In math, numbers come in many forms. And these many forms can be mathematically added up or subtracted from each others. Whole numbers should be easy to manage, but, how about manipulation of fractions? It may not be easy for some.
First, we need to clarify the name of the terms, for fraction, before we proceed.
Fraction is written as n / d, where the "n" is known as the NUMERATOR and the "d" is the DENOMINATOR. Note: "d" is below the dividing line.
Explanation of fraction representation:1/5 means one part of a whole (which is divided into 5 equal parts).
2/4 means two parts of a whole that consists of 4 equal parts.
In ratio term, 2/4 means the same as 1/2 regardless of physical size.
(Thinking of the cake as an example may helps).
Rule for Addition of Fraction: a / b + c / b = (a + c) / b <== same denominator.
When the denominators are the same, we can simply add the numerators together keeping the denominator as it is. Example: 1/4 + 2/4 = (1 + 2) / 4 = 3 / 4. This is simple.
How about when the denominators are different?
Example: 1 / 4 + 1 / 2 = ?
Tips: Make the denominator for both terms the same so that the rule for fraction addition can be applied.
In this case we have different denominators "4" and "2". We noticed that "2" is related to "4" by 2 times.
Therefore, we can intentionally multiply the second term denominator by 2, which gives us 2 x 2 = 4, and which matches the first term denominator.
But take note, by multiplying the second term denominator by 2, we also need to multiply the second term numerator by the same amount, that is, 2 also.
This is to ensure that we did not change the meaning for the second term 1/2. By multiplying the second term by 2/2, which is 1, we did not change anything since anything multiplied by 1 is still the same as original (in this case, 1/2). Make sense?
So the math example of above,1 / 4 + 1 / 2 becomes 1 / 4 + [(1 x 2) / (2 x 2)] = 1 /4 + 2 / 4 = 3 / 4.
Another example:(2 / 5) + (1 / 10) = [(2 x 2) / (5 x 2)] + 1 /10 = (4 / 10) + (1 / 10) ==> same denominator now!Answer: ( 4 + 1 ) / 10 = 5 / 10 = 1 / 2.
So, to be able to apply the rule of fraction addition, we simply make the denominators for all the terms the same.
This rule of fraction addition applies equally to fraction subtraction also.
Common mistakes made during fraction addition
(s / b) + (s / c ) is not equal to s / ( b + c ) !
This is a very common mistake students make. Only common denominator allows us to add the numerators. Common numerators does not qualify for simply addition of denominators. We need to make the denominators the same before we can add the numerators.
For more information about learning fraction and its implication, click this link.