Helpful Tools for Calculus, Chapter 0: Numbers, Notations and Notes
Previous Section: 0.5 Fractions and Decimals
Fractions are so common that is very important to know how to use them in algebra. This section will review how to add, subtract, multiply, divide and solve fractions.
Adding and Subtracting Fractions
In order to add or subtract two fractions they need to be converted to have the same denominator first. Generally this is taught by calculating the lowest common multiples of both denominators then multiplying by the other factor of that lowest common multiple for each fraction. An alternate method is what I like to call “Moth Method.”
To add two fractions with Moth Method we do the following:
Cross-multiply the diagonals and place the answers on top, keeping the operation:
Then multiply the denominators together:
Place the diagonals on top and the denominator on the bottom, and you’re done!
Just simplify as needed!
This is referred to as Moth Method (and by others as the Butterfly Method) because if you draw it out, it looks like this:
Here’s a moth to compare:
Here are a few examples:
Multiplying and Dividing Fractions
When multiplying fractions do it straight across. The top and bottom don’t interact at all.
Here are a few examples:
To divide fractions, there are a couple of things to keep track of. First, if you are dividing fractions, it is helpful to write each part of the larger fraction as a fraction and write the smaller fractions diagonally.
Use “Keep it, Change it, Flip it” to solve the resulting problem. “Keep” the top fraction. “Change” the sign to multiplication. “Flip” the bottom fraction.
As another example, let’s divide the following:
Fractions and Exponents
When raising a fraction to an exponent (or doing a root) we can distribute the operation to each part of the fraction.
As some examples:
Review
