Fractions and Decimals Class 7 MCQ Questions

Answer: (a) Yes

Explanation: Proper fraction is a fraction which represents the part of whole number. In proper fraction numerator is always less than its denominator.

In generalize form for any two integer ‘a’ and ‘b’

a/b where (a < b)

i.e., Numerator < Denominator

Numerator = 3

Denominator = 4

Here 3 < 4

i.e., Numerator < Denominator

Hence, 3/4 is a proper fraction.

Answer: (b) No

Explanation: Improper fractions are the combination of whole number and a proper fraction. Improper fraction is opposite of proper fraction, since in improper fraction numerator is greater than its denominator

In generalize form for any two integer ‘a’ and ‘b’

a/b where (a > b)

i.e., Numerator > Denominator

Numerator = 1

Denominator = 2

Here, 1 < 2

i.e., Numerator < Denominator

Hence, 1/2 is not an improper fraction.

Answer: (b) Unlike fractions

Explanation: In case of Like Fraction, the denominator of the fractions are the same.

While, In case of Unlike Fraction denominator of the fractions are not same.

In the present case, the given fractions are

5/7,7/8 and 6/9

Since the Denominator in the present cases are 7 , 8 , 9 which are not same. So, the given fractions are Unlike Fractions

Answer: (d) 3/4

Explanation: 36/48

Taking HCF of 36 and 48 is 12

Divide numerator and denominator by their HCF i.e., 12

(36 ÷ 12)/(48 ÷ 12) = 3/4

Answer: (a) Yes

Explanation: Cross Multiplying (3/4) and (15/20)

3 x 20 = 60

and

15 x 4 = 60

Since,

3 x 20 = 15 x 4

Hence, Value of (3/4) = (15/20) on cross multiplication, they are equivalent fraction.

Answer: (b) (7/12) < (7/6)

Explanation: On Cross multiplying 7/12 and 7/6

We multiply 7 x 6 = 42

Similarly, we multiply 12 x 7 = 84

Since, 42 < 84

Hence,

(7/12) < (7/6)

Answer: (c) 14/40 and 85/40

Explanation: Step1: Find LCM of given Fractions

LCM of 20 and 8 is 40

Step 2: Divide LCM by the denominators of the given fractions

(40÷20)/(40÷8) = 2/5

Step 3: Multiply the quotient by the numerator and keep denominator equal to LCM. i.e.,

(2×7)/40 = 14/40

(5×17)/40 = 85/40

So, 14/40 and 85/40 are like fractions.

Answer: (a) 2(2/5)

Explanation: Given Fraction:

(12/5)

Divide the Numerator by the Denominator

On dividing 12 by 5

We get Quotient = 2

Remainder = 2

For a Mixed Fraction we have to write

Quotient + (Remainder/Divisor)

So, the Mixed Fraction is 2 + (2/5) = 2(2/5).

Answer: (a) 19/4

Explanation: A combination of Whole Number and a Proper Fraction is called a Mixed Fraction.

Here,

Mixed Fraction = 4(3/4)

Whole Number Part = 4

Numerator = 3

Denominator = 4

Step 1 : Multiply the Whole Number Part and Denominator of the Mixed Fraction

4 x 4 = 16

Step 2 : Add the Numerator to the product obtained in Step 1

3 + 16 = 19

Write the sum as the numerator and denominator would remain the same , as in the Mixed Fraction.

(19/4)

Hence, 4(3/4) = 19/4.

Answer: (b) 7/5

Explanation: Sum of Like Fraction = Sum of their Numerators / Common Denominator

= (14+7)/15

= 21/15

Hence, the sum of 14/15 and 7/15 is 21/15

Simplifying further,

HCF of 21 and 15 is 3

Dividing both Numerator and Denominator by their HCF i.e.,

(21÷3)/(15÷3) = 7/5

Hence, the sum of (14/15) and (7/15) = 7/5.

Answer: (c) 5/12

Explanation:
In order to add Unlike Fraction

Firstly, we have to change the Unlike Fraction, into equivalent Like Fractions, and then add the two equivalent Like Fractions

Take LCM of 24 and 60 is 120

Converting the Unlike Fraction into Equivalent Like Fraction

We have to multiply , both the numerator and denominator of (8/24) by 5

(8×5)/(24×5) = 40/120

We have to multiply , both the numerator and denominator of 560by 2

(5×2)/(60×2) = 10/120

Now (40/120) + (10/120) = 50/120

Simplifying further,

HCF of 50 and 120 is 10

Dividing both Numerator and Denominator by their HCF i.e.,

(50÷10)/(120÷10) = 5/12

Hence, the sum of 8/24 and 5/60 = 5/12.

