Rational Numbers Test

Result

Rational Numbers Test - 15

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

The property under multiplication used is:
$$-\dfrac{13}{17}\times\dfrac{-2}{7}=\dfrac{-2}{7}\times \dfrac{-13}{17}$$

A
Associative Property

B
Commutative Property

C
Distributive Property

D
Identity Property

Solution

Commutative property says that if $$a$$ and $$b$$ are two number then
$$a\times{b}=b\times{a}$$
So correct answer will be Option B
Question 2
1 / -0

Two rational numbers between $$\dfrac{2}{3}$$ and $$\dfrac{5}{3}$$ are :

A
$$\dfrac{1}{6}$$ and $$\dfrac{2}{6}$$

B
$$\dfrac{1}{2}$$ and $$\dfrac{2}{1}$$

C
$$\dfrac{5}{6}$$ and $$\dfrac{7}{6}$$

D
$$\dfrac{2}{3}$$ and $$\dfrac{4}{3}$$

Solution

Changing the denominators of both numbers to 6, we get
$$\dfrac { 2 }{ 3 } =\dfrac { 4 }{ 6 } \quad \& \quad \dfrac { 5 }{ 3 } =\dfrac { 10 }{ 6 }$$
Numbers between the given rational numbers from the options are
$$\dfrac { 5 }{ 6 } \quad \& \quad \dfrac { 7 }{ 6 } $$
So, correct answer is option C.
Question 3
1 / -0

Choose the correct option for the following statement.
The property allows you to compute $$\displaystyle \frac{1}{3}\times \left ( 6 \times\frac{4}{3} \right )as \left ( \frac{1}{3} \times 6\right )\times \frac{4}{3}$$ is Associativity.

A
The given statement is true.

B
The given statement is false.

C
Incomplete information

D
None of these

Solution

For any element $$a,b,c\in A$$, associative property states that
$$a(bc)=(ab)c$$

Take $$a=\dfrac{1}{3}, b=6, c=\dfrac{4}{3}$$, we get

$$\dfrac{1}{3}\times \left(6\times \dfrac{4}{3}\right)=\left(\dfrac{1}{3}\times 6\right)\times \dfrac{4}{3}$$

Hence, the statement is true.
Question 4
1 / -0

Between any two rational numbers,

A
there is no rational number

B
there is exactly one rational number

C
there are infinitely many rational numbers

D
there are only rational numbers and no irrational numbers

Solution

Recall that to find a rational number between $$r$$ and $$s,$$ you can add

$$r$$ and $$s$$ and divide the sum by $$2,$$ that is $$\displaystyle \frac { r+s }{ 2 }$$ lies between r and s.
For example, $$\displaystyle \frac { 5 }{ 2 }$$ is a number between $$2$$ and

$$3.$$ We can proceed in this manner to find many more rational numbers between $$2$$ and $$3.$$
Hence, we can conclude that there are infinitely many rational numbers between any two given rational numbers.
Question 5
1 / -0

The property under multiplication used in each of the following is the
$$\dfrac{-19}{29}\times\dfrac{29}{-19}=1$$

A
Commutative Property

B
Multiplicative inverse

C
Associative Property

D
Indentity Property

Solution

The multiplicative inverse for any number $$n$$ is $$\dfrac {1}{n}$$ where $$n\ne0.$$ The product of a number and its multiplicative inverse is $$1$$.

Let us take a number $$n=\dfrac {-19}{29}$$, then according to the definition, the multiplicative inverse of $$n$$ is

$$\dfrac { 1 }{ n } =\dfrac { 29 }{ -19 }$$

Now consider the product of $$n$$ and $$\dfrac {1}{n}$$ as follows:

$$\dfrac { -19 }{ 29 } \times \dfrac { 29 }{ -19 } =1$$

Hence, multiplicative inverse property is used in $$\dfrac { -19 }{ 29 } \times \dfrac { 29 }{ -19 } =1$$
Question 6
1 / -0

If D be subset of `the set of all rational numbers, which can be expressed as terminating decimals, then D is closed under the binary operations of

A
addition, subtraction and division.

B
addition, multiplication and division.

C
addition, subtraction and multiplication.

D
subtraction, multiplication and division.

Solution

The sum, difference or product of two rational numbers will be a number that can be expressed as a terminating decimal.
The ratio of two rational numbers need not be always expressible as a terminating decimal.
So, the answer is option C.
Question 7
1 / -0

Find the nine rational numbers between $$0$$ and $$1$$.

