example-1Multiple choice
Which of the following fractions is the smallest? 11 11 11 11
- (A)
- (B)
- (C)
- (D)9 7 10 6
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Solution: Answer is (C)
Chapter 4 – Fractions And Decimals
Class 6 Mathematics · 116 questions · 81 with answers
Solved examples
example-2Multiple choice
0.7625 lies between
- (A)0.7 and 0.76
- (B)0.77 and 0.78
- (C)0.76 and 0.761
- (D)0.76 and 0.763
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Solution: Answer is (D) 11.4.2018 MATHEMATICS
example-3Fill in the blanks
Fill in the blanks so that the statement is true: Decimal 8.125 is equal to the fraction ________. 65 1 8125
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Solution: or 8 (because 8.125 = ) 8 8 1000
example-4Fill in the blanks
Fill in the blanks so that the statement is true: 6.45 – 3.78 = _________.
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Solution: 2.67
example-5True / False
State true or false: The fraction 14 is equal to 14.2.
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Solution: False [Hint: 14 = 14.2]
example-6Fill in the blanks
Fill in the blanks using > or < : 8 16 – 45 89 8 8× 2 16
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Solution: = = 45 45× 2 90 16 16 8 16 Now, < , so, < 90 89 45 89 Another method: 8 × 89 = 712 and 16 × 45 =720 8 16 As 712 < 720, therefore < 45 89
example-7Short answer
Express as a decimal. 12 12 × 4
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Solution: = 25 25× 4 = = 0.48
example-8Short answer
Convert 5809g to kg. 5809
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Solution: Since 1000g = 1kg, therefore, 5809g = kg 1000 = 5.809kg. FRACTIONS AND DECIMALS 55 11.4.2018
example-9Short answer
Round off 87.952 to tenths place.
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Solution: For rounding off to tenths place, we look at the hundredths place. Here the digit is 5. So, the digit at the tenths place (9) will be increased by 1 (i.e., it will become 9 + 1) Hence, rounding off 87.952 to tenths place, we get 88.0 (Note: Do not write it as 88.) 3 5
example-10Short answer
Add the fractions 5 and 8 16 3 5 43 5
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Solution: 5 + = + 8 16 8 16 43× 2 5 86 5 = + = + 8× 2 16 16 16 86 + 5 91 11 = = = 5 16 16 16
example-11Short answer
What should be added to 37.28 to obtain 46.8?
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Solution: Here, we want to fill in the box in 37.28 + = 46.8. For this, We will have to find 46.8 – 37.28. We perform this operation as follows by writing the two numbers having equal number of decimal places: (Since 46.8 = 46.80) 46.80 – 37.28 Hence, the required number to be added 9.52 to 37.28 is 9.52.
example-12Short answer
Arrange the following in ascending order. 2.2, 2.023, 2.0226, 22.1, 20.42
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Solution: We have to arrange them from the smallest to the greatest number. We arrange them as follows (using the idea of place value and comparing their digits at different places); 2.0226, 2.023, 2.2, 20.42, 22.1 (Note: Using the < sign, these numbers can also be written as 2.0226 < 2.023 < 2.2 < 20.42 < 22.1.) 11.4.2018 MATHEMATICS
example-13Short answer
Gorang purchased 2kg 280g apples, 3kg 375g bananas, 225g grapes and 5kg 385g oranges. Find the total weight of the fruits purchased by Gorang in kg.