Answer: (b) 10/9

Explanation: Difference of Like Fraction = Difference of their Numerators/Common Denominator

= (45−25)/18

= 20/18

Simplifying further,

HCF of 20 and 18 is 2

Dividing both Numerator and Denominator by their HCF i.e.,

(20÷2)/(18÷2) = 10/9

Hence, the difference of 45/18 and 25/18 = 10/9.

Answer: (c) 1/3

Explanation: To find the difference of Unlike Fraction

Firstly, we have to change the Unlike Fraction into equivalent Like Fraction, and then subtract the two equivalent Like Fraction

Take LCM of 24 and 16 is 48

Converting the Unlike Fraction into Equivalent Like Fraction

We have to multiply Numerator and Denominator of 11/24 by 2

(11×2)/(24×2) = 22/48

We have to multiply Numerator and Denominator of 2/16 by 3

(2×3)/(16×3) = 6/48

Now (22/48) – (6/48) = 16/48

Simplifying further,

HCF of 16 and 48 is 16

Dividing both Numerator and Denominator by their HCF i.e.,

(16÷16)/(48÷16) = 1/3

Hence, the difference of 11/24 and 2/16= 1/3.

Answer: (c) 47/5

Explanation: Sum of Like Fraction = Sum of their Numerators/Common Denominator

= (10+13+24)/5

= 47/5

Hence, the sum of 10/5, 13/5 and 24/5 is 47/5.

Answer: (a) 9(2/3)

Explanation: 7(1/3)+ 2(1/3)

Converting the Mixed Fractions into Improper Fractions

= (22/3) + (7/3)

Sum of Like Fraction = Sum of their Numerators / Common Denominator

= (22+7)/3

= 29/3

= 9(2/3)

Hence, the sum is 9(2/3).

Answer: (a) 21/4

Explanation: In this question ‘of’ means to multiply

When any fractions either proper or improper are multiplied with a whole number, the numerators are multiplied with whole number and the denominator will remains the same.

So, 42/56 of 7

= (7/1) x (42/56)

= 294/56

HCF of 294 and 56 is 14

Since, both numerator and denominator are divide by their HCF i.e.,

(294÷14)/(56÷14) = 21/4

So, the answer is 21/4.

Answer: (b) 7(5/12)

Explanation: 4(3/12) + 3(1/6)

Converting the Mixed Fractions into Improper Fractions

(51/12) + (19/6)

Take the LCM of the two denominators 12 and 6 which is 12

= (51×1+19×2)/12

= (51+38)/12

= 89/12

Converting the result into Mixed Fraction

= 7(5/12) ( Quotient (Remainder/Divisor))

Answer: (a) 12/35

Explanation: Product of Fraction = Product of their Numerators /Product of their Denominators

(4/5) x (3/7) = (4×3)/(5×7) = 12/35

Hence, product of (4/5) x (3/7) = 12/35.

Answer: (a) 9/10

Explanation: When any two or More Fractions (Whether Proper or Improper) are to be multiplied, the Numerators are multiplied with Numerator , and Denominators are multiplied with denominator.

Product of Fractions = Product of their Numerators /Product of their Denominators

Here, Numerators are 3 , 12 , 10

Denominators are 10 , 5 , 8

Hence, Product of Fractions would be

(3/10) x (12/5) x (10/8) = (3×12×10)/(10×5×8) = 360/400 = 9/10.

Answer: (b) 23/9

Explanation: In order to multiply a Mixed Fraction with a Improper/ Proper Fraction, we first convert mixed Fraction into improper Fraction , and then multiply it with the Improper/Proper Fraction

7(4/6)

7(4/6) means Quotient(Remainder/Divisor)

Converting Mixed Fraction into an Improper Fraction = ((Quotient× Divisor)+Remainder)/Divisor

= ((7×6)+4)/6

= 46/6

Multiplying the Improper Fraction obtained by conversion of Mixed Fraction, with given Fraction

46/6 x (1/3) = (46×1)/(6×3) = 46/18

Converting the result into Simplest form

HCF of 46 and 18 is 2

(46÷2)/(18÷2) = 23/9

Answer: (b) 7 months

Explanation: We know that, 1 Year = 12 months

7/12 of a Year

= (7/12) of 12 months

((7/12) x 12) months ( here ” of ” means to multiply ” x ” )

= (84/12) months = 7 months

Answer: (a) 480 m

Explanation: We know that, 1 km = 1000 m

(12/25) of a km

= (12/25) of 1000 m

= ( 12/25 x 1000 ) m ( here ” of ” means to multiply ” x ” )

= ( 12000/25 ) m = 480 m

Answer: (c) 80 cm

Explanation: We know that, 1 m = 100 cm

4/5 of a metre (m)

