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Math: Basic Tutorials : Order of Operations
Order of Operations: sub-module 4 of 4 of math tutorials
It is important that every expression is simplified in a way that it always gives the same result. So if a given expression has multiple operations (multiplying, adding, etc.), how do we know which operation to do first? To eliminate this confusion, mathematicians developed a set of rules called the order of operations that define the order in which we simplify an expression. In this module, you will learn the order of operations and how to use it to simplify expressions.
Order of Operations
Order of Operations Video transcript - RTFExamples & Activity
Examples
Click on the titles below to view each example.
Simplify the expression open bracket 4 plus 3 close bracket times 6 divided by 2.
Line 1: Identify that there are brackets in the expression open bracket 4 plus 3 close bracket times 6 divided by 2.
Line 2: Simplify inside the brackets so the expression is 7 times 6 divided by 2
Line 3: Identify that there are no exponents in the expression.
Line 4: Identify that there is multiplication and division in the expression.
Line 5: Complete the multiplication first because we multiply and divide from left to right in the order they appear. The expression is 24 divided by 2.
Line 6: Divide so the answer is 21.
Simplify 5 plus 2 cubed plus 3 times open square brackets minus 3 times open brackets 4 minus 2 close brackets close square brackets.
Line 1: Identify that there are brackets in the expression 5 plus 2 cubed plus 3 times open square brackets minus 3 times open brackets 4 minus 2 close brackets close square brackets.
Line 2: Simplify the innermost brackets first so the expression is 5 plus 2 cubed plus 3 times open square brackets 6 minus 3 times 2 close square brackets.
Line 3: Continue to simply inside the square brackets by multiplying so the expression is 5 plus 2 cubed plus 3 times open square brackets 6 minus 6 close square brackets.
Line 4: Continue to simply inside the square brackets by subtracting so the expression is 5 plus 2 cubed plus 3 times 0.
Line 5: All of the brackets are no simplified, so we look for any exponents, and identify we have exponents in the expression.
Line 6: Simplify the exponent so the expression is 5 plus 8 plus 3 times 0.
Line 7: Look for multiplication and division next, and identify there is multiplication in the expression.
Line 8: Simplify the multiplication so the expression is 5 plus 8 plus 0.
Line 9: Look for addition and subtraction, and identify there is addition left in the expression.
Line 10: Add from left to right so the expression is 13 plus 0.
Line 11: Complete the last addition to get the answer of 13.
Simplify the expression with a numerator of 4 plus 8 over a denominator of 5 minus 3.
Line 1: Note that fraction bars act as grouping symbols, so the expressions in the numerator and denominator are treated as if they are in brackets. This means that the expression with a numerator of 4 plus 8 over a denominator of 5 minus 3 is the same as open bracket 4 plus 8 close bracket divided by open bracket 5 minus 3 close bracket.
Line 2: Simplify the expression in the numerator so the numerator is 12 and the denominator is 5 minus 3.
Line 3: Simplify the expression in the denominator so the numerator is 12 and the denominator is 2.
Line 4: Simplify the fraction 12 over 2, so the answer is 6.
Activity
Try this activity to test your skills. If you have trouble, check out the information in the module for help.
Summary and Worksheet
- Summary: Order of Operations - PDF - Opens in a new windowThis document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
- Worksheet: Order of Operations - PDF - Opens in a new windowThis document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.