Substitution and evaluating expressions
Part 2
In math, equations can be written in many different forms. Just like in real life how we have synonyms, math has something similar called equivalent expressions. Equivalent expressions are written differently, but they have the same value. For example, 3x + 4x = 7x. Our goal is to reduce these equations to their smallest form possible. So, instead of writing 3x + 4x, we can just write 7x.
The main thing to remember when reducing or simplifying the expression is that like terms go together. 5x + 3x = 8x, but 5 + 3 =8. Finally, 5x + 3 simply equals 5x + 3.
This rule is essentially the same during multiplication, but it looks different. For example, take 5 times 5x. We multiply 5 by the coefficient of x, which is 5, to get 25x.
At the same time, you should always remember to multiply across the parenthesis. For example, 5(3x+4) equals 15x+20. Make sure you multiply the outside number across everything in the parenthesis. While this may seem easy, many students lose points over forgetting this exact step.
Finally, you need to use the order of operations or PEMDAS. PEMDAS is how math is done. In equation 6(5+1), how do you know what to do first? This problem is exactly what PEMDAS helps to solve. Check out this dropdown menu below to see how you can solve math problems in the correct order.
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.
Now, let's test your knowledge of PEMDAS. Answer these questions below to test your knowledge.
Questions
What is the first step of simplifying this problem: 4x+6-4(3x+2)
Choose 1 answer
What is the next step in simplifying this problem: 4x+6-12x+8
Choose 1 answer
SWhat is the next step in simplifying this problem: -8x+6+8
Choose 1 answer
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