NCERT Exemplar Solutions: Fractions & Decimals

# NCERT Exemplar Solutions: Fractions & Decimals | Mathematics (Maths) Class 6 PDF Download

## Exercise Page: 57

In questions 1 to 20, out of the four options, only one answer is correct. Choose the correct answer.
Q.1. The fraction which is not equal to 4/5 is
(a) 40/50
(b) 12/15
(c) 16/20
(d) 9/15

(D) 9/15
All the options given in the question are further simplified as,
(A) 40/50 = 4/5
(B) 12/15
Divide both numerator and denominator by 3.
= 4/5
(C) 16/20
Divide both numerator and denominator by 4.
= 4/5
(D) 9/15
Divide both numerator and denominator by 3.
= 3/5
Therefore, 3/5 ≠ 4/5

Q.2. The two consecutive integers between which the fraction 5/7 lies are
(a) 5 and 6
(b) 0 and 1
(c) 5 and 7
(d) 6 and 7

A fraction whose numerator is less than the denominator is called a proper fraction.
So, 5/7 = 0.715
Therefore, 5/7 lies between 0 and 1.

Q.3. When ¼ is written with denominator as 12, its numerator is
(a) 3
(b) 8
(c) 24
(d) 12

(1 × 3)/(4 × 3) = 3/12
Consider, 3/12
Divide both numerator and denominator by 3.
= 1/4

Q.4. Which of the following is not in the lowest form?
(a) 7/5
(b) 15/20
(c) 13/33
(d) 27/28

Divide both numerator and denominator by 5.
= ¾

Q.5. If (5/8) = (20/p), then value of p is
(a) 23
(b) 2
(c) 32
(d) 16

Consider the given fraction, (5/8) = (20/P)
P = 20 × (8/5)
P= 4 × 8
P = 32

Q.6. Which of the following is not equal to the others?
(a) 6/8
(b) 12/16
(c) 15/25
(d) 18/24

(C) 15/25
All the options given in the question are further simplified as,
(A) 6/8
Divide both numerator and denominator by 2.
= 3/4
(B) 12/16
Divide both numerator and denominator by 4.
= 3/4
(C) 15/25
Divide both numerator and denominator by 5.
= 3/5
(D) 18/24
Divide both numerator and denominator by 6.
= ¾
Comparing all results, (¾ = ¾ = ¾) ≠ 3/5
Therefore, (6/8 = 12/16 = 18/24) ≠ 15/25

Q.7. Which of the following fractions is the greatest?
(a) 5/7
(b) 5/6
(c) 5/9
(d) 5/8

We know that, among all fractions with same numerator, the one having smaller denominator will be the highest fraction.
5/9 < 5/8 < 5/7 < 5/6
Therefore, among four options, (b) 5/6 has small denominator. So, it is the greatest fraction.

Q.8. Which of the following fractions is the smallest?
(a) 7/8
(b) 9/8
(c) 3/8
(d) 5/8

We know that, among all fractions with same denominator, the one having smaller numerator will be the smallest fraction.
3/8 < 5/8 < 7/8 < 9/8
Therefore, among four options, (c) 3/8 has small numerator. So, it is the smallest fraction.

Q.9. Sum of 4/17 and 15/17 is
(a) 19/17
(b) 11/17
(c) 19/34
(d) 2/17

If denominators of the given fractions are same, we can add both fractions.
So, (4/17) + (15/17)
= (4 + 15)/17
= 19/17

Q.10. On subtracting 5/9 from 19/9, the result is
(a) 24/9
(b) 14/9
(c) 14/18
(d) 14/0

If denominators of the given fractions are same, we can subtract both fractions.
So, (19/9) – (5/9)
= (19 – 5)/9
= 14/9

Q.11. 0.7499 lies between
(a) 0.7 and 0.74
(b) 0.75 and 0.79
(c) 0.749 and 0.75
(d) 0.74992 and 0.75

0.7499 lies between 0.749 and 0.75

Q.12. 0. 023 lies between
(a) 0.2 and 0.3
(b) 0.02 and 0.03
(c) 0.03 and 0.029
(d) 0.026 and 0.024

0. 023 lies between 0.02 and 0.03

Q.13. 11/7 can be expressed in the form
(a)
(b)
(c)
(d)

Q.14. The mixed fraction  can be expressed as
(a) 33/7
(b) 39/7
(c) 33/4
(d) 39/4

can be expressed as = 5 + (4/7)
= (35 + 4)/7
= 39/7

Q.15. 0.07 + 0.008 is equal to
(a) 0.15
(b) 0.015
(c) 0.078
(d) 0.78

First we have to convert given decimals into like decimals = 0.070 + 0.008
So, sum of 0.070 and 0.008 = 0.070 + 0.008
= 0.078

Q.16. Which of the following decimals is the greatest?
(a) 0.182
(b) 0.0925
(c) 0.29
(d) 0.038

First we have to convert given decimals into like decimals = 0.1820, 0.0925, 0.2900, 0.0380
Now, by comparing 4 decimal numbers, 0.2900 is the greatest.

