Rational Numbers Test

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Rational Numbers Test - 30

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$8\times 2\dfrac {4}{5} + 8\times 3\dfrac {1}{5}$$ is

A
$$\dfrac {8}{5}$$

B
$$24$$

C
$$48$$

D
$$-48$$

Solution

$$8\times 2\dfrac {4}{5} + 8\times 3\dfrac {1}{5}$$

$$= 8\times \dfrac {14}{5} + 8\times \dfrac {16}{5}$$

$$= \dfrac {8}{5} \times 14 + \dfrac {8}{5} \times 16$$

$$= \dfrac {8}{5} \times (14 + 16)$$ ($$\because$$ distributive property)

$$= \dfrac {8}{5}\times 30$$

$$= 8\times 6$$

$$= 48$$.
Question 2
1 / -0

Fill in the blank: $$\dfrac {4}{7}\left (\dfrac {7}{15} - \dfrac {21}{4}\right ) = \dfrac {4}{7} \times \dfrac {7}{15} - ....\times \dfrac {4}{7}$$

A
$$\dfrac {4}{7}$$

B
$$\dfrac {21}{4}$$

C
$$\dfrac {-21}{4}$$

D
$$\dfrac {7}{15}$$

Solution

Distributive property over subtraction holds true for rational numbers.
Thus, $$a (b - c) = a\times b - a\times c$$

$$\therefore \dfrac {4}{7} \left (\dfrac {7}{15} - \dfrac {21}{4}\right ) = \dfrac {4}{7} \times \dfrac {7}{15} - \dfrac {4}{7} \times \dfrac {21}{4}$$

$$= \dfrac {4}{7} \times \dfrac {7}{15} - \dfrac {21}{4} \times \dfrac {4}{7}$$ ($$\because$$ commutative property).
Question 3
1 / -0

The value of $$\dfrac {1}{5} \left (\dfrac {15}{7} - \dfrac {20}{14}\right )$$ is

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

B
$$\dfrac {3}{7}$$

C
$$\dfrac {1}{7}$$

D
$$7$$

Solution

$$\dfrac {1}{5} \left (\dfrac {15}{7} - \dfrac {20}{14}\right )$$

$$= \dfrac {1}{5} \left (\dfrac {15}{7} - \dfrac {10}{7}\right )$$

$$= \dfrac {1}{5} \times \dfrac {15}{7} - \dfrac {1}{5}\times \dfrac {10}{7}$$ ($$\because$$ distributive property)

$$= \dfrac {3}{7} - \dfrac {2}{7}$$

$$= \dfrac {1}{7}$$
Question 4
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The value of $$\dfrac {3}{5} \times \dfrac {35}{24} + \dfrac {10}{1}\times \dfrac {3}{5} $$ is

A
$$\dfrac {55}{8}$$

B
$$\dfrac {8}{55}$$

C
$$\dfrac {3}{5}$$

D
$$\dfrac {35}{8}$$

Solution

$$\dfrac {3}{5} \times \dfrac {35}{24} + \dfrac {10}{1}\times \dfrac {3}{5}$$

$$= \dfrac {3}{5} \times \dfrac {35}{24} + \dfrac {10}{1}\times \dfrac {3}{5}$$

$$= \dfrac {3}{5} \times \dfrac {35}{24} + \dfrac {3}{5}\times \dfrac {10}{1}$$ ($$\because$$ commutative property)

$$= \dfrac {3}{5} \left (\dfrac {35}{24} + 10\right )$$ ($$\because$$ distributive property)

$$= \dfrac {3}{5} \times \dfrac {35 + 240}{24}$$

$$=\dfrac {275}{8\times 5}$$

$$= \dfrac {55}{8}$$.
Question 5
1 / -0

The value of $$2\dfrac {1}{2} \times 10 - 4\dfrac {1}{3} \times 10$$ is

A
$$\dfrac {-3}{55}$$

B
$$\dfrac {3}{55}$$

C
$$\dfrac {55}{3}$$

D
$$\dfrac {-55}{3}$$

Solution

$$2\dfrac {1}{2} \times 10 - 4\dfrac {1}{3} \times 10$$

$$= \dfrac {5}{2}\times 10 - \dfrac {13}{3} \times 10$$

$$= 10\times \dfrac {5}{2} - 10\times \dfrac {13}{3}$$ ($$\because$$ commutative property)

$$= 10 \left (\dfrac {5}{2} - \dfrac {13}{3}\right )$$ ($$\because$$ distributive property)

$$= 10\times \left (\dfrac {15 - 26}{6}\right )$$

$$= 10\times \left (\dfrac {-11}{6}\right )$$

$$= \dfrac {-55}{3}$$.
Question 6
1 / -0

A rational number between $$\dfrac {-9}{10}$$ and $$\dfrac {4}{5}$$ is:

A
$$\left (\dfrac {-9}{10} + \dfrac {4}{5}\right ) \times \dfrac {1}{2}$$

B
$$\left (\dfrac {-9}{10} - \dfrac {4}{5}\right ) + \dfrac {1}{2}$$

C
$$\left (\dfrac {-9}{10} + \dfrac {4}{5}\right ) \times 2$$

D
All above are correct

Solution

Mean of two numbers always lies between the two numbers.

