Rational Numbers Test

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Rational Numbers Test - 21

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Weekly Quiz Competition

Question 1
1 / -0

Fill in the blank: $$(-12) + \left (4 + \dfrac {1}{8}\right ) = [(-12) + .....] + \dfrac {1}{8}$$

A
$$(-12)$$

B
$$4$$

C
$$1$$

D
$$\dfrac {1}{8}$$

Solution

Addition is associative for rational numbers
i.e. $$a + (b + c) = (a + b) + c$$
$$\therefore (-12) + \left (4 + \dfrac {1}{8}\right ) = [(-12) + 4] + \dfrac {1}{8}$$
Question 2
1 / -0

Simplify using commutative and associative property :
$$\left [\dfrac {2}{5} + \dfrac {5}{7} + \dfrac {-12}{5}\right ]$$

A
$$-2\dfrac {5}{7}$$

B
$$\dfrac {9}{7}$$

C
$$\dfrac {-7}{9}$$

D
$$\dfrac {-9}{7}$$

Solution

$$\dfrac {2}{5} + \dfrac {5}{7} + \dfrac {-12}{5} = \dfrac {2}{5} + \left (\dfrac {5}{7} + \dfrac {-12}{5}\right )$$

$$= \dfrac {2}{5} + \left (\dfrac {-12}{5} + \dfrac {5}{7}\right )$$ (commutative property)

$$= \left (\dfrac {2}{5} + \dfrac {-12}{5}\right ) + \dfrac {5}{7}$$ (associative property)

$$= \dfrac {2 - 12}{5} + \dfrac {5}{7}$$

$$= \dfrac {-10}{5} + \dfrac {5}{7}$$

$$= \dfrac {-70 + 25}{35}$$

$$= -\dfrac {45}{35}$$

$$= \dfrac {-9}{7}$$
Or
$$= -2 + \dfrac {5}{7}$$

$$= \dfrac {-14 + 5}{7}$$

$$= \dfrac {-9}{7}$$
Question 3
1 / -0

The additive inverse of $$6$$ is .........

A
$$6$$

B
$$-6$$

C
$$0$$

D
$$1$$

Solution

For the given integer $$6$$, its negative is $$-6$$.

Addition of both results to zero.
$$6+(-6)=0$$

Hence, $$-6$$ is the additive inverse of $$6$$.
Question 4
1 / -0

Fill in the blank: $$\dfrac {2}{3} \times \left (-6 \times \dfrac {4}{5}\right ) = [ ..... \times -6] \times ....$$

A
$$\dfrac {2}{3}, \dfrac {4}{5}$$

B
$$\dfrac {-4}{5}, \dfrac {2}{3}$$

C
$$\dfrac {-2}{3}, \dfrac {-4}{5}$$

D
$$-6, -6$$

Solution

Multiplication is associative for rational numbers.
i.e. $$a \times (b\times c) = (a\times b)\times c$$
$$\therefore \dfrac {2}{3} \times \left (-6\times \dfrac {4}{5}\right ) = \left [\dfrac {2}{3} \times (-6)\right ] \times \dfrac {4}{5}$$
$$\therefore$$ The missing terms are $$\dfrac {2}{3}, \dfrac {4}{5}$$.
Question 5
1 / -0

The value of $$\dfrac {4}{5} + \dfrac {2}{3} + \dfrac {2}{5} $$ is
(Use associative and commutative properties)

A
$$\dfrac {28}{15}$$

B
$$\dfrac {15}{26}$$

C
$$\dfrac {10}{15}$$

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

Solution

$$\dfrac {4}{5} + \dfrac {2}{3} + \dfrac {2}{5} = \dfrac {4}{5} + \left (\dfrac {2}{3} + \dfrac {2}{5}\right )$$

$$= \dfrac {4}{5} + \left (\dfrac {2}{5} + \dfrac {2}{3}\right )$$ (commutative property)

$$= \left (\dfrac {4}{5} + \dfrac {2}{5} \right )+ \dfrac {2}{3}$$ (associative property)

$$= \dfrac {6}{5} + \dfrac {2}{3}$$

$$= \dfrac {28}{15}$$
Question 6
1 / -0

For any rational number $$\dfrac {a}{b}$$, its additive inverse is ..........