Q.17. Which of the following decimals is the smallest?
(a) 0.27
(b) 1.5
(c) 0.082
(d) 0.103

First we have to convert given decimals into like decimals = 0.270, 1.500, 0.082, 0.103
Now, by comparing 4 decimal numbers, 0.082 is the smallest.

Q.18. 13.572 correct to the tenths place is
(a) 10
(b) 13.57
(c) 14.5
(d) 13.6

Place value of the place immediately after the decimal point (i.e. tenth place) is 1/10, that of next place (i.e. hundredths place) is 1/100 and so on.
13.572 correct to the tenths place is 13.6

Q.19. 15.8 – 6.73 is equal to
(a) 8.07
(b) 9.07
(c) 9.13
(d) 9.25

First we have to convert given decimals into like decimals = 15.80
Now, 15.80 – 6.73 = 9.07

Q.20. The decimal 0.238 is equal to the fraction
(a) 119/500
(b) 238/25
(c) 119/25
(d) 119/50

Decimals can be converted into fractions by removing their decimal points and writing 10,100, etc in the denominators, depending upon the number of decimal places in the decimals.
So, 0.238 = 238/1000
Divide both numerator and denominator by 2
= 119/500

### In questions 21 to 44, fill in the blanks to make the statements true:

Q.21. A number representing a part of a _________ is called a fraction.

A number representing a part of a whole is called a fraction.
Example: ¼, ¾, 1/5, 3/6 etc.

Q.22. A fraction with denominator greater than the numerator is called a _________ fraction.

A fraction with denominator greater than the numerator is called a proper fraction.
Example: 2/5, 3/8, 10/11 etc. are proper fractions.

Q.23. Fractions with the same denominator are called _________ fractions.

Fractions with the same denominator are called like fractions.
Example: ½, 3/2, 5/2, 7/2 etc.

Q.24. 135/18  is a _________ fraction.

Mixed fraction.

Q.25. 18/5 is an fraction.

18/5 is an improper fraction.
A fraction whose numerator is greater than the denominator is called an improper fraction.

Q.26. 7/19 is a fraction.

7/19 is a proper fraction.
A fraction whose numerator is less than the denominator is called a proper fraction.

Q.27. 5/8 and 3/8 are proper fraction.

5/8 and 3/8 are like proper fraction.
Fractions with same denominators are called like fractions.

Q.28. 6/11 and 6/13 are proper fractions.

6/11 and 6/13 are unlike proper fractions.
If the denominators are different, then they are called unlike fractions.

Q.29. The fraction 6/15 in simplest form is.

The fraction 6/15 in simplest form is 2/5.
The given fraction 6/15, is further simplified by dividing both numerator and denominator by 3.
= 2/5

Q.30. The fraction 17/34 in simplest form is .

The fraction 17/34 in simplest form is ½.
The given fraction 17/34, is further simplified by dividing both numerator and denominator by 17.
= ½

Q.31. 18/135 and 90/675 are proper, unlike and fractions.

18/135 and 90/675 are proper, unlike and equivalent fractions.
Consider the two given fractions, 18/135 and 90/675
So, (18/135) = (90/675)
By cross multiplication, we get
(18 × 675) = (90 × 135)
12,150 = 12,150
Therefore, 18/135 and 90/675 are proper, unlike and equivalent fractions.

Q.32.  is equal to the improper fraction.

is equal to the improper fraction 58/7.
Given mixed fraction is converted into improper fraction as = ((7 × 8) + 2)/7
= (56 + 2)/7
= 58/7

Q.33. 87/7 is equal to the mixed fraction ______.
87/7 is equal to the mixed fraction

We know that, mixed fraction = Quotient Remainder/Divisor

Therefore, 87/7 is equal to the mixed fraction

Q.34. 9 + (2/10) + (6/100) is equal to the decimal number ______.

9 + (2/10) + (6/100) is equal to the decimal number 9.26.
Fractions with denominators 10,100, etc. can be written in a form, using a decimal point, called decimal numbers or decimals.
9 + (2/10) + (6/100) = 9 + 0.2 + 0.06
= 9.26

Q.35. Decimal 16.25 is equal to the fraction ______.

Decimal 16.25 is equal to the fraction 16¼ or 65/4.
Decimals can be converted into fractions by removing their decimal points and writing 10,100, etc in the denominators, depending upon the number of decimal places in the decimals.
16.25 = 1625/100
Divide both numerator and denominator by 25.
= 65/4
= 16¼

Q.36. Fraction 7/25 is equal to the decimal number ______.