= (4/5) of 100 cm

((4/5) x 100 ) cm ( here ” of ” means to multiply ” x ” )

= ( 400/5 ) cm = 80 cm

Answer: (c) 16 paise

Explanation: We know that, 1 Rupee = 100 paise

(4/25) of a Rupee

= (4/25) of 100 paise

((4/25) x 100 ) paise ( here ” of ” means to multiply ” x ” )

= ( 400/25 ) paise = 16 paise

Answer: (c) 96 min

Explanation: We know that, (1 Hour = 60 min )

(8/5) of an Hour

= (8/5) of 60 min

= ((8/5)x 60 ) min ( here ” of ” means to multiply ” x ” )

= ( 480/5 ) min = 96 min

Answer: (a) 2/3

Explanation: We have, (5/16) ÷ (15/32)

In order to divide a Fraction by another Fraction

We have to multiply First Fraction with Reciprocal of the second Fraction

We have (5/16) ÷ (15/32)

= (5/16) x (32/15) (Since, Reciprocal of 1532is 3215)

(5×32)/(16×15) = 160/240

Simplifying the given Fraction,

HCF of 160 and 240 is 80

= (160÷80)/(240÷80) = 2/3

Answer: (c) 35/9

Explanation: We have, (3(1/3)) ÷ (6/7)

Simplifying, the above equation, we get (10/3) ÷ (6/7)

In order to divide a Fraction by another Fraction

We have to multiply First Fraction with Reciprocal of the second Fraction

(10/3) x (6/7) (Since, Reciprocal of 6/7 is 7/6 )

(10×7)/(3×6) = 70/18

Simplifying the given Fraction,

HCF of 70 and 18 is 2

= (70÷2)/(18÷2) = 35/9

Answer: (b) 6000

Explanation: Total population of town = 10000

It is given that,

Two fifths of the people own flat

Therefore, Number of people who have their own flat = 25 of Total population of town

= (2/5) x 10000

On simplifying it

= (2/1) x 2000

= 4000

So, Number of people who have their own flat = 4000

Now, the number of people do not have own flat = Total population of town – Number of people who have their own flat

= 10000 – 4000

= 6000

Therefore, the number of people do not have own flat = 6000

Answer: (b) 1/21

Explanation: We have, (4/7) ÷ 12

In order to divide a Fraction by another Fraction

We have to multiply First Fraction with Reciprocal of the second Fraction

(4/7) x (1/12) (Since, Reciprocal of 12/1 is 1/12 )

(4×1)/(7×12) = 4/84

Simplifying the given Fraction,

HCF of 4 and 84 is 4

= (4÷4)/(84÷4) = 1/21

Answer: (d) 2/3

Explanation: We have, 5 ÷ (15/2)

In order to divide a whole number by a Fraction, we need to multiply the whole number with the reciprocal of that Fraction.

We have to multiply Whole number by Reciprocal of that Fraction

5 x (2/15) (Since, Reciprocal of 15/2 is 2/15 )

5×(2/15) = 10/15

Simplifying the given Fraction,

HCF of 10 and 15 is 5

= (10÷5)/(15÷5) = 2/3

Answer: (d) (a) and (c)

Explanation: Decimal Numbers, having the same number of Decimal places are called Like Decimals.

The number of Decimal places in 14.08 is 2

The number of Decimal places in 14.2 is 1

The number of Decimal places in 26.71 is 2

Hence, 14.08 and 26.71 are Like Decimals since these two numbers have 2 Decimal places, while 14.2 has only 1 Decimal place.

Answer: (b) 32.7

Explanation: Where the number of Decimal places in two Decimals are different, they are called Unlike Decimals.

The number of Decimal places in 14.59 is 2

The number of Decimal places in 32.7 is 1

The number of Decimal places in 17.34 is 2

The number of Decimal places in 23.48 is 2

Hence, 32.7 is the unlike Decimal amongst the given Decimals since it has only 1 Decimal place while all other numbers have 2 Decimal places.

Answer: (c) 900

Explanation: If we plot the given number on the place value Table, we would get:

In the given Table, place value of 9 = 9 Hundreds = 900

So, the place value of 9 in 4926.371 is 900

Answer: (c) 22.2

Explanation: Whenever, we have a mixed fraction, it would consist of two parts.

Whole Number Part = 22

Fraction Part = 1/5

The Whole Number Part would remain the same.

The Fraction Part should be converted into decimal.

When we convert 1/5 into decimal we would get 0.2

The Decimal value of the given fraction = Whole Number Part . Decimal value of Fraction Part

The Decimal value of the given fraction = 22.2

Answer: (a) 13/50

Explanation: Step 1: Write the given Decimal without the Decimal point as the numerator of the fraction 26

Step 2: Write 1 followed by as many zeroes, as there are Decimal places in the given Decimal 100 (Since there was 2 decimal place in the given number, we have added 2 zero at the end of 1 )

= (26/100)

Step 3: Convert the fraction 26/100 into simplest form

HCF of 26 and 100 is 2.

