
Q) Which fraction has the numerator less than the denominator?
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Q) Which fraction has the numerator greater than the denominator?
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Q) Which fraction have the same denominators?
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Q) What is the reciprocal of 0?
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Q) Which fraction is a combination of a whole number and a proper fraction?
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Q) What is the reciprocal of 4/5?
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Q) What fraction of Rs 1 is 50 paise is?
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Q) Reciprocal of 0 is?
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Q) An expression that indicates the quotient of two quantities is called a?
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Q) The below image represents which Fraction?
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Q) Compare the fraction 4/6 and 3/4 with <, >, +?
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Q) What fraction of Rs 1 is 50 paise is?
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Q) Multiplicative inverse of 7/9 is?
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Q) Compare the fraction 3/8 and 1/8?
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Q) Subtract 1/2 from 5/8?
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Q) Write 1/4, 2/5 and 3/8 fractions in ascending order?
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Q) Write the 2/3, 3/5 and 3/4 in descending order?
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Q) Add 1/8 and 7/12?
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Q) What is multiplication of fractions?
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Q) What is fractions?
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Q) Compare the fractions 5/8 and 3/8?
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Q) Subtract 3/4 from 7/8?
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Q) Add the mixed numbers 2 3/4 and 1 5/8?
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Q) If each bag weights 1/2 kg, what would be the weight of 8 bags?
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Q) Naresh was asked to study for 4 hours. He only studied for 3/4 of that time. How much time did he spend on study?
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Q) Find the value of (19/6) ÷ 8 ?
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Q) Meghana bought 8 1/ 2 kgs of sugar. If the cost of 1 kg of sugar is Rs 32 1/2, find the total cost of sugar?
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Q) What is Division Of Fractions and give an example?
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Q) What are the properties of addition and subtraction?
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Q) What is comparing and ordering fractions and give an example?
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Q) What is fractions and give an example?
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Q) Compare the fractions 2/3 and 3/4? And Compare the fractions 7/6 and 5/3?
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Q) Multiply 6/5 by 10?
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Definition
"An expression that indicates the quotient of two quantities is called a fraction"
Example:Some facts about fractions:
 A fraction represents equal part of a whole
 A proper fraction has the numerator less than the denominator.
 An improper fractionhas the numerator greater than the denominator
 A mixed fraction is a combination of a whole number and a proper fraction.
 Like fractions have the same denominators
 Unlike fractions have different denominators Example:
 Unit fractions have only digit 1 as the numerator. Example:
 Equivalent fractions have the same value even though the numerators and denominators are different Example:
 A fraction can also represent part of a set.
Comparing Like Fractions
Like fractions are easy to compare, as they have same denominators. Only the numerators are compared.
Example:Compare the fractions 5/8 and 3/8.
Solution:Here, the denominators are same.
Numerator 5>3.
So, 5/8>3/8.
Comparing Unlike Fractions
When the denominators are different, we compare the fractions in two ways:
 By cross multiplication.
 The side which has the bigger product has the bigger fraction.
 By converting unlike fractions into like fractions.
 a) Compare the fractions 2/3 and 3/4
 Comparing the fractions by cross multiplication. Solution:
 b) Compare the fractions 7/6 and 5/3.
 c) Arrange the following fractions into ascending and descending order.
On cross multiplying the two fractions, we get:
Cross product = 2 ⨯4 = 8 and 3 ⨯3 = 9
Since, 8 <9,
So, we can say that 2/3 <3/4.
Comparing the fractions by converting them into like fractions.
Solution:Converting the given fractions into like fractions, we get:
7/6 = 7/6 ⨯1/1 = 7/6 ;
5/3 = 5/3 ⨯ 2/2 = 10/6
Since, the LCM of 3 and 6 is 6.
On comparing the numerators,
we get 10>7.
So, 7/6 <10/6 or 7/6 <5/3.
3/4 , 2/3 and 5/6.
Solution: Find the LCM of the denominators by the division method.
 Write equivalent fractions.
 Compare the numerators and write the fractions in order:
So, LCM = 2 ⨯2 ⨯3 = 12.
2/3 ⨯4/4 = 8/12 ;
3/4 ⨯3/3= 9/12 ;
5/6 ⨯2/2 = 10/12.
So, 8/12 < 9/12 < 10/12
Or
2/3 < 3/4 < 5/6
In ascending order: 2/3, 3/4, 5/6.
In descending order: 5/6, 3/4, 2/3.
Addition And Subtraction Of Unlike Fractions
In order to add or subtract unlike fractions i.e.,
Fractions with having different denominators,
we first convert the fractions into equivalent fractions with a common denominator
Example:
 Add 7/9 and 5/6.
Solution:
 We first find the LCM of the denominators
 Write equivalent fractions with LCM as the denominator.
 Add numerators and changed to a mixed number.
So,LCM of 9 and 6 = 18.
7/9 ⨯2/2 = 14/18 and 5/6 ⨯3/3 = 15/18.
So, 14/18 + 15/18 = 29/18 = 1 11/18
2)Subtract 3/4 from 7/8.
Solution:
 Find the LCM of the denominators.
 So, the LCM of 4 and 8 is 8.
 Write equivalent fractions with LCM as the denominator.
 7/8 ⨯1/1 = 7/8 and 3/4 ⨯2/2 = 6/8.
 Subtract the numerators.
 7/86/8 = 1/8.