Mean

$$= \dfrac{\left (\dfrac {-9}{10} + \dfrac {4}{5}\right )}{2}$$

$$= \left (\dfrac {-9}{10} + \dfrac {4}{5}\right )\times \dfrac {1}{2}$$.

So, answer is option $$A.$$
Question 7
1 / -0

Which of the following rational numbers lies between $$\dfrac {-4}{5}$$ and $$\dfrac {-7}{5}$$?

A
$$\dfrac {-36}{45}$$

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

C
$$\dfrac {-39}{45}$$

D
$$\dfrac {-63}{45}$$

Solution

As per the given options, let us multiply both numbers with $$\dfrac {9}{9}$$.

$$\therefore \dfrac {-4}{5}\times \dfrac {9}{9} = \dfrac {-36}{45}$$ and $$\dfrac {-7}{5}\times \dfrac {9}{9} = \dfrac {-63}{45}$$

$$\therefore$$ Clearly, $$\dfrac {-39}{45}$$ lies between $$\dfrac {-4}{5}$$ and $$\dfrac {-7}{5}$$.
Question 8
1 / -0

The points $$A, B$$ and $$C$$ on the given number line represents

A
$$\dfrac {-3}{10}, \dfrac {-1}{10}, \dfrac {3}{4}$$

B
$$\dfrac {-3}{10}, \dfrac {1}{10}, \dfrac {3}{4}$$

C
$$\dfrac {3}{10}, \dfrac {-1}{10}, \dfrac {-3}{4}$$

D
$$4, -1, 3$$

Solution

The given number line can be completed as:
Thus, $$A = \dfrac {-3}{10}, B = \dfrac {-1}{10}$$ and $$C = \dfrac {3}{4}$$.
Question 9
1 / -0

Which of the following numbers lies between $$-1$$ and $$-2$$?

A
$$\dfrac {-1}{2}$$

B
$$\dfrac {-3}{2}$$

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

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

Solution

Mean $$= \dfrac {(-1) + (-2)}{2} = \dfrac {-1 -2}{2} = \dfrac {-3}{2}$$.
Mean of two numbers always lies between the two numbers.
So, answer is option $$B.$$
Question 10
1 / -0

Which of the following numbers lies between $$\dfrac {5}{24}$$ and $$\dfrac {3}{8}$$?

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

B
$$1$$

C
$$\dfrac {7}{24}$$

D
$$0$$

Solution

Mean $$= \dfrac {\dfrac {3}{8} + \dfrac {5}{24}}{2} = \dfrac {\dfrac {9 + 5}{24}}{2} = \dfrac{\left (\dfrac {14}{24}\right )}{2}$$

$$= \dfrac {7}{12}\times \dfrac {1}{2}$$

$$= \dfrac {7}{24}$$

Mean of two numbers lies between the two numbers.
So, $$ \dfrac {7}{24}$$ lies between $$\dfrac {3}{8}$$ and $$\dfrac {5}{24}.$$

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Re-Attempt Weekly Quiz Competition

Rational Numbers Test - 30

Result

Rational Numbers Test - 30

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SHARING IS CARING

Question 1

$$\dfrac {8}{5}$$

$$24$$

$$48$$

$$-48$$

Solution

Question 2

$$\dfrac {4}{7}$$

$$\dfrac {21}{4}$$

$$\dfrac {-21}{4}$$

$$\dfrac {7}{15}$$

Solution

Question 3

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

$$\dfrac {3}{7}$$

$$\dfrac {1}{7}$$

$$7$$

Solution

Question 4

$$\dfrac {55}{8}$$

$$\dfrac {8}{55}$$

$$\dfrac {3}{5}$$

$$\dfrac {35}{8}$$

Solution

Question 5

$$\dfrac {-3}{55}$$

$$\dfrac {3}{55}$$

$$\dfrac {55}{3}$$

$$\dfrac {-55}{3}$$

Solution

Question 6

$$\left (\dfrac {-9}{10} + \dfrac {4}{5}\right ) \times \dfrac {1}{2}$$

$$\left (\dfrac {-9}{10} - \dfrac {4}{5}\right ) + \dfrac {1}{2}$$

$$\left (\dfrac {-9}{10} + \dfrac {4}{5}\right ) \times 2$$

All above are correct

Solution

Question 7

$$\dfrac {-36}{45}$$

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

$$\dfrac {-39}{45}$$

$$\dfrac {-63}{45}$$

Solution

Question 8

$$\dfrac {-3}{10}, \dfrac {-1}{10}, \dfrac {3}{4}$$

$$\dfrac {-3}{10}, \dfrac {1}{10}, \dfrac {3}{4}$$

$$\dfrac {3}{10}, \dfrac {-1}{10}, \dfrac {-3}{4}$$

$$4, -1, 3$$

Solution

Question 9

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

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

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

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

Solution

Question 10

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

$$1$$

$$\dfrac {7}{24}$$

$$0$$

Solution

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