Basic Concepts on Fraction
Fraction – is defined as a part of a whole. In some other books, it is defined as a number written in the form ab , where “a” and “b” are numbers and “b” is not equal to zero.
Basic Parts of a Fraction
* Numerator – the number above tells how many parts are taken.
* Denominator – the number below tells how many equal parts the whole is divided.
* Fraction bar – line that separates the two numbers. It also indicates division.
There are several kinds of fraction and they are grouped into two: INDIVIDUAL FRACTIONS and GROUP FRACTIONS
Individual Fractions are taken as one. They are—
1. Proper Fraction
- a fraction whose numerator is less than the denominator
34 , 78 , 57
2. Improper Fraction
- a fraction whose numerator is greater than or equal to the denominator.
43 , 78 , 57
3. Mixed Fraction
- combination of a whole number and a fraction.
4 29 , 15 137 , 12 910
4. Unit Fraction
- proper fraction whose numerator is always 1. Examples:
111 , 16 , 15
Group Fraction – a fraction taken by group or set of fraction. 1. Similar Fraction
- group or set of fraction with similar denominators.
612 , 812 , 912 , 412
2. Dissimilar Fraction
- group or set of fraction with different denominators.
3. Equivalent Fraction
- fractions which is equal in value.
23 = 812
Changing Improper Fraction to Mixed Number, to Whole Number, and Vice Versa a. Improper Fraction to Mixed Fraction – divide the numerator by the denominator, the quotient will be the whole number and the divisor will be the denominator.
94 = 49 = 2 14
b. Mixed Fraction to Improper Fraction -- multiply the denominator into the whole number then add the product to the numerator. The Sum will be the numerator and copy the same denominator.
7 45 = 5 x 7 + 14 = 395
Reducing and Simplifying Fraction
Reducing fractions to lowest term is just one way of simplifying fractions, To reduce a fraction to its lowest term, there are two steps that need to be followed. First, we must find the GCF of the numerator and denominator. Then, divide both by their GCF to obtain lowest term.
Example: What is the lowest term of 912 ?
First, find the GCF of 9 and 12.
Since the GCF of 9 and 12 is 3, divide each by 3.
9 12 ÷33= 34
Thus, the lowest term of 912 is 34
Changing Dissimilar Fractions to Similar Fractions
What is Least Common Denominator or LCD?
Least Common Denominator (LCD) is the name as LCM only the numbers here are used as denominators of fractions. The process of finding the LCD is the same as the process used in getting the LCM is used to make dissimilar fractions similar.
Example: Find the LCD of 23 and14.
Solution: To find the LCD of 23 and14, get the LCM of the denominators.
Since the LCM of 3 and 4 is 12; therefore, the LCD of 23 and 14 is 12.
Seeing that 23 and14 are dissimilar fractions, how can these be change to similar fractions? Given the fact that the LCD of these two fractions is 12, to make them similar, we have to –
1. Divide the LCD by the old denominators.
12÷3 = 4
12÷4 = 3
2. Multiply the quotients found by the numerators of the original fractions.
4 x 2 = 8
3 x 1 = 3
3. Write the products obtained as the new numerators and copy the LCD as the new Denominators.
23 = 812
Original or given fractions
New set of Fractions
14 = 312...
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