Fraction 7/25 is equal to the decimal number 0.28.
Multiply numerator and denominator by 4 to get denominator 100.
(7/25) = (7 × 4)/(25 × 4)
= 28/100
We know that, fractions with denominators 10,100, etc. can be written in a form, using a decimal point, called decimal numbers or decimals.
= 0.28

Q.37. (17/9) + (41/9) = .

(17/9) + (41/9) = 58/9.
Fractions with same denominators are called like fractions.
Sum of two like fractions = (17 + 41)/9
= 58/9

Q.38. (67/14) – (24/14) = .

(67/14) – (24/14) = 43/14.
Fractions with same denominators are called like fractions.
Difference of two fractions = (67 – 24)/14
= 43/14

Q.39. 17/2 + 3½ = .

17/2 + 3½ = 12.
First we have to convert mixed fraction into improper fraction = 3½ = 7/2
Fractions with same denominators are called like fractions.
Sum of two like fractions = (17/2) + (7/2)
= (17 + 7)/2
= 24/2
= 12

Q.40. 9 ¼ – 5/4 = _________.

9 ¼ – 5/4 = 37/4 – 5/4 = (37 – 5)/4 = 32/4 = 8.

Q.41. 4.55 + 9.73 = ______.

4.55 + 9.73 = 14.28.

Q.42. 8.76 – 2.68 = ______.

8.76 – 2.68 = 6.08.

Q.43. The value of 50 coins of 50 paisa = ₹______.

The value of 50 coins of 50 paisa = ₹25.
We know that, ₹ 1 = 100 paisa
So, 50 coins of 50 paisa = 50 × 50
= 2500 paisa.
Then,
= 2500/100
= ₹ 25

Q.44. 3 Hundredths + 3 tenths = ______.

3 Hundredths + 3 tenths = 0.33.
Place value of the place immediately after the decimal point (i.e. tenth place) is 1/10, that of next place (i.e. hundredths place) is 1/100 and so on.
3 Hundredths is written as = 3 × (1/100)
= 0.03
3 tenths is written as = 3 × (1/10)
= 0.3
Then sum of 3 Hundredths, 3 tenths = 0.03 + 0.3
= 0.33

In each of the questions 45 to 65, state whether the statement is true or false:

Q.45. Fractions with same numerator are called like fractions.

False.
Fractions with same denominators are called like fractions.

Q.46. Fraction 18/39 is in its lowest form.

False.
Lowest form of given fraction 18/39
Divide both numerator and denominator by 3,
= 6/13

Q.47. Fractions 15/39 and 45/117 are equivalent fractions.

True.
Consider the two given fractions, 15/39 and 45/117
So, (15/39) = (45/117)
By cross multiplication, we get
(15 × 117) = (45 × 39)
1,755 = 1,755

Q.48. The sum of two fractions is always a fraction.

True.
For example: consider two fractions 10/5 and 15/5.
Sum of two fractions = (10 + 15)/5
= 25/5
= 5
= 5/1
A fraction in which there is no common factor, except 1, in its numerator and denominator is called a fraction in the simplest or lowest form.
When 2 fractions are added, the result in most cases will be a fraction p/q form, but in some case if it does happen to be just an integer, it can always be written with denominator 1 (hence p/q form).

Q.49. The result obtained by subtracting a fraction from another fraction is necessarily a fraction.

False.
Not necessarily a fraction. But can be written in fraction.

Q.50. If a whole or an object is divided into a number of equal parts, then each part represents a fraction.

True.
A fraction is a number representing a part of a whole. This whole may be a single object or a group of objects.
For example: consider a circle is divided into 4 equal parts. Out of four equal parts 3 of them are shaded.
So, it can be represented in the form of fraction = 3/4

Q.51. The place value of a digit at the tenths place is 10 times the same digit at the ones place.

False.
Let us assume a digit be ‘y’.
The place value of a digit at the tenths place = y × (1/10)
= y/10
Then,
The tenths place is 10 times the same digit at the ones place.
y/10 = 10y is not possible.

Q.52. The place value of a digit at the hundredths place is 1/10 times the same digit at the tenths place.

True
Let ‘a’ be the same digit at tens and hundreds place in a number.
Place value of digit at tens place = 10 × a = 10a
Place value of digit at hundreds place = 100 × a = 100a
Hence, the place value of a digit at the hundreds place is 10 times the same digit at the tens place.

Q.53. The decimal 3.725 is equal to 3.72 correct to two decimal places.