To simplify this we have to divide both the numerator and denominator of the fraction by their HCF i.e.,

26 and 100 by 2

In other words (26/100) = (26÷2)/(100÷2) = 13/50

Hence, 0.26 = 13/50

Answer: (c) 24.347 km

Explanation: First, we have to convert 347 m into km

As we know that, 1000 m = 1 km

1 m = 1/1000 km

347 m = (1/1000)x 347 km

347 m = (347/1000) km

347 m = 0.347 km

Now we have to convert, 24 km 347 m into km

24 km + 347 m

= 24 km + 0.347 km (From above 347 m = 0.347 km )

= 24.347 km

Answer:(b) 16.178 kg

Explanation: First, we have to convert 178 g into kg

As we know that, 1000 g = 1 kg

1 g = (1/1000) kg

178 g = (1/1000) x 178 kg

178 g = (178/1000) kg

178 g = 0.178 kg

Now we have to convert, 16 kg 178 g into kg

16 kg + 178 g

= 16 kg + 0.178 kg (From above 178 g = 0.178 kg )

= 16.178 kg

Answer: (d) ₹ 51.45

Explanation: First, we have to convert 45 paise into rupees

As we know that, 100 paise = 1 rupees

1 paise = (1/100) rupees

45 paise = (1/100) x 45 rupees

45 paise = ₹ (45/100)

45 paise = ₹ 0.45

Now we have to convert, ₹ 51 and 45 paise into rupees

₹ 51 + 45 paise

= ₹ 51 + ₹ 0.45 (From above 45 paise = ₹ 0.45 )

= ₹ 51.45

Answer:(c) 29.72

Explanation: Let us say the number to be added to 49.76 to get 79.48 is x

This implies that 49.76 + x = 79.48

or x = 79.48 -49.76

79.48

– 49.76

= 29.72

Hence, if we add 29.72 to 49.76 we would get 79.48.

Answer: (c) 16.70

Explanation: Lets us say that the number to be subtracted from 69.13 to get 52.43 is x

This implies that 69.13 – x = 52.43

or x = 69.13 – 52.43

69.13

– 52.43

=16.70

Hence, if we subtract 16.70 from 69.13 we would get 52.43.

Answer: (a) 62383.7

Explanation: When a Decimal is multiplied by 1000, the Decimal point is shifted to the right by three places.

When we need to multiply 62.3837 x 1000

We would need to move the Decimal of 62.3837 by 3 digit to the right side

we would get, 62383.7

Hence, 62.3837 x 1000 = 62383.7

Answer: (c) 27.99

Explanation: Step I : Remove the Decimal Point from the Decimal number, and multiply it with the whole number.

i.e., 1866 x 15 = 27990

Step II : Count the Decimal Places in the given numbers, and add the same number of decimal places in the answer.

Number of Decimal places in the given Decimal is 3

If we add 3 decimal places to 27990 it would become 27.99

Hence, 1.866 x 15 = 27.99

Answer:(a) 0.02205

Explanation: Step I : Remove the Decimal Point from both the Decimal numbers, and multiply them

105 x 21 = 2205

Step II : Count the Decimal Places in both the decimal numbers, and add the same number of decimal places in the answer.

Number of Decimal place in the given Decimals = 3 + 2 = 5

So, the product will contain 5 Decimal point

If we add 5 decimal places to 2205 it would become 0.02205

Hence, 0.105 x 0.21 = 0.02205

Answer: (c) 18.473

Explanation: Step I : Remove the Decimal Point from all the Decimal number, and multiply them.

29 x 13 x 49 = 18473

Step II : Count the Decimal Places in all the decimal numbers, and add the same number of decimal places in the answer.

Number of Decimal place in the given Decimals = 1 + 1 + 1 = 3

So, the product will contain 3 Decimal point

If we add 3 decimal places to 18473 it would become 18.473

Hence, 2.9 x 1.3 x 4.9 = 18.473

Answer: (c) ₹ 388

Explanation: Cost of 1 pen = ₹ 24.25

Cost of 16 pens = ₹ ( 24.25 x 16 )

= ₹ 388

Hence, the cost of 16 such pens = ₹ 388

Answer: (a) 0.76526

Explanation: When a Decimal is divided by 1000, the Decimal point is shifted to the left by three places.

When we need to divide 765.26 by 1000

We would need to move the Decimal of 765.26 by three digit to the left side.

we would get, 0.76526

Hence, 765.26 ÷ 1000 = 0.76526