Writing A Fraction in its simplest Form :
A fraction is in its simplest Form when it's Numerator and denominator have no common factors other than 1.
Fractions such as ¹/7,³/5,⁵/9 are All fractions in their simplest Form.
In ¹/7, there is no common factors of 1 and 7 (except 1). likewise,the only common factors of 3 and 5 in ³/5 is 1 and of 5 and 9 in ⁵/9 is 1.
Example: express fraction ⁶/8 in their simplest Form.
Solution:
Step 1 - find the factors of Numerator 6
The factors are 1,2,3,6.
Step 2 - find the factors of denominator 8
The factors are 1,2,4,8.
Step 3 - find the common factor of 6 and 8
The common factor is 2.
Step 4 - devide both (Numerator 6 and denominator 8) by the common
Factor 2.
Step 5 - We find 6÷2=3 and 8÷2=4.
Step 6 - now check the common factor of 3 and 4 there is no common factor except 1.
Now we can write ³/4 is the simplest Form of ⁶/8.
Comparing Fractions:
Comparing Fractions with the like Denominators :
Note - if two or more fractions have the same denominator, the fraction with the greater Numerator is the greatest number and the small Numerator ie the smallest number.
Example: compair the Fractions ⁶/13,⁸/13.
Solution:
Step 1 - take note the denominators (13) is same of all fractions.
Step 2 - now see the Numerators we can see that 8 is greater than 3.
So we can express fractions ⁶/13<⁸/13. The fraction ⁸/13 is greater than ³/13.
Comparing Fractions with unlike denominators :
First we talk about what is "unlike denominators" mean?
Fractions have denominators are not same called unlike denominators.
Example: ¹/3,²/5.
Solution:
Let's comparing by the LCM (lowest common factor) mathod.
Step 1- find the LCM of denominators 3 and 5.
Step 2- the LCM is 3×5=15.
Step 3- in fraction ¹/3 multiply by 5 separately in Numerator and denominator we got ⁵/15.
Step 4- in fraction ²/5 multiply by 3 separately in Numerator and denominator we got ⁶/15.
Step 5- now we find that denominators are same for both fractions ⁵/15,⁶/15.
Since, ⁶/15>⁵/15, therefore, ²/5>¹/3.
Ordering fractions:
Now that we know how to compare fractions, we can order them in any order increasing or decreasing.
Example: Arrange the Fractions ³/8,⁵/12,³/4 in increasing order.
Solution:
Step 1- find the LCM of the denominators 8,12 and 4. The LCM is 24.
Step 2- find the equivalent fractions with denominator 24.
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Step 3- Compare the equivalent fractions: 19/24,10/24 and 18/24. Arranging the Fractions in increasing order, 10/24<18/24<19/24, therefore 5/12<3/4<3/8.
We can also write the same Fractions in decreasing order as 3/8>3/4>3/8.
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