Using Common Math Procedures

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After reading this lesson, you'll be more familiar with some very common math procedures you need to use every time you do math. You'll learn what they are and how to use them.

Order of Operations

The first math procedure we'll talk about is the order of operations. This rule tells you in what order you should perform your operations if you have several in your problem. For example, if you have 2 + 3 * 5, the order of operations tells you to first multiply before adding. The order of operations tells you that you need to work out your math problems in this order:

1: Parentheses
2: Exponents
3: Multiplication
4: Division
5: Addition
6: Subtraction

So, according to the order of operations, you'll first work inside any parentheses you see, then comes exponents, followed by multiplication and division. Last comes addition and subtraction. Everything is worked from left to right. A good way to remember your order of operations is to remember the acronym PEMDAS along with the phrase Please Excuse My Dear Aunt Sally. If you can remember the first letter of each word and the phrase, then you'll be able to remember the order.

So if you see 2 * (4 + 3), you'll perform the addition inside the parentheses first. Then you go ahead and multiply. Your answer is 2 * 7 = 14. If you didn't follow your order of operations, your answer would be 8 + 3 = 11, totally different. Remember, if you have parentheses and the inside of your parentheses has various math operations, then you'll need to follow the order of operations inside the parentheses as well.

Adding and Subtracting

When it comes to adding and subtracting your numbers, you also have to follow the procedures for these two operations. For addition, you add up your numbers from left to right. Once you get familiar with addition, you'll learn that addition also has the property where you can add up your numbers in any order and you'll still get the same answer. For example 1 + 3 + 2 is the same as 2 + 1 + 3.

For subtraction, you always subtract the number to the right of the subtraction symbol from the number to the left of the subtraction symbol. Subtraction means to take away. So 9 - 4 means you subtract or take away the 4 from the 9. Also, if the number you are subtracting is larger than the first number, then your answer will be negative. For example 4 - 9 = -5. Subtraction, unlike addition, must be done in order. You cannot go out of order or you'll get a different wrong answer.

Multiplication and Division

Your multiplication and division operations also have procedures you need to follow. Multiplication can be likened to your addition in that you multiply from left to right and you can multiply your numbers in any order. For example 2 * 3 * 4 is the same as 3 * 4 * 2. Both equal 24. Multiplication tells you how many groups of a certain number you have. 3 * 2 says you have three groups of 2. 4 * 6 says you have four groups of 6. Adding up all your groups gives you the answer.

Division can be likened to subtraction in that you always divide by the number to the right of the division symbol. Also, division, like subtraction, must be done in order. Unlike multiplication, if you go out of order with division, your answer will be different. For example 12 / 2 = 6 but 2 / 12 is equal to 1 / 6 or 0.167. Very different answers. Division tells you how many of the second number go into the first number. 12 / 2 = 6 says that 2 goes into 12 six times. In other words, you can separate 12 cookies into 2 groups of 6.

Fractions

Fractions are not whole numbers. They are part of a whole. For example 1/4 is a quarter of a whole. When you get 1/4 of a pie, you get a quarter of the whole pie. They have to cut the slice out of a whole pie. When working with fractions, you also have procedures to follow.

Before adding or subtracting fractions, you have to make sure that all your fractions have the same denominator (the denominator is the bottom of the fraction; the numerator is at the top). For example, to add 1/2 + 3/4, you have to make sure both have a common denominator. To do this, you'll need to figure out the least common denominator by finding a multiple that both have in common. In this case it is 4. You can multiply the 2 to get to a 4. Since you have to multiply the 2 to get to a 4, you also have to multiply the top, so your problem now is 2/4 + 3/4. Now you can go ahead and add just the numerator together to get 5/4. You follow the same steps for subtraction and you subtract just the numerator.

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