How to Simplify Math Expressions

Step-by-Step Guide

1. 1

   Step 1: Know the order of operations.

   When simplifying math expressions, you can't simply proceed from left to right, multiplying, adding, subtracting, and so on as you go.
   
   Some math operations take precedence over others and must be done first.
   
   In fact, doing operations out of order can give you the wrong answer.
   
   The order of operations is: terms in parentheses, exponents, multiplication, division, addition, and, finally, subtraction.
   
   A handy acronym you can use to remember this is "Please excuse my Dear Aunt Sally," or "PEMDAS".
   
   Note that, while basic knowledge of the order of operations makes it possible to simplify most basic expressions, specialized techniques are needed to simplify many variable expressions, including nearly all polynomials.
   
   See Method Two below for more information.
2. 2

   Step 2: Start by solving all of the terms in parentheses.

   In math, parentheses indicate that the terms inside should be calculated separately from the surrounding expression.
   
   Regardless of the operations being performed within them, be sure to tackle the terms in parentheses as your first act when you attempt to simplify an expression.
   
   Note that, however, within each pair of parentheses, the order of operations still applies.
   
   For instance, within parentheses, you should multiply before you add, subtract, etc.
   
   As an example, let's try to simplify the expression 2x + 4(5 + 2) + 32
   - (3 + 4/2).
   
   In this expression, we would solve the terms in parentheses, 5 + 2 and 3 + 4/2, first. 5 + 2 =
   7. 3 + 4/2 = 3 + 2 =
   5.
   
   The second parenthetical term simplifies to 5 because, owing to the order of operations, we divide 4/2 as our first act inside the parentheses.
   
   If we simply went from left to right, we might instead add 3 and 4 first, then divide by 2, giving the incorrect answer of 7/2.
   
   Note
   - if there are multiple parentheses nested inside one another, solve the innermost terms first, than the second-innermost, and so on. , After tackling parentheses, next, solve your expression's exponents.
   
   This is easy to remember because, in exponents, the base number and the power are positioned right next to each other.
   
   Find the answer to each exponent problem, then substitute the answers back into your equation in place of the exponents themselves.
   
   After dealing with the parentheses, our example expression is now 2x + 4(7) + 32
   -
   5.
   
   The only exponent in our example is 32, which equals
   9.
   
   Add this back into the equation in the place of 32 to get 2x + 4(7) + 9
   -
   5. , Next, perform any necessary multiplication in your expression.
   
   Remember that multiplication can be written several ways.
   
   A × symbol, a dot, or an asterisk are all ways to show multiplication.
   
   However, a number hugging a parentheses or a variable (like 4(x)) also denotes multiplication.
   
   There are two instances of multiplication in our problem: 2x (2x is 2 × x) and 4(7).
   
   We don't know the value of x, so let's leave 2x as it is.. 4(7) = 4 × 7 =
   28.
   
   We can rewrite our equation as 2x + 28 + 9
   -
   5. , As you search for division problems in your expression, keep in mind that, like multiplication, division can be written multiple ways.
   
   The simple ÷ symbol is one, but also remember that slashes and bars in a fraction (like 3/4, for instance) signify division.
   
   Because we already solved a division problem (4/2) when we tackled the terms in parentheses, our example no longer has any division in it, so we will skip this step.
   
   This brings up an important point
   - you don't have to perform every operation in the PEMDAS acronym when simplifying an expression, just the ones that are present in your problem. , Next, perform any addition problems in your expression.
   
   You can simply proceed from left to right through your expression, but you may find it easiest to add numbers that combine in simple, manageable ways first.
   
   For instance, in the expression 49 + 29 + 51 +71, it's easier to add 49 + 51 = 100, 29 + 71 = 100, and 100 + 100 = 200, rather than 49 + 29 = 78, 78 + 51 = 129, and 129 + 71 =
   200.
   
   Our example expression has been partially simplified to "2x + 28 + 9
   - 5".
   
   Now, we must add what we can
   - let's look at each addition problem from left to right.
   
   We can't add 2x and 28 because we don't know the value of x, so let's skip it. 28 + 9 = 37, so let's rewrite or expression as "2x + 37
   - 5". , The very last step in PEMDAS is subtraction.
   
   Proceed through your problem, solving any remaining subtraction problems.
   
   You may address the addition of negative numbers in this step, or in the same step as the normal addition problems
   - it won't effect your answer..
   
   In our expression, "2x + 37
   - 5"
   
   there is only one subtraction problem. 37
   - 5 = 32 , After proceeding through the order of operations, you should be left with your expression in simplest terms.
   
   However, if your expression contains one or more variables, understand that the variable terms will remain largely untouched.
   
   Simplifying variable expressions requires you to find the values of your variables or to use specialized techniques to simplify the expression (see below).
   
   Our final answer is "2x + 32".
   
   We can't address this final addition problem until we know the value of x, but when we do, this expression will be much easier to solve than our initial lengthy expression.
3. 3

   Step 3: Solve the exponents.

4. 4

   Step 4: Solve the multiplication problems in your expression.

5. 5

   Step 5: Move on to division.

6. 6

   Step 6: Subtract.

7. 7

   Step 7: Review your expression.

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