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Solution: Weight of apples = 2kg 280g = 2280g (Since 1kg = 1000g) Weight of bananas = 3kg 375g = 3375g Weight of grapes = 225g Weight of oranges = 5kg 385g = 5385g Total weight = 2280g + 3375g + 225g + 5385g 2280g + 3375g + 225g + 5385g 11265 11265g Thus, total weight = 11265g = kg 1000 = 11.265kg i.e. 11kg 265g
example-14Short answer
What is wrong in the following? 7 5 7 + 5 12 + = = =2 4 2 4+2 6 7 5 7+5
Show solution
Solution: Writing 4 + 2 = 4 + 2 is wrong. It should be as follows: 7 5 7 10 + = + (Converting into like fractions) 4 2 4 4 7 + 10 17 = (Only numerators are added) 4 4
Questions
Q1Multiple choice
The fraction which is not equal to is 40 12 16 9
- (A)
- (B)
- (C)
- (D)50 15 20 15 FRACTIONS AND DECIMALS 57 11.4.2018 UNIT-4
Show answer
(D) 50 15 20 15 FRACTIONS AND DECIMALS 57 11.4.2018 UNIT-4
Q2Multiple choice
The two consecutive integers between which the fraction lies are
- (A)5 and 6
- (B)0 and 1
- (C)5 and 7
- (D)6 and 7
Show answer
(B) 0 and 1
Q3Multiple choice
When is written with denominator as 12, its numerator is
- (A)3
- (B)8
- (C)24
- (D)12
Show answer
(A) 3
Q4Short answer
Which of the following is not in the lowest form?
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(B)
Q7Multiple choice
15 13 27
- (A)
- (B)
- (C)
- (D)5 20 33 28 5 20 5. If 8 = p , then value of p is (A) 23 (B) 2 (C) 32 (D) 16 6. Which of the following is not equal to the others? 6 12 15 18 (A) (B) (C) (D)
Show answer
(B)
Q8Multiple choice
16 25 24 7. Which of the following fractions is the greatest? 5 5 5 5
- (A)
- (B)
- (C)
- (D)7 6 9 8 8. Which of the following fractions is the smallest? 7 9 3 5 (A) (B) (C) (D) 8 8 8 8 4 15
Show answer
(C)
Q9Multiple choice
Sum of and is 17 17 19 11 19 2
- (A)
- (B)
- (C)
- (D)17 17 34 17 5 19
Show answer
(A)
Q10Multiple choice
On subtracting from , the result is 9 9 24 14 14 14
- (A)
- (B)
- (C)
- (D)9 9 18 0
Show answer
(B)
Q11Multiple choice
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 11.4.2018 MATHEMATICS
Show answer
(C) 0.749 and 0.75
Q12Multiple choice
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
Show answer
(B) 0.02 and 0.03
Q13Multiple choice
can be expressed in the form 1 1 4 1
- (A)7
- (B)4
- (C)1
- (D)11 4 7 7 7
Show answer
(C) 1
Q14Multiple choice
The mixed fraction 5 can be expressed as 33 39 33 39
- (A)
- (B)
- (C)
- (D)7 7 4 4
Show answer
(B)
Q15Multiple choice
0.07 + 0.008 is equal to
- (A)0.15
- (B)0.015
- (C)0.078
- (D)0.78
Show answer
(C) 0.078
Q16Multiple choice
Which of the following decimals is the greatest?
- (A)0.182
- (B)0.0925
- (C)0.29
- (D)0.038
Show answer
(C) 0.29
Q17Multiple choice
Which of the following decimals is the smallest?
- (A)0.27
- (B)1.5
- (C)0.082
- (D)0.103
Show answer
(C) 0.082
Q18Multiple choice
13.572 correct to the tenths place is
- (A)10
- (B)13.57
- (C)14.5
- (D)13.6
Show answer
(D) 13.6
Q19Multiple choice
15.8 – 6.73 is equal to
- (A)8.07
- (B)9.07
- (C)9.13
- (D)9.25
Show answer
(B) 9.07
Q20Multiple choice
The decimal 0.238 is equal to the fraction 119 238 119 119
- (A)
- (B)
- (C)
- (D)500 25 25 50 In questions 21 to 44, fill in the blanks to make the statements true:
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(A)
Q21Fill in the blanks
A number representing a part of a _________ is called a fraction.
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Whole
Q22Fill in the blanks
A fraction with denominator greater than the numerator is called a _________ fraction.
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proper
Q23Fill in the blanks
Fractions with the same denominator are called _________ fractions.
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like
Q24Fill in the blanks
13 is a _________ fraction. FRACTIONS AND DECIMALS 59 11.4.2018 UNIT-4 18 7
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mixed
Q25Fill in the blanks
is an ______ fraction. 26. is a ______ fraction. 5 19 5 3
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improper
Q27Fill in the blanks
and are ______ proper fractions. 8 8 6 6
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like
Q28Fill in the blanks
and are ______ proper fractions. 11 13
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unlike
Q29Fill in the blanks
The fraction in simplest form is ______.
