Fractions

 Mind Maps

Class V - maths: Fractions
Q) Which fraction has the numerator less than the denominator?

Q) Which fraction has the numerator greater than the denominator?

Q) Which fraction have the same denominators?

Q) What is the reciprocal of 0?

Q) Which fraction is a combination of a whole number and a proper fraction?

Q) What is the reciprocal of 4/5?

Q) What fraction of Rs 1 is 50 paise is?

Q) Reciprocal of 0 is?

Q) An expression that indicates the quotient of two quantities is called a?

Q) The below image represents which Fraction? Q) Compare the fraction 4/6 and 3/4 with <, >, +?

Q) What fraction of Rs 1 is 50 paise is?

Q) Multiplicative inverse of 7/9 is?

Q) Compare the fraction 3/8 and 1/8?

Q) Subtract 1/2 from 5/8?

Q) Write 1/4, 2/5 and 3/8 fractions in ascending order?

Q) Write the 2/3, 3/5 and 3/4 in descending order?

Q) What is multiplication of fractions?

Q) What is fractions?

Q) Compare the fractions 5/8 and 3/8?

Q) Subtract 3/4 from 7/8?

Q) Add the mixed numbers 2 3/4 and 1 5/8?

Q) If each bag weights 1/2 kg, what would be the weight of 8 bags?

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?

Q) Find the value of (19/6) ÷ 8 ?

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?

Q) What is Division Of Fractions and give an example?

Q) What are the properties of addition and subtraction?

Q) What is comparing and ordering fractions and give an example?

Q) What is fractions and give an example?

Q) Compare the fractions 2/3 and 3/4? And Compare the fractions 7/6 and 5/3?

Q) Multiply 6/5 by 10?

FRACTIONS

Definition

"An expression that indicates the quotient of two quantities is called a fraction"

Example: • A fraction represents equal part of a whole

Example: • A proper fraction has the numerator less than the denominator.

Example: • An improper fractionhas the numerator greater than the denominator

Example: • A mixed fraction is a combination of a whole number and a proper fraction.

Example: • Like fractions have the same denominators

Example: • 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 AND ORDERING FRACTIONS

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:

1. By cross multiplication.
2. The side which has the bigger product has the bigger fraction.
3. By converting unlike fractions into like fractions.

Example:

• a) Compare the fractions 2/3 and 3/4
• Comparing the fractions by cross multiplication.
• Solution:

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. • b) Compare the fractions 7/6 and 5/3.
• 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.

• c) Arrange the following fractions into ascending and descending order.
• 3/4 , 2/3 and 5/6.

Solution:

• Find the LCM of the denominators by the division method.
• So, LCM = 2 ⨯2 ⨯3 = 12.

• Write equivalent fractions.
• 2/3 ⨯4/4 = 8/12 ;
3/4 ⨯3/3= 9/12 ;
5/6 ⨯2/2 = 10/12.

• Compare the numerators and write the fractions in order:
• 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:

Solution:

• We first find the LCM of the denominators

• So,LCM of 9 and 6 = 18.

• Write equivalent fractions with LCM as the denominator.
• 7/9 ⨯2/2 = 14/18 and 5/6 ⨯3/3 = 15/18.

• Add numerators and changed to a mixed number.

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.
• 7/8-6/8 = 1/8.

Addition And Subtraction Of Mixed Numbers

Same steps are to be followed to add or subtract mixed numbers

Example1:

Solution:

Method:1

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

=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 3/4-3 1/2 = 27/4-7/2.
• Find the LCM of the denominators.
• LCM of 4 and 2 is 4.

• Find equivalent fractions.
• 27/4 ⨯1/1 = 27/4 -7/2 ⨯2/2 = 14/4

• Subtract the numerators.
• 27/4-14/4 = 13/4.

• Write as mixed number.
• 33÷4=3 1/4

PROPERTIES OF ADDITION AND SUBTRACTION OF FRACTIONS

1. Zero Property:
2. The sum and difference of zero and a fraction is the number itself.

Example :

2/3 + 0 = 2/3 and 2/3-0 = 2/3.

3. Commutative Property:
4. 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 4/5-2/8 ≠2/8-4/5.

5. Associative Property:
6. 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 OF FRACTIONS

"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:   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.
• 6/5 ÷10/1

• Multiply the numerators.
• 6 ÷10 = 60.

• Multiply the denominators.
• 5 ÷1 = 5.

• Reduce the fraction, if needed.
• So, the required fraction is 60/5 = 12.

METHOD 2:

• Simplify the numerator with a denominator. Denominator 5 can divide the numerator 10.
• 6/5 ÷10 = 6/1 ÷2/1.

• Multiply the numerators.
• 6 ÷2 = 12.

• Multiply the denominators.
• 1 ÷1 = 1

• Simplify: 12/1 = 12.
• MULTIPLICATION OF A FRACTION BY A MIXED NUMBER

Example :

Multiply 3 4/9 by 5/6.

Solution:

• Change mixed numbers into improper fractions.
• 3 4/9 ÷ 5/6 = 31/9 ÷ 5/6

• 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.

155/54 = 2 47/54

DIVISION OF FRACTIONS

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 “⨯”.
• 7÷1/5 = 7/1 ⨯5/1.

• Multiply the numerators.
• 7 ⨯5 = 35.

• Multiply the denominators.
• 1 ⨯1 = 1.

• Simplify: 35/1 = 35.

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.
• 3 4/7 ÷ 5 = 25/7 ÷ 5

• 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,
• 25/7 ⨯1/5 = 5/7.

WORD PROBLEMS BASED ON FOUR FUNDAMENTAL OPERATIONS

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.

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.

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