Addition And Subtraction Of Mixed Numbers
Same steps are to be followed to add or subtract mixed numbers
Example1:
1) Add {(4/7)⨯3}+{(2/13)⨯5}
Solution:
Method:1
Add The Whole Numbers
solving the addition of mixed numbers
Find equivalent fractions with LCM as the denominator
L.C.M of of the denominators
=13⨯7=91
={(4/7⨯3+{(12/13⨯5)}
=[{(12÷7)⨯91}+{(2÷13)⨯91)⨯5)}]÷91
=[{(12⨯13)+(14⨯5)}]÷91
={[{156+70}]÷91}=[226÷91]
=[226÷91]
=2.4835
Method:2
Change To Improper Fractions
2) Add 9 2÷3+4 5÷7
=9 2÷3+4 5÷7
={[(9⨯3+2)÷3]+[(4⨯7+5)]÷7}
={[(29÷3)+(33÷7)]}
L.C.M. Of Denominators
=7⨯3
=21
={[(29÷3)⨯21]+[(33÷7)⨯21]}÷21
={{[29⨯7]+[33⨯3]}÷21}
={[203+99]÷21]}
={302÷21}
=14.380
3.Subtract 3 1/2 from 63/4.
Solution:
 Change the mixed fraction into improper fraction. 6 3/43 1/2 = 27/47/2.
 Find the LCM of the denominators.
 Find equivalent fractions.
 Subtract the numerators.
 Write as mixed number.
LCM of 4 and 2 is 4.
27/4 ⨯1/1 = 27/4 7/2 ⨯2/2 = 14/4
27/414/4 = 13/4.
33÷4=3 1/4
 Zero Property:
 Commutative Property:
 Associative Property:
The sum and difference of zero and a fraction is the number itself.
Example :
2/3 + 0 = 2/3 and 2/30 = 2/3.
The sum stays the same when the order of addends is changed in addition, but not in subtraction.
Example :
4/5 + 2/8 = 2/8 + 4/5 but 4/52/8 ≠2/84/5.
The sum stays the same when the grouping of the addends is changed, but not in subtraction.
Example :
(6/9 + 2/5) + 3/8 = 6/9 + (2/5 + 3/8).
Multiplication is repeated addition.
"Multiplication of fractions can also be repeated addition".
Example :
A pizza is divided equally among friends, if the fraction is 1/8,each piece of pizza, can 8 of the friends share equally.
Solution:
Repeated addition:
We can also multiply, 1/8 by 8 to find out 1/8 ÷8 = 1/8 ÷8/1 = 8/8 = 1.
So, each of the friends can share the pizza equally.
Multiplication Of A Fraction By A Whole Number
Example:
Multiply 6/5 by 10.
Solution:
METHOD1:
 The whole number is written as a fraction by placing 1 as the denominator.
 Multiply the numerators.
 Multiply the denominators.
 Reduce the fraction, if needed.
6/5 ÷10/1
6 ÷10 = 60.
5 ÷1 = 5.
So, the required fraction is 60/5 = 12.
METHOD 2:
 Simplify the numerator with a denominator. Denominator 5 can divide the numerator 10.
 Multiply the numerators.
 Multiply the denominators.
 Simplify: 12/1 = 12.
 Change mixed numbers into improper fractions.
 Simplify numerators with denominators, if needed.
 Multiply the numerators: 31 ÷5 = 155
 Multiply the denominators: 9 ÷6 = 54.
 Write the fraction as a mixed number.
6/5 ÷10 = 6/1 ÷2/1.
6 ÷2 = 12.
1 ÷1 = 1
MULTIPLICATION OF A FRACTION BY A MIXED NUMBER
Example :
Multiply 3 4/9 by 5/6.
Solution:
3 4/9 ÷ 5/6 = 31/9 ÷ 5/6
155/54 = 2 47/54
Before we move on to division, let us understand the word reciprocal.
The reciprocal of a fraction is obtained by interchanging the numerator and the denominator i.e., by inverting the fraction.
In the fraction 5/9, its reciprocal is 9/5.
This is also called multiplicative inverse.
Let us take a look at some of the fraction and their reciprocals or multiplicative inverse.
Division Of Whole Numbers By A Fraction
Division By Using The Reciprocal
Example
Simplify 7÷1/5 (Dividend = 7 ; Divisor = 1/5 )
Solution:
 Change the divisor to its reciprocal and change the “÷” sign to “⨯”.
 Multiply the numerators.
 Multiply the denominators.
 Simplify: 35/1 = 35.
7÷1/5 = 7/1 ⨯5/1.
7 ⨯5 = 35.
1 ⨯1 = 1.
Division Of A Fraction By A Fraction
Example:
Simplify 10/14 ÷ 5/7.
Solution:
Here the divisor is 5/7 and the dividend is 10/14.
The divisor becomes the multiplicative inverse or the reciprocal and the division sign changes to multiplication sign.
So, 10/14 ÷ 5/7 = 10/14 ⨯7/5 = 2 ⨯1/ 2 ⨯1 = 1/1 = 1.
Division Of A Mixed Number
Example:
Simplify: 3 4/7 ÷ 5
Solution:
 Change into an improper fraction.
 Change the divisor to its reciprocal and the division sign to the multiplication sign. 25/7 ⨯1/5
 Multiply the numerators and denominators and simplify,
3 4/7 ÷ 5 = 25/7 ÷ 5
25/7 ⨯1/5 = 5/7.
Example:
a.How many baskets of fruits weighing 5/8 kg can be arranged from 70 kg baskets?
Solution:
Total weight of baskets = 70 kg
Weight of 1 basket = 5/8 kg.
So, number of baskets that can be arranged from 70 kg baskets =
= 70 ÷ 5/8
= 70 ⨯8/5
= 14 ⨯8
= 112.
So,112 baskets can be arranged.
b)The cost of one colour box is ₨13 1/4. Find the cost of 20 such colour boxes.
Solution:
Cost of 1 colour box=₨13 1/4 =₨53/4
So, cost of 10 colour boxes = 20 ⨯₨53/4
= 5 ⨯₨53
=₨265.