Rational Numbers Test

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Rational Numbers Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

Which property is being used in the following

$$ \displaystyle \frac{2}{3} $$+ $$ \displaystyle \frac{4}{7} $$=$$ \displaystyle \frac{4}{7} $$+$$ \displaystyle \frac{2}{3} $$

A
Additive identity

B
Commutative property of addition

C
Commutative property of multipication

D
Associative property of addition

Solution

commutative property of addition states that
(a+b) = (b+a)
Here we have $$ \displaystyle \frac{2}{3} $$+ $$ \displaystyle \frac{4}{7} $$=$$ \displaystyle \frac{4}{7} $$+$$ \displaystyle \frac{2}{3} $$ which is of the form $$a+b=b+a$$
Question 2
1 / -0

The number with which when $$82$$ is multiplied product remains the same.

A
$$82$$

B
$$0$$

C
$$\displaystyle \frac{1}{82}$$

D
$$1$$

Solution

Any number when multiplied by $$1$$, results in that number itself.
Hence, $$82 \displaystyle \times 1 =82$$
So, option D is correct.
Question 3
1 / -0

If $$4\div 5= a$$ and $$5\div 4= b$$, then which of the following is true?

A
$$a=b$$

B
$$a\neq b$$

C
This is closure property

D
None of the above

Solution

$$4\div 5 =0.8 = a$$
$$5\div 4=1.25 = b $$
$$\therefore a \neq b$$
So, option $$B$$ is correct.
Question 4
1 / -0

Out of the following, identify which option states commutative property.

A
$$-2 \times (1+8) = (-2 \times 1) + (-2 \times 8)$$

B
$$-16 \times 19 = 19 \times -16$$

C
$$1+ (2+3) = (1+2) + 3$$

D
All of the above

Solution

Commutative property means $$A \times B = B \times A $$
Hence option $$B$$ is correct.
Question 5
1 / -0

Select the appropriate property:
$$a\times b(c)=a \times(c) b$$

A
commutative property of multiplication

B
identity property of multiplication

C
distributive property

D
associative property of multiplication

Solution

According to the question, the numbers a, b and c are multiplied regardless of any order, which represents the commutative property of multiplication.
Question 6
1 / -0

Rational numbers are closed under ..........

A
addition

B
subtraction

C
multiplication

D
all of the above

Solution

For any two rational numbers $$a$$ and $$b,$$
$$(a + b), (a - b), (b - a)$$ & $$(a\times b)$$ are all rational numbers.
Thus, rational numbers are closed under addition, subtraction and multiplication.
Question 7
1 / -0

Given that, $$\dfrac {-15}{2} \times \dfrac {12}{5} = \dfrac {12}{5} \times \dfrac {-15}{2}$$
This is the best example for

A
associative property of multiplication

B
distributive property of multiplication

C
closure property of multiplication

D
commutative property of multiplication

Solution

Commutativity is satisfied with respect to multiplication in rational numbers.
$$a \times b = b \times a$$
Hence, option $$D$$ is correct.
Question 8
1 / -0

For any rational number, multiplicative identity is

A
$$1$$

B
$$0$$

C
$$100$$

D
$$11$$

Solution

Option $$A$$ is correct.
eg. $$1 \times 0 = 0$$ and $$508 \times 1 = 508$$
Here, the identity of a number maintained.
Question 9
1 / -0

Find the missing value: $$\dfrac {-5}{9} \times \dfrac {6}{-1} = ..... \times \dfrac {-5}{9}$$

A
$$6$$

B
$$-6$$

C
$$\dfrac {5}{9}$$

D
$$\dfrac {-5}{9}$$

Solution

Multiplication is commutative for rational numbers. i.e. $$a\times b = b\times a$$

$$\therefore \dfrac {-5}{9} \times \dfrac {6}{-1} = \dfrac {6}{-1} \times \dfrac {-5}{9}$$

$$= -6\times \dfrac {-5}{9}$$.
Question 10
1 / -0

Which of the following statements is incorrect, if $$a, b, c$$ and $$d$$ are any rational numbers?

A
$$\dfrac {a}{b} + \dfrac {c}{d} = \dfrac {c}{d} + \dfrac {a}{b}$$

B
$$\dfrac {a}{b}\times \dfrac {c}{d} = \dfrac {c}{d} \times \dfrac {a}{b}$$

C
$$\dfrac {a}{b} - \dfrac {c}{d} = \dfrac {c}{d} - \dfrac {a}{b}$$

D
none of these

Solution

For rational number, subtraction is not commutative.
i.e. $$p - q \neq q - p$$.
$$\therefore \dfrac {a}{b} - \dfrac {c}{d} = \dfrac {c}{d} - \dfrac {a}{b}$$ is not true.
Thus, it is an incorrect statement.

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Rational Numbers Test - 18

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Rational Numbers Test - 18

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Question 1

Additive identity

Commutative property of addition

Commutative property of multipication

Associative property of addition

Solution

Question 2

$$82$$

$$0$$

$$\displaystyle \frac{1}{82}$$

$$1$$

Solution

Question 3

$$a=b$$

$$a\neq b$$

This is closure property

None of the above

Solution

Question 4

$$-2 \times (1+8) = (-2 \times 1) + (-2 \times 8)$$

$$-16 \times 19 = 19 \times -16$$

$$1+ (2+3) = (1+2) + 3$$

All of the above

Solution

Question 5

commutative property of multiplication

identity property of multiplication

distributive property

associative property of multiplication

Solution

Question 6

addition

subtraction

multiplication

all of the above

Solution

Question 7

associative property of multiplication

distributive property of multiplication

closure property of multiplication

commutative property of multiplication

Solution

Question 8

$$1$$

$$0$$

$$100$$

$$11$$

Solution

Question 9

$$6$$

$$-6$$

$$\dfrac {5}{9}$$

$$\dfrac {-5}{9}$$

Solution

Question 10

$$\dfrac {a}{b} + \dfrac {c}{d} = \dfrac {c}{d} + \dfrac {a}{b}$$

$$\dfrac {a}{b}\times \dfrac {c}{d} = \dfrac {c}{d} \times \dfrac {a}{b}$$

$$\dfrac {a}{b} - \dfrac {c}{d} = \dfrac {c}{d} - \dfrac {a}{b}$$

none of these

Solution

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