infinite

Solution

There exists infinite number of rational numbers between any two rational numbers. i.e. in this case between $\dfrac {2}{5}$ and $\dfrac {4}{5}$ .

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Re-Attempt Weekly Quiz Competition

Rational Numbers Test - 22

Result

Rational Numbers Test - 22

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Question 1

−311\dfrac {-3}{11}11−3​

113\dfrac {11}{3}311​

−1-1−1

311\dfrac {3}{11}113​

Solution

Question 2

27\dfrac {2}{7}72​

−27\dfrac {-2}{7}7−2​

72\dfrac {7}{2}27​

−72\dfrac {-7}{2}2−7​

Solution

Question 3

000

222

444

infinite

Solution

Question 4

whole numbers

integers

rational numbers

all of the above

Solution

Question 5

3x3x3x

yyy

3xy\dfrac {3x}{y}y3x​

111

Solution

Question 6

−13\dfrac {-1}{3}3−1​

13\dfrac {1}{3}31​

111

000

Solution

Question 7

111

−1-1−1

000

the given rational number

Solution

Question 8

All of the above

Question 9

111

−1-1−1

000

none

Solution

Question 10

000

111

555

infinite

Solution

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$\dfrac {-3}{11}$

$\dfrac {11}{3}$

$-1$

$\dfrac {3}{11}$

$\dfrac {2}{7}$

$\dfrac {-2}{7}$

$\dfrac {7}{2}$

$\dfrac {-7}{2}$

$0$

$2$

$4$

$3x$

$y$

$\dfrac {3x}{y}$

$1$

$\dfrac {-1}{3}$

$\dfrac {1}{3}$

$1$

$0$

$1$

$-1$

$0$

$1$

$-1$

$0$

$0$

$1$

$5$