A
$$0.1,0.2,0.3, ... ,0.9$$

B
$$ 1.1,0.2 ,10.3, ... ,0.9$$

C
$$0.1,0.2,0.3, ... ,20.9 $$

D
$$0.1 , 0.2 , 10.3 , ... , 0.9 $$

Solution

$$0 < (0+0.1)=0.1 <(0.1+0.1)= 0.2 < (0.2+0.1)=0.3 < ... < (0.8+1)=0.9 <(0.9+0.1)= 1$$
$$0 < 0.1 < 0.2 < 0.3 < ... < 0.9 < 1$$

$$\therefore$$ The nine rational numbers between $$0$$ and $$1$$ are
$$0.1,0.2,0.3, ... ,0.9$$
Question 8
1 / -0

Two rational numbers between $$\dfrac{1}{5}$$ and $$\dfrac{4}{5}$$ are :

A
1 and $$\dfrac{3}{5}$$

B
$$\dfrac{2}{5}$$ and $$\dfrac{3}{5}$$

C
$$\dfrac{1}{2}$$ and $$\dfrac{2}{1}$$

D
$$\dfrac{3}{5}$$ and $$\dfrac{6}{5}$$

Solution

Since the denominator of both rational numbers are same. So, for getting the rational numbers between the given rational numbers, we only have to consider the numerators of the rational numbers.
Two numbers between 1 & 4 are 2 and 3.
So, two rational numbers between the given rational numbers will be $$\dfrac { 2 }{ 5 }$$ and $$ \dfrac { 3 }{ 5 } $$
So, correct answer is option B.
Question 9
1 / -0

Find the five rational numbers between $$\displaystyle \frac{1}{2}$$ and $$\displaystyle \frac{3}{2}$$

A
$$0.5 < 0.6 < 0.7 < 0.8 ... < 1.1 < ... < 1.15 < 1.50$$

B
$$0.5 < 0.6 < 1.7 < 3.8 ... < 1.8< ... < 1.15 < 1.50$$

C
$$0.5 < 0.6 < 0.7 < 2.8 ... < 1.1 < ... < 1.15 < 1.50$$

D
$$0.5 < 0.6 < 0.7 < 0.8 ... < 3.1 < ... < 1.15 < 1.50$$
Question 10
1 / -0

A rational number between $$\displaystyle \frac{1}{4}$$ and $$\displaystyle \frac{1}{3}$$ is

A
$$\displaystyle \frac{7}{24}$$

B
$$\displaystyle \frac{16}{48}$$

C
$$\displaystyle \frac{13}{48}$$

D
All the above

Solution

$$\dfrac{1}{4} = \dfrac{6}{24} = \dfrac{12}{48} $$

$$\dfrac{1}{3} = \dfrac{8}{24} = \dfrac{16}{48}$$

From this, we can see $$\dfrac{7}{24} , \dfrac{13}{48}, \dfrac{16}{48}$$ all lie between $$\dfrac{1}{4}$$ and $$\dfrac{1}{3}$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Rational Numbers Test - 15

Result

Rational Numbers Test - 15

Score

-

Rank

-

SHARING IS CARING

Question 1

Associative Property

Commutative Property

Distributive Property

Identity Property

Solution

Question 2

$$\dfrac{1}{6}$$ and $$\dfrac{2}{6}$$

$$\dfrac{1}{2}$$ and $$\dfrac{2}{1}$$

$$\dfrac{5}{6}$$ and $$\dfrac{7}{6}$$

$$\dfrac{2}{3}$$ and $$\dfrac{4}{3}$$

Solution

Question 3

The given statement is true.

The given statement is false.

Incomplete information

None of these

Solution

Question 4

there is no rational number

there is exactly one rational number

there are infinitely many rational numbers

there are only rational numbers and no irrational numbers

Solution

Question 5

Commutative Property

Multiplicative inverse

Associative Property

Indentity Property

Solution

Question 6

addition, subtraction and division.

addition, multiplication and division.

addition, subtraction and multiplication.

subtraction, multiplication and division.

Solution

Question 7

$$0.1,0.2,0.3, ... ,0.9$$

$$ 1.1,0.2 ,10.3, ... ,0.9$$

$$0.1,0.2,0.3, ... ,20.9 $$

$$0.1 , 0.2 , 10.3 , ... , 0.9 $$

Solution

Question 8

1 and $$\dfrac{3}{5}$$

$$\dfrac{2}{5}$$ and $$\dfrac{3}{5}$$

$$\dfrac{1}{2}$$ and $$\dfrac{2}{1}$$

$$\dfrac{3}{5}$$ and $$\dfrac{6}{5}$$

Solution

Question 9

$$0.5 < 0.6 < 0.7 < 0.8 ... < 1.1 < ... < 1.15 < 1.50$$

$$0.5 < 0.6 < 1.7 < 3.8 ... < 1.8< ... < 1.15 < 1.50$$

$$0.5 < 0.6 < 0.7 < 2.8 ... < 1.1 < ... < 1.15 < 1.50$$

$$0.5 < 0.6 < 0.7 < 0.8 ... < 3.1 < ... < 1.15 < 1.50$$

Question 10

$$\displaystyle \frac{7}{24}$$

$$\displaystyle \frac{16}{48}$$

$$\displaystyle \frac{13}{48}$$

All the above

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.