Fractions MCQ Quiz - Objective Question with Answer for Fractions - Download Free PDF

Given:

Formula Used:

Follow the order of operations (PEMDAS/BODMAS)

Calculation:

Calculate the values step by step:

(-2 - 3) = -5

(5 + 3) = 8

(-2 - 3) = -5

(-6 - 4) = -10

(-7 - 5) = -12

Now substitute back into the expression:

Simplify inside the parentheses first:

-5 × 8 = -40

-40 ÷ -5 = 8

Simplify the second part:

-10 ÷ -12 =

Now divide the results:

8 ÷  = 8 × (6/5)

48/5 = 9.6

The correct answer is option 4, 9.6.

Given:

Formula Used:

Sum of recurring decimals = Decimal 1 + Decimal 2.

Calculation:

Convert recurring decimals into fractions:

 = 68/99

 = 73/99

Add the fractions:

Total = (68/99) + (73/99)

⇒ Total = (68 + 73) / 99

⇒ Total = 141 / 99

Convert back to a recurring decimal:

141 ÷ 99 = 

 + =

The correct option is Option 1.

Given:

Expression to evaluate: (1)/(1×3) + (1)/(3×5) + (1)/(5×7) + (1)/(7×9)

Formula Used:

General term of the series: 1n(n+2)=12(1n−1n+2)" id="MathJax-Element-130-Frame" role="presentation" style="position: relative;" tabindex="0">General term of the series: 1n(n+2)=12(1n−1n+2)General term of the series: 1n(n+2)=12(1n−1n+2) $\text{General term of the series: } \frac{1}{n(n+2)} = \frac{1}{2} \left( \frac{1}{n} - \frac{1}{n+2} \right)$

Calculation:

⇒ 1/2 × [(1/1 - 1/3) + (1/3 - 1/5) + (1/5 - 1/7) + (1/7 - 1/9)]

Observe cancellation of terms:

⇒ 1/2 × (1/1 - 1/9)

Simplify:

⇒ 1/2 × (1 - 1/9)

⇒ 1/2 × [(9 - 1)/9]

⇒ 1/2 × (8/9)

⇒ 8/18

⇒ 4/9

Given:

Recurring decimal =

Formula used:

Algebraic method for converting recurring decimals to fractions.

Calculations:

Let X = --- (1)

⇒ 1000X = --- (2)

Now, multiply equation (2) by 100 (since there are 2 repeating digits) to shift one block of repeating digits past the decimal point:

⇒ 100 × 1000X = 100 ×

⇒ 100000X = --- (3)

Subtract equation (2) from equation (3) to eliminate the repeating part:

⇒ 100000X - 1000X = -

⇒ 99000X = 84181 - 841

⇒ 99000X = 83340

⇒ X =

⇒ X =

⇒ X =

⇒ X =

⇒ X =

The fraction in its lowest terms is .

Numerator = 463

Denominator = 550

Difference between the denominator and the numerator = Denominator - Numerator

⇒ Difference = 550 - 463

⇒ Difference = 87

∴ The difference between the denominator and the numerator is 87.

Given:

Formula used:

Basic arithmetic operations

Calculation:

⇒11/2 + 3 + 8/3 + 15/2 + 19/3

⇒ (11 × 3 + 3 × 6 + 8 × 2 + 15 × 3 + 19 × 2) / 6

⇒ (33 + 18 + 16 + 45 + 38) / 6

⇒ 150 / 6 = 25

∴ The correct answer is option (3).

Solution:

= 25/2 + 37/3 + 73/6

= (75 + 74 + 73)/6

= 222/6

= 37

Shortcut Trick

= 12 + 12 + 12 + (1/2 + 1/3 + 1/6)

= 36 + 1 = 37

Let that fraction be x.

⇒ x + 5/8 = 1

⇒ x = 1 – 5/8

⇒ x = 3/8 = 6/16

⇒ 59/20

(7/13) = 0.538

(2/3) = 0.666

(4/11) = 0.3636

(5/9) = 0.5555

Out of 2/3, 7/13, 4/11, 5/9

2/3 is the largest number followed by 5/9 then 7/13 and the smallest is 4/11.

∴ The ascending order will be 4/11, 7/13, 5/9, 2/3.

Given:

(5x - 2y) ∶ (x - 2y) = 9 ∶ 17

Calculation:

The given ratio can be written as:

(5x - 2y)/(x - 2y) = 9/17

17 × (5x - 2y) = 9 × (x - 2y)

85x - 34y = 9x - 18y

76x = 16y

x/y = 16/76

x/y = 4/19

9 × (4/19)/13 = 36/247

So, 9x/13y = 36/247.

Let the number of people be x and number of the chair be y.

Number of available chair = y × (9/13) = 9y/13

Number of empty chair = y - (9y/13) = 4y/13

Given, Number of empty chairs = 28

According to the question

4y/13 = 28

y = 28 × (13/4) = 91

Total number of chairs = 91

Number of chairs in which people are sitting = 91 - 28 = 63

Number of people who sit = x × (7/9) = 7x/9

According to the question

7x/9 = 63

x = 63 × (9/7) = 81

Total number of people are = 81

Chairs would have been still empty if everyone in the hall was sitting = 91 - 81 = 10

Formula used:

a² - b² = (a + b)(a - b)

Calculation

⇒ 

⇒ [(p + q - r)(p - q + r)]/[(p + q + r)(p - q + r)] + [(p + q - r)(q - p + r)]/[(p + q + r)(p + q - r)] + [(p - q + r)(q  -p + r)]/[(p + q + r)(q - p + r)]

⇒ [(p + q - r)]/[(p + q + r)] + [q - p + r)]/[(p + q + r)] + [(p - q + r)]/[(p + q + r)]

⇒ [(p + q - r)]/[(p + q + r)] + [q - p + r)]/[(p + q + r)] + [(p - q + r)]/[(p + q + r)]

⇒ (p + q + r)/(p + q + r)

⇒ 1.

The value is 1.

Shortcut Trick

Let put p = q = r = 1

So,

⇒ 

⇒ 

⇒ 1/3 + 1/3 + 1/3 = 1

Hence, The value is 1.

Given:

Calculation:

⇒ 5x/(2 – x) = 1

⇒ 5x = 2 – x

⇒ 6x = 2

⇒ x = 2/6

∴ The required value of x is 1/3.

Given:

The fractions are 13/19, 25/ 31, 28/31, 70/79.

Calculation:

The values are-

13/19 = 0.68

25/31 = 0.80

28/31 = 0.90

70/79 = 0.88

∴ Option C is correct.

Concept Used:

Follow BODMAS rule to solve this question, as per the order given below,

Calculations:

Given expression is,

⇒ ? = 144/18

⇒ ? = 8