Category : 4th Class
LEARNING OBJECTIVES
This lesson will help you to:—
Real Life Examples
Sharing food is a good way to introduce various concepts about fractions. For example, using a chocolate bar and dividing it into pieces.
Measurements during baking uses fractions such as one fo0urth of a cup of milk or half a spoonful of sugar etc.
QUICK CONCEPT REVIEW
Whole Number: Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5... (and so on).They're not fractions, they are not decimals, they are simply whole numbers.
No Fractions!
Fraction: A fraction is a part of a whole.
Fraction= Numerator / Denominator.
TYPES OF FRACTION
There are three types of fraction:
Mixed Fractions
\[\begin{matrix}
Proper Fraction |
Larger (or equal) \[\to \] 9 smaller \[\to \] 5 (or equal) |
\[2\frac{1}{3}\]
Mixed Fraction |
Numerator: The upper part of fraction that represents the number of parts you have.
Denominator: The lower part of fraction that represents the number of parts the whole is divided into.
Half (1/2)
One-Fourth (1/4)
Two-third (2/ 3)
Three-fourth (3/4)
Equivalence:
Some fractions may look different, but are really the same, for example:
Amazing Facts
The word “fraction” originates from the Latin word, “fractus”, which means broken.
Only improper fractions can be converted into mixed numbers.
The bricks that were used to build the great bath Indus valley civilization were in perfect 4 : 2 : 1 ratio.
=1 + 3/4 = 1 3/4 = 7/4
Whole Number\[\text{2}\frac{\text{1}}{\text{3}}_{\text{Denominator}}^{\text{Narrator}}\]
Historical Preview
Fractions were firstly used in the Indus Valley civilization. Followed by the Egyptians and the Greeks.
The Egyptians wrote numbers (based on tens) alongside pictures called hieroglyphs.
For example: 1/3 + 1/5 would be represented as shown below:
Notice the man’s feet is pointing towards the direction of writing (from left to right). When the feet pointing toward the direction of writing means add. Otherwise, it means subtract. In this case, it is pointing towards the direction of writing.
Notice also that there is a shape that looks like an open mouth (the ellipse). It refers to a fraction.
Mixed Fractions
Ex. 1 2/3, 2 3/5 etc.
CONVERTING IMPROPER FRACTIONS TO MIXED FRACTIONS
To convert an improper fraction to a mixed fraction, follow these steps:
Addition and Subtraction of Fractions
Addition/Subtraction when the denominator is same: You can add/subtract fractions easily if the bottom number (the denominator) is the same. Example:
5/8 + 1/8 = 6/8 = 3/4
Addition/Subtraction when the denominator is different: When the denominator is not same, then we need to make the denominator same. The denominator can be made same by the following two methods:
Common Denominator: This method involves multiplying the given denominators together.
Example: 1/3 + 1/6 =?
Multiplying the current denominators 3 and 6 we get,\[3\times 6=18\]. Now instead of having 3 or 6 totals, we will have 18.
Thus, 6/18 + 3/18 = 9/18
Least Common Denominator: In the above example, 18 is a relatively larger number. Instead of using the common denominator way, we can also opt for least common denominator.
Here is how to find out;
1/3 List the multiples of 3: 3, 6, 9 , 12, 15, 18, 21.....
1/6 List the multiples of 6: 6, 12, 18, 24, 30, 36......
Then find the smallest number that is the same. The answer is 6, and that is the least common denominator.
The question now looks like:
2/6 +176 = 3/6
Thus the steps followed are:
MULTIPLICATION OF FRACTIONS
There are 3 simple steps to multiply fractions
DIVISION OF FRACTIONS
There, are 3 simple steps to divide fractions;
Misconcept/Concept
Misconcept: The fractions with numerator other than 1 are greater than 1.
Concept: You can’t have a fraction that is bigger than one.
Misconcept: The bigger the number on the bottom, the bigger the fraction.
Concept: This is not true. The smaller the number on the denominator, the bigger will be the fraction. For example: 1/2 is bigger than 1/6.
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