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1 58 3
Q30Fill in the blanks
The fraction in simplest form is ______. 18 90
Q31Fill in the blanks
and are proper, unlike and ______ fractions. 135 675
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equivalent
Q32Fill in the blanks
8 is equal to the improper fraction ______.
Q33Fill in the blanks
is equal to the mixed fraction ______. 2 6
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12
Q34Fill in the blanks
9 + + is equal to the decimal number ______. 10 100
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9.26 2 7 7 1 65 58 43
Q35Fill in the blanks
Decimal 16.25 is equal to the fraction ______.
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16 or
Q36Fill in the blanks
Fraction is equal to the decimal number ______. 17 41 67 24
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0.28
Q37Fill in the blanks
+ = ______. 38. − = ______. 9 9 14 14 17 1 1 5
Q39Fill in the blanks
+ 3 = ______. 40. 9 − = ______. 2 2 4 4
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12
Q41Fill in the blanks
4.55 + 9.73 = ______. 42. 8.76 – 2.68 = ______.
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14.28
Q43Fill in the blanks
The value of 50 coins of 50 paisa = Rs ______.
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Rs 25
Q44Fill in the blanks
3 Hundredths + 3 tenths = ______. In each of the questions 45 to 65, state whether the statement is true or false:
Show answer
0.33
Q45Short answer
Fractions with same numerator are called like fractions.
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T
Q46Short answer
Fraction is in its lowest form. 11.4.2018 MATHEMATICS 15 45
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F
Q47Short answer
Fractions and are equivalent fractions. 39 117
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T
Q48Short answer
The sum of two fractions is always a fraction.
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F
Q49Short answer
The result obtained by subtracting a fraction from another fraction is necessarily a fraction.
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F
Q50Short answer
If a whole or an object is divided into a number of equal parts, then each part represents a fraction.
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T
Q51Short answer
The place value of a digit at the tenths place is 10 times the same digit at the ones place.
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F
Q52Short answer
The place value of a digit at the hundredths place is times the same digit at the tenths place.
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T
Q53Short answer
The decimal 3.725 is equal to 3.72 correct to two decimal places.
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F
Q54Short answer
In the decimal form, fraction = 3.125.
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T
Q55Short answer
The decimal 23.2 = 23
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F
Q56Short answer
The fraction represented by the shaded portion in the adjoining figure is .
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T
Q57Short answer
The fraction represented by the unshaded portion in the adjoining figure is . 25 6 31 8 8 8
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F
Q58Short answer
+ = 59. – = 19 19 38 18 15 3 7 11 3
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F
Q60Short answer
+ = 61. 3.03 + 0.016 =3.019 12 12 2 16 13
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T
Q62Short answer
42.28 – 3.19 = 39.09 63. > 25 25
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T
Q64Fill in the blanks
19.25 < 19.053 65. 13.730 = 13.73 In each of the questions 66 to 71, fill in the blanks using ‘>’, ‘<’ or ‘=’ : 11 14 8 95
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F
Q66Short answer
... 67. ... 16 15 15 14 FRACTIONS AND DECIMALS 61 11.4.2018 UNIT-4 12 32
Show answer
<
Q68Short answer
... 69. 3.25... 3.4 75 200 18 25
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=
Q70Short answer
...1.3 71. 6.25... 15 4
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< 7 4 1
Q72Short answer
Write the fraction represented by the shaded portion of the adjoining figure:
Q73Short answer
Write the fraction represented by the unshaded portion of the adjoining figure:
Q74Short answer
Ali divided one fruit cake equally among six persons. What part of the cake he gave to each person?
Show answer
8 15 6
Q75Short answer
Arrange 12.142, 12.124, 12.104, 12.401 and 12.214 in ascending order.
Show answer
12.104, 12.122, 12.142, 12.214, 12.401
Q76Short answer
Write the largest four digit decimal number less than1using the digits 1, 5, 3 and 8 once.
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0.8531 20 41 3
Q77Short answer
Using the digits 2, 4, 5 and 3 once, write the smallest four digit decimal number.