A
$$\dfrac {b}{a}$$

B
$$\dfrac {-b}{a}$$

C
$$\dfrac {a}{b}$$

D
$$\dfrac {-a}{b}$$

Solution

If $$\dfrac {a}{b}$$ is a rational number, then its negative $$\dfrac {-a}{b}$$ is called the additive inverse of $$\dfrac {a}{b}$$.
Question 7
1 / -0

Simplify using associative property :
$$\dfrac {-11}{7}\times \dfrac {4}{14}\times \dfrac {21}{33}$$

A
$$1$$

B
$$-1$$

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

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

Solution

$$\dfrac {-11}{7}\times \dfrac {4}{14}\times \dfrac {21}{33} = \dfrac {-11}{7} \times \left (\dfrac {4}{14} \times \dfrac {21}{33}\right ) = \dfrac {-11}{7} \times \left (\dfrac {21}{33} \times \dfrac {4}{14}\right )$$ ($$\because$$ commutative property)

$$= \left (\dfrac {-11}{7}\times \dfrac {21}{33}\right ) \times \dfrac {4}{14} (\because$$ associative property)

$$= -1\times \dfrac {4}{14} = -\dfrac {2}{7}$$
Question 8
1 / -0

The multiplicative identity for integers is .....

A
$$0$$

B
$$-1$$

C
$$1$$

D
None of these

Solution

$${\textbf{Step-1: Identity of any integer a is a number.}}$$

$${\text{The multiplicative identity of any integer a is a number b which when multiplied with}}\\ \text{a, leaves it unchanged.}$$
$${\text{ i.e. b is called as the multiplicative identity of any integer a if}}$$ $$a \times b = a.$$

$${\textbf{Step-2: When we multiply 1 with any integers.}}$$

$${\text{Now, when we multiply 1 with any of the integers a we get}}$$ $$a \times 1 = a = 1 \times a.$$
$${\text{So, 1 is the multiplicative identity for integers.}}$$

$${\textbf{Hence ,The correct option is (C).The multiplicative identity for integers is 1.}}$$
Question 9
1 / -0

........... is the only rational number which is equal to its additive inverse.

A
$$1$$

B
$$-1$$

C
$$0$$

D
$$\dfrac {1}{2}$$

Solution

$$0$$ is the only number whose negative is $$0$$ itself. Thus, $$0$$ is the only rational number which is equal to its additive inverse.
Question 10
1 / -0

The sum of an integer and its additive inverse is always .........

A
$$1$$

B
$$-1$$

C
$$0$$

D
$$2$$

Solution

The sum of an integer and its additive inverse is always $$0$$, because for any integer $$a$$ and its additive inverse $$(-a)$$, the sum is $$a + (-a)$$
$$=a - a$$
$$= 0$$.

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Rational Numbers Test - 21

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Rational Numbers Test - 21

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Question 1

$$(-12)$$

$$4$$

$$1$$

$$\dfrac {1}{8}$$

Solution

Question 2

$$-2\dfrac {5}{7}$$

$$\dfrac {9}{7}$$

$$\dfrac {-7}{9}$$

$$\dfrac {-9}{7}$$

Solution

Question 3

$$6$$

$$-6$$

$$0$$

$$1$$

Solution

Question 4

$$\dfrac {2}{3}, \dfrac {4}{5}$$

$$\dfrac {-4}{5}, \dfrac {2}{3}$$

$$\dfrac {-2}{3}, \dfrac {-4}{5}$$

$$-6, -6$$

Solution

Question 5

$$\dfrac {28}{15}$$

$$\dfrac {15}{26}$$

$$\dfrac {10}{15}$$

$$\dfrac {2}{3}$$

Solution

Question 6

$$\dfrac {b}{a}$$

$$\dfrac {-b}{a}$$

$$\dfrac {a}{b}$$

$$\dfrac {-a}{b}$$

Solution

Question 7

$$1$$

$$-1$$

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

$$\dfrac {2}{7}$$

Solution

Question 8

$$0$$

$$-1$$

$$1$$

None of these

Solution

Question 9

$$1$$

$$-1$$

$$0$$

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

Solution

Question 10

$$1$$

$$-1$$

$$0$$

$$2$$

Solution

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