False.
Consider the given decimal number, 3.725
The thousandths place has number 5.
Then, hundredths has number 2 it will be increased by 1 number to correct two decimal places.
Therefore, the decimal 3.725 is equal to 3.73 correct to two decimal places.

Q.54. In the decimal form, fraction 25/8 = 3.125

True.
25/8 can be further simplified by dividing both numerator and denominator by 8.
= 3.125

Q.55. The decimal 23.2 =

False.
The decimal 23.2 = 232/10
Dividing both denominator and numerator by 2, we get.
= 116/5 =

Q.56. The fraction represented by the shaded portion in the adjoining figure is 3/8.

True.
Circle is divided into 8 equal parts. Out of 8 equal parts 3 of them are shaded.

Q.57. The fraction represented by the unshaded portion in the adjoining figure is 5/9.

False.
Rectangle is divided into 9 equal parts. Out of 9 equal parts 4 of them are unshaded. So, fraction represented by the unshaded portion in the adjoining figure = 4/9.

Q.58. (25/19) + (6/19) = 31/38

False.
So, (25/19) + (6/19)
= (25 + 6)/19
= 31/19
Hence, 31/19 ≠ 31/38

Q.59. (8/18) – (8/15) = 8/3

False.
Consider Left Hand Side (LHS),
LCM of 18 and 15 = 90
Then,
(8/18) = (8 × 5)/(18 × 5) = 40/90
(8/15) = (8 × 6)/(15 × 6) = 48/90
Difference of two fractions (40/90) – (48/90)
= -8/90
Right Hand Side (RHS) = 8/3
By comparing LHS and RHS,
LHS ≠ RHS
-8/90 ≠ 8/3

Q.60. (7/12) + (11/12) = 3/2

True.
Consider Left Hand Side (LHS),
Sum of like fractions = (7/12) + (11/12)
= (7 + 11)/12
= 18/12
Divide both numerator and denominator by 6, we get,
= 3/2
Right Hand Side (RHS) = 3/2
By comparing LHS and RHS,
LHS = RHS
3/2 = 3/2

The document NCERT Exemplar Solutions: Fractions & Decimals | Mathematics (Maths) Class 6 is a part of the Class 6 Course Mathematics (Maths) Class 6.
All you need of Class 6 at this link: Class 6

## Mathematics (Maths) Class 6

134 videos|323 docs|42 tests

## FAQs on NCERT Exemplar Solutions: Fractions & Decimals - Mathematics (Maths) Class 6

 1. What are fractions and decimals?
Ans. Fractions and decimals are types of numbers that represent parts of a whole. Fractions are numbers expressed in the form of a numerator and a denominator, where the numerator represents the part and the denominator represents the whole. Decimals, on the other hand, are numbers expressed with a decimal point, where the digits after the decimal point represent parts of a whole.
 2. How can fractions and decimals be converted into each other?
Ans. Fractions can be converted into decimals by dividing the numerator by the denominator. For example, the fraction 3/4 can be converted to a decimal by dividing 3 by 4, which equals 0.75. Decimals can be converted into fractions by expressing the digits after the decimal point as the numerator and the place value of the last digit as the denominator. For example, the decimal 0.6 can be converted to a fraction as 6/10, which can be further simplified to 3/5.
 3. How can fractions and decimals be added or subtracted?
Ans. To add or subtract fractions, the fractions must have a common denominator. If they have different denominators, they need to be converted to fractions with the same denominator. Once they have the same denominator, the numerators can be added or subtracted. For example, to add 1/4 and 2/5, we need to convert them to fractions with a common denominator, which is 20. So, 1/4 becomes 5/20 and 2/5 becomes 8/20. Adding these fractions gives us 5/20 + 8/20 = 13/20. Adding or subtracting decimals follows the same concept as adding or subtracting whole numbers.
 4. How can fractions and decimals be multiplied or divided?
Ans. To multiply fractions, we simply multiply the numerators and denominators. For example, to multiply 2/3 and 4/5, we multiply 2 by 4 to get the numerator, which is 8, and multiply 3 by 5 to get the denominator, which is 15. So, the product of 2/3 and 4/5 is 8/15. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. For example, to divide 2/3 by 4/5, we multiply 2/3 by 5/4, which gives us 10/12. This fraction can be further simplified to 5/6.
 5. How can fractions and decimals be compared?
Ans. Fractions and decimals can be compared by converting them into the same form. For example, to compare the fraction 3/4 and the decimal 0.75, we can convert the fraction to a decimal by dividing 3 by 4, which gives us 0.75. Since both the fraction and decimal representation are the same, we can conclude that 3/4 is equal to 0.75. To compare fractions, we can also compare their numerators after converting them to fractions with the same denominator. The fraction with the greater numerator is greater than the other fraction.

## Mathematics (Maths) Class 6

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