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0.2345
Q78Short answer
Express as a decimal.
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0.55
Q79Short answer
Express 6 as an improper fraction.
Q80Short answer
Express 3 as a decimal.
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3.4
Q81Short answer
Express 0.041 as a fraction.
Q82Short answer
Express 6.03 as a mixed fraction.
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6 3 1000 100 9 1537
Q83Short answer
Convert 5201g to kg. 11.4.2018 MATHEMATICS
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5.201kg
Q84Short answer
Convert 2009 paise to rupees and express the result as a mixed fraction.
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Rs 20.09, Rs 20
Q85Short answer
Convert 1537cm to m and express the result as an improper fraction.
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15.37 m, m 100 100 87 1 2 3 5 7 6 4 3 33
Q86Short answer
Convert 2435m to km and express the result as mixed fraction. 2 3 1 5
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2.435km, 2 km
Q87Short answer
Arrange the fractions , , and in ascending order. 3 4 2 6 6 7 4 3
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, , ,
Q88Short answer
Arrange the fractions , , and in descending order. 7 8 5 4
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, , ,
Q89Short answer
Write as a fraction with denominator 44.
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200 2 3 4 6 8 7 5 4 44 60 1 25
Q90Short answer
Write as a fraction with numerator 60.
Q91Short answer
Write as a mixed fraction.
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16
Q92Short answer
Round off 20.83 to nearest tenths.
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20.8
Q93Short answer
Round off 75.195 to nearest hundredths.
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75.20
Q94Short answer
Round off 27.981 to nearest tenths. 3 2
Show answer
28.0
Q95Short answer
Add the fractions and . 8 3 3 3
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72 8 24 1 1 7 1 3 1
Q96Short answer
Add the fractions and 6 . 8 4 1 1
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7
Q97Short answer
Subtract from . 6 2 1 100
Q98Short answer
Subtract 8 from . 3 9 1 1
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2
Q99Short answer
Subtract 1 from 6 . 4 2 1 1
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5
Q100Short answer
Add 1 and 6 . 4 2 1 3
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7
Q101Short answer
Katrina rode her bicycle 6 km in the morning and 8 km in the 2 4 evening. Find the distance travelled by her altogether on that day. FRACTIONS AND DECIMALS 63 11.4.2018 UNIT-4
Show answer
15 8 3 9 4 4 4 889 9 3 1
Q102Short answer
A rectangle is divided into certain number of equal parts. If 16 of the parts so formed represent the fraction , find the number of parts in which the rectangle has been divided.
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64
Q103Short answer
Grip size of a tennis racquet is 11 cm. Express the size as an improper fraction.
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cm104. 105. 106. 107. 24.5 80 10 5 6 108. 9.850kg 109. 0.011, 0.101, 0.110, 1.001 110. 22.022 11 1 30 2 3 111. (i) (ii) 112. Milk, Rice, 113. 114. 1 m 70 10 53 3 4 ANSWERS 155 OOLRLPNOV _lqucpq 5 1 3 1 115. 47 kg 116. 27 litres 117. 2 litres 118. 110 cm 8 4 4 20 5 1 1 119. 4 km 120. 1 kg 121. 2 m 8 4 4 122. (a) Equal denominators too have been added. (b) Numerators and denominators have been added. 5 6 123. 2.6 metres 124. (i) (D) (ii) (A) (iii) (E) (iv) (B) 125. , 6 6 3 4 7 9 5 1 126. , , 127. and 128. 7 7 7 22 22 2 129. (i) Bag I (ii) Bag II (iii) Bag III (iv) Bag I (v)Bag I (vi) Bag I (vii) Bag II (viii) Bag I (ix) Bag I (x) Bag I
Q104Short answer
On an average of the food eaten is turned into organism’s own body and is available for the next level of consumer in a food chain. What fraction of the food eaten is not available for the next level?
Q105Short answer
Mr. Rajan got a job at the age of 24 years and he got retired from the job at the age of 60 years. What fraction of his age till retirement was he in the job?
Q106Short answer
The food we eat remains in the stomach for a maximum of 4 hours. For what fraction of a day, does it remain there?
