Fractions are simple but can be complicated at times, there are rules to guide us at these difficult times and they make things easy. The most useful is the lowest common denominator, this rule combines fractions, makes them one and back to a simple equation or expression.
You could be expected to add, subtract, divide or multiply a fraction in an expression or be required to solve for an unknown variable in an equation that involves fractions.
How to find lowest common denominator (LCD)?
The number below the division line is the denominator; yes, that one below numerator. It is also an imaginary 1 below any number, that means any number that is not a fraction has a denominator of 1. To find LCD, multiply all the denominators together; just like that and there you have it. However, if the denominators are the same you don’t multiply them, multiply only the different ones. The LCD is the common factor between the factors of all the denominators.
If the denominators are 2, 3 and 2; the LCD is 6. That being 2x3 and we won’t multiply by the third denominator because it is the same as the first. Factors of 2 are 2,4,6; factors of 3 are 3,6,9;… the lowest common factor is 6, that being the lowest common denominator as the name goes.
If the denominators are all the same, the LCD is that number. In this case we don’t multiply because that number is already a lowest common factor.
Addition of fractions:
When we add fractions, two three or more; the number one thing to look for is the lowest common denominator. Once we have the LCD we then:
- Draw a long enough division line and put your LCD under the line
- Multiply each numerator by the number of times it divides the LCD (i.e. 2 divides 6 three times, therefore 2x3 will be the first numerator)
- Do these to all the numerators and separate them with the given sign, addition.
- Add the numerators and divide them with that LCD
- Then simplify the fraction
There you have it, it can’t be any harder but could be simpler. Maths is only hard if you let it be, if you want it to be simple you make it simple.
Subtraction of fractions:
What then when we subtract these fractions? Once again, the LCD is our very good friend, look for LCD and do the very same thing you do when you add the fractions. The only difference now is that you will separate the numerators in step 3 above with a subtraction sing instead of addition.
Subtraction and addition can also be put in one expression or equation, on this case you do exactly what the examiner did, mix the signs. This means in step 3 above you will separate the numerators with the signs that the examiner separated the fractions.
Equations with fractions:
Remember this always: when a negative jump an equal sign it becomes what? Yes, Positive. And positive becomes negative.
- In an equation with fractions you look for LCD once again, don’t get tired of this guy (LCD).
- Then multiply each factor by that LCD
These two simple steps will land you in an equation with no LCD and you deal with the equation, I separately detail dealing with equations with unknow variables in a separate blog.
Division and multiplication of fractions:
These are very good friends and they made math simple by their long-made friendship; when you divide you simply multiply, that’s it.
When a fraction divides another fraction
- Switch the denominator and the numerator of the dividing fraction (i.e. the second fraction)
- And then multiply the fractions.
When a fraction multiplies the other
- Multiply the numerator with the other numerator and that becomes your new numerator
- Multiply the denominator with what? With the other denominator of cause. And there you have your new denominator.
- This is a straight-line relationship of multiplication.
- Then solve for the unknown variable.
Operating Disclaimer:
This blog post is not the first step towards learning the concepts of math but the coupling step to ease the use of your study guide and other study material. Read it over and over again to keep the concepts at the back of your head. Math is a subject of rules; know the rules, be able to duplicate them on a blank paper and go fetch your distinction.