Introduction to equivalent expressions
Part 1
Equivalent means equaling the same. In math, just because an expression looks different than another does not mean that it necessarily is different. We can simplify an expression, and it can still be equal to the same value. For example, in real life, 2 groups of 3 cookies are the same as 6 cookies in value. Functions work the same way. For example, 2(4+3x) = 8+6x. Equivalent functions are easy as long as you remember a few key rules.
1. The first rule to remember is that like terms go together. For example, 3x + 5x = 8x. 5x + 5 = 5x + 5. However, 3 + 5 = 8. The one time we can combine both terms is in multiplication. In multiplication, we can multiply the number by the variable, or the coefficient, by the multiplies. So, 3 times 6x = 18x. 18x divided by 3 = 6x.
2. The next rule to remember is to always distribute to all of the numbers. A common mistake is to forget to multiply the number outside of the parenthesis by all of the numbers in the parenthesis. 3(6 + 2x) = 18 + 6x, not 18 + 2x. Every number in the parenthesis must be multiplied by the outside number.
Finally, you need to understand the order of how to solve these problems. How do you know in problem 5(3+1)-6 which part to do first? The answser is Pemdas or
P - Parenthesis
Math written in parenthesis is always done first. For example, in 5(3+2), we would solve 3+2 = 5, before multiplying that number by 5. Parenthesis can also include brackets or curly brackets. All PEMDAS rules also stay the same inside of the parenthesis.
E - Exponents
Exponents should always be done second. For example, in 5^2 * 3, we should solve 5^2 first.
M - Multiplication
Multiplication always comes third. However, it should be noted that it is on the same level as division. So, whichever comes first in the problem, multiplication or division, is what should be done as the third step.
D - Division
Division also always comes third. However, it is on the same level as multiplication. Divisions should be completed on the third step in whatever order it or multiplication occurs.
A - Addition
Addition comes last. Addition is on the same level as subtraction. In question 3+6(5), the answer is 33, since you multiply 6 and 5 first, then finally add.
S - Subtraction
Addition comes last. Addition is on the same level as subtraction. In question 3+6(5), the answer is 33, since you multiply 6 and 5 first, then finally add.
Click on each letter to see exactly what it means.
Remembering "PEMDAS" is extremely important in solving math problems. One great way to remember the acronym is "Please excuse my dear Aunt Sally."
One of the most important things you need to understand about "PEMDAS" is that all math needs to happen in that order. For example, in the problem 3x(5-2), we follow P first, which stands for parenthesis. So, we do 5-2 = 3. Then, we can skip E because we do not have any exponents. So, then we get to multiplication, which means that we multiply 3x by 3 to get 9x.
There are, however, a few exceptions to this rule. The "PEMDAS" acronym is not entirely true. Multiplication does not come before division, and addition does not come before subtraction. Division and multiplication are on an even plane, and the first to come up in a problem is the one you do first. The same is true for addition and subtraction. However, multiplication and division will always come before addition and subtraction. For example, take the problem 6/2 - 5 * 3. First er do 6/2, which gives us 3. Then, we do 5 * 3, which gives us 15. When we subtract the two numbers we get -12, so our final answer is -12.
Try some examples below.
Questions
Simplify 7x -4x + 3
Choose 1 answer
Simplify 5(3+2x):
Choose 1 answer
Solve 4x-6(5x+2):
Choose 1 answer
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