Order of Operations with Fractions

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  • 0:04 Why Order Matters
  • 1:31 Some Practice
  • 2:57 Lesson Summary
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Lesson Transcript
Instructor: Mark Boster
Have you ever tried to put your socks on after putting on your shoes? It doesn't work does it? In math, there is also a certain order in which equations have to be solved to get the correct answer. In this lesson, you will learn this important order of operations.

Why Order Matters

Matter, really, does, what in order go you it? Wait, none of that made any sense! Let's put that sentence in order! 'Does it really matter what order you go in?' Clearly, of course it does! Try to eat a banana before you peel it or a watermelon before you cut it. Well, order really does matter when adding, subtracting, multiplying, or dividing fractions.

Just like we put our socks on before our shoes, when solving equations, even ones that contain fractions, order matters. Look at Equation 1 below. You can see it does matter in what order you solve the equation.

Example 1

When it was solved the first time, the multiplication was done before the addition. The second time it was solved, addition was done before multiplication! So what order should you go in?

Just like when you are solving equations with whole numbers, solving equations with fractions has the same order of operations. The order of operations is the order in which you solve the problem. If numbers are in parentheses, you do them first. Second, you solve for any numbers with exponents. Then, you go from left to right and do the multiplication and division. Finally, you go back and do the addition and subtraction - again, from left to right.

Sounds like a lot, right? Well, there is a very popular mnemonic device to help you remember the order of operations: PEMDAS (Please Excuse My Dear Aunt Sally) helps us remember:

P - Parentheses

E - Exponents

M & D - Multiplication and Division (left to right)

A & S - Addition and Subtraction (left to right)

Some Practice

How about trying

OOO with fractions

There is both addition and multiplication in this equation, so what's the first step? Remember your PEMDAS.

There are no parentheses or exponents, so multiplication comes first. As we can see:



So now you have the first part done.


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