Fractions and Decimals Test

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Fractions and Decimals Test - 33

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Weekly Quiz Competition

Question 1
1 / -0

If the numerator and denominator of a proper fraction are increased by the same quantity, then the resulting fraction is?

A
Always greater than the original fraction

B
Always less than the original fraction

C
Always equal to the original fraction

D
None of the above

Solution

If the numerator and denominator of a proper fraction are increased by the same quantity, then the resulting fraction is always greater than the original fraction.

Let us understand and verify it with the help of couple of examples:

$$(i)$$ Let $$\dfrac{1}{2}$$ be an original fraction.
$$\dfrac{1}{2}=0.5$$
If the numerator and denominator are increased by $$5$$, the fraction becomes:
$$\dfrac{1+5}{2+5}=\dfrac{5}{7}=0.71$$

$$\therefore$$ $$\dfrac{1}{2}<\dfrac{5}{7}$$

$$(ii)$$ Let $$\dfrac{7}{9}$$ be an original fraction.
$$\dfrac{7}{9}\approx 0.78$$
If the numerator and denominator are increased by $$1$$, the fraction becomes:
$$\dfrac{7+1}{9+1}=\dfrac{8}{10}=0.8$$

$$\therefore$$ $$\dfrac{7}{9}<\dfrac{8}{10}$$

Hence, if the numerator and denominator of a proper fraction are increased by the same quantity, then the resulting fraction is always greater than the original fraction.

Therefore, option A is correct.
Question 2
1 / -0

The simplification of $$33.6 - 2 { .05 } + 0.133$$ is equal to

A
$$31.63$$

B
$$29.643$$

C
$$25. { 61 }3$$

D
None of these

Solution
Question 3
1 / -0

Evaluate: $$3.7-1.9$$

A
$$0.6$$

B
$$7.3$$

C
$$3.4$$

D
$$1.8$$

Solution

$$3.7-1.9$$
$$=1.8$$
Question 4
1 / -0

A proper fraction with denominator $$3$$ , which is less than 1 is

A
$$\frac{4}{3}$$

B
$$\frac{2}{3}$$

C
$$1 \frac{2}{3}$$

D
None

Solution

Clearly from question denominator$$=3$$
numerator $$=2$$
Fraction $$=\dfrac{2}{3}$$
Question 5
1 / -0

A fraction whose numerator is greater than its denominator is fraction.

A
an improper

B
a proper

C
a mixed

D
None of these

Solution

That will be an improper fraction
Ex $$\dfrac{6}{5}$$
Question 6
1 / -0

Multiply $$\dfrac{6}{13}$$ by the reciprocal of $$\dfrac{-7}{16}$$

A
$$\dfrac{-95}{91}$$

B
$$\dfrac{-96}{91}$$

C
$$\dfrac{96}{91}$$

D
None of these

Solution

Reciprocal of $$\dfrac{-7}{16}$$ is $$\dfrac{-16}{7}$$

Now $$\dfrac{6}{13}\times$$ Reciprocal of $$\dfrac{-7}{16}$$

$$=\dfrac{6}{13}\times\dfrac{-16}{7}$$

$$=\dfrac{6\times -16}{13\times 7}=\dfrac{-96}{91}$$
Question 7
1 / -0

Which of the following is a proper fraction?

A
$$\dfrac78$$

B
$$1\dfrac{7}{8}$$

C
$$\dfrac87$$

D
none of these

Solution

We know that, if the numerator is less than the denominator then the fraction is called as proper fraction.
Amongst the given fractions only $$\dfrac78$$ has a numerator that is less than the denominator.

Hence, $$\dfrac78$$ is a proper fraction.
Question 8
1 / -0

Mark against the correct answer in each of the following:
$$ ( 1.007 - 0.7) = ? $$

A
$$ 1 $$

B
$$ 0.37 $$

C
$$ 0.307 $$

D
None of these

Solution

$$ 3.07 $$
First convert the given decimals into like decimals

$$ = (1.007 – 0.700)$$

$$ = 0.307 $$
Question 9
1 / -0

Which of the following is an improper fraction?

A
$$\dfrac{7}{10}$$

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

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

D
none of these

Solution

Improper fraction is a fraction in which numerator is greater than denominator.
$$\cfrac{9}{7}$$ follows this condition.
Hence, option $$(C)$$ is correct.
Question 10
1 / -0

$$5.2 - 3.6$$ is equal to

A
$$0.16$$

B
$$2.6$$

C
$$0.26$$

D
$$1.6$$

Solution

$$5.2 - 3.6 = \dfrac{52}{10} - \dfrac{36}{10} $$

$$= \dfrac{16}{10}$$

$$=1.6$$

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Fractions and Decimals Test - 33

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Fractions and Decimals Test - 33

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SHARING IS CARING

Question 1

Always greater than the original fraction

Always less than the original fraction

Always equal to the original fraction

None of the above

Solution

Question 2

$$31.63$$

$$29.643$$

$$25. { 61 }3$$

None of these

Solution

Question 3

$$0.6$$

$$7.3$$

$$3.4$$

$$1.8$$

Solution

Question 4

$$\frac{4}{3}$$

$$\frac{2}{3}$$

$$1 \frac{2}{3}$$

None

Solution

Question 5

an improper

a proper

a mixed

None of these

Solution

Question 6

$$\dfrac{-95}{91}$$

$$\dfrac{-96}{91}$$

$$\dfrac{96}{91}$$

None of these

Solution

Question 7

$$\dfrac78$$

$$1\dfrac{7}{8}$$

$$\dfrac87$$

none of these

Solution

Question 8

$$ 1 $$

$$ 0.37 $$

$$ 0.307 $$

None of these

Solution

Question 9

$$\dfrac{7}{10}$$

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

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

none of these

Solution

Question 10

$$0.16$$

$$2.6$$

$$0.26$$

$$1.6$$

Solution

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