Q107Short answer
What should be added to 25.5 to get 50?
Q108Short answer
Alok purchased 1kg 200g potatoes, 250g dhania, 5kg 300g onion, 500g palak and 2kg 600g tomatoes. Find the total weight of his purchases in kilograms.
Q109Short answer
Arrange in ascending order: 0.011, 1.001, 0.101, 0.110
Q110Short answer
Add the following: 20.02 and 2.002
Q111Multiple choice
It was estimated that because of people switching to Metro trains, about 33000 tonnes of CNG, 3300 tonnes of diesel and 21000 tonnes of petrol was saved by the end of year 2007. Find the fraction of :
- (i)the quantity of diesel saved to the quantity of petrol saved.
- (ii)the quantity of diesel saved to the quantity of CNG saved. 11.4.2018 MATHEMATICS
Q112Short answer
Energy content of different foods are as follows: Food Energy Content per kg. Wheat 3.2 Joules Rice 5.3 Joules Potatoes (Cooked) 3.7 Joules Milk 3.0 Joules Which food provides the least energy and which provides the maximum? Express the least energy as a fraction of the maximum energy.
Q113Short answer
A cup is full of milk. What part of the cup is still to be filled by milk to make it full? 1 3
Q114Short answer
Mary bought 3 m of lace. She used 1 m of lace for her new dress. 2 4 How much lace is left with her?
Q115Short answer
When Sunita weighed herself on Monday, she found that she had 1 3 gained 1 5kg. Earlier her weight was 46 kg. What was her weight 4 8 on Monday? 1 3
Q116Short answer
Sunil purchased 12 litres of juice on Monday and 14 litres of juice 2 4 on Tuesday. How many litres of juice did he purchase together in two days? 3 1
Q117Short answer
Nazima gave 2 litres out of the 5 litres of juice she purchased to 4 2 her friends. How many litres of juice is left with her?
Q118Short answer
Roma gave a wooden board of length 150 cm to a carpenter for making a shelf. The Carpenter sawed off a piece of 40 cm from it. What is the length of the remaining piece? FRACTIONS AND DECIMALS 65 11.4.2018 UNIT-4 1 1
Q119Short answer
Nasir travelled 3 km in a bus and then walked 1 km to reach a 2 8 town. How much did he travel to reach the town?
Q120Short answer
The fish caught by Neetu was of weight 3 kg and the fish caught by Narendra was of weight 2 kg. How much more did Neetu’s fish weigh than that of Narendra?
Q121Short answer
Neelam’s father needs 1 m of cloth for the skirt of Neelam’s new dress and m for the scarf. How much cloth must he buy in all?
Q122Multiple choice
What is wrong in the following additions?
- (a)
- (b)1 2 1 8 =8 6 2 4 2 1 1 1 +4 = 4 +2 4 4 4 3 2 1 =12 =8 =8 8 6 3
Q123Short answer
Which one is greater? 1 metre 40 centimetres + 60 centimetres or 2.6 metres.
Q124Multiple choice
Match the fractions of Column I with the shaded or marked portion of figures of Column II: Column I Column II (i)
- (A)(ii)
- (B)11.4.2018 (iii)
- (C)(iv)
- (D)(E)
Q125Short answer
Find the fraction that represents the number of natural numbers to total numbers in the collection 0, 1, 2, 3, 4, 5. What fraction will it be for whole numbers?
Q126Short answer
Write the fraction representing the total number of natural numbers in the collection of numbers –3, – 2, –1, 0, 1, 2, 3. What fraction will it be for whole numbers? What fraction will it be for integers? 7 2
Q127Short answer
Write a pair of fractions whose sum is and difference is . 11 11
Q128Short answer
What fraction of a straight angle is a right angle?
Q129Multiple choice
Put the right card in the right bag. Cards Bags
- (i)
- (ii)11.4.2018
- (iii)
- (iv)(v) (vi) (vii) (viii) (ix) (x) Activity: Find the number of boys and girls in your school and write: (i) The fraction representing boys among the total students (ii) The fraction representing girls among the total students (iii) check that the sum of two fractions in (i) and (ii) is 1. 11.4.2018