Unit 3


Numberical Expressions

Sometimes expressions may just look like some one mixed up numbers with the alphabet, but there is so much more than that! I think of it like solving a mystery. You use the numbers around the missing number, or exponent, to solve for the missing number. What many people forget to use the opposite operation wile solving an expression with a missing number. For example: X-45=50. Although this is a very easy equation, some people may subtract 45 from 50. Let's try this out! Some people may do 50-45. That would be 5, right? Could X=5? No! 5-45=-40. But that's another lesson. If you do it right, you would do the opposite operation. Let's try it now. 45+50=95. If X=95, let's try it. 95-45=50. Now let's try a harder one. 163+x=2,043. Well, The opposite operation is subtraction. So, 2,043-163=1,880. Let's plug it in 1,880=163=2,043. We got it!

Evaluating Expressions

Like I explained before, you have to do the opposite operation to find out the missing number. Another way to help you solve an expression is to simplify it. The way to do this is to combine like terms. This means anything with the same exponent, or any numbers with the same value. (As in the small number at the top right-hand corner of the number.) A great way to help solve the problem, and keep your work neat, is using parenthaseses! Using parentheses tells you what you've already done and what you need to work on. Here is a great game to help you with expressions. Just keep Kiwi happy! http://www.math-play.com/Equation-Game.html

Writing Expressions

What do you do if you see a problem on a test that looks like this: "Subtract 5x from 32 if x=2?" Well, 5x=10 because 2=x and 2x5=10. So it would be 32-10. This equals 22. Using the language used you can find out what operation is occurring. This video helps you to use vocabulary to help you solve expressions. http://learnzillion.com/lessons/138-write-word-problems-as-algebraic-expressions Here is a great game to play to test your knowledge about writing expressions! http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.html


Why is vocabulary important in math? Well, sometimes subjects have to mix to help you understand the standard. Do you the definition of sum, term, product, factor, quotient, and coefficient? Well, a sum is the answer to an addition problem. A term is just a number in a problem. A product is the answer to a multiplication problem. Factors are the terms (or numbers other than the product) in a multiplication problem. In 5x6=30. 5 and 6 are the factors while 30 is the product. A quotient is the answer to a division problem. A coefficient is the number used to multiply a number. For example 5x. "X" is the coefficient.

Order of Operations

Here is a great brainpop video to help you with order of operations. http://www.brainpop.com/math/numbersandoperations/orderofoperations/ http://www.brainpop.com/games/primarykrypto/

Many people know the order of operations as:

  • P(erenthases)
  • E(xponents)
  • M(ultiplication)
  • D(ivision)
  • A(ddition)
  • S(ubtraction)

I like to write it as:

  • P
  • E
  • MD
  • AS
This is because how other people write make you believe that multiplication comes before division and addition before subtraction, even though this isn't true. The rule actually is that you do parentheses, exponents, then either multiplication OR division. The same rule applies for addition and subtraction. This is a VERY important rule to remember.

The Distributive Property

The distributive property is pretty much distributing out a certain number. Example: 5(3+4). Instead of doing 3+4 and then multiply the sum by 5, you could multiply 3 by 5 and 4 by 5 first. 5x3=15 & 5x4=20. 15+20=35. Conclusion: 5(3+4)=35. This link explains the distributive property. http://www.coolmath.com/prealgebra/06-properties/05-properties-distributive-01.htm

Equivalent Expressions

The name of "equivalent expressions" explains what an equivalent expression is. Equivalent is another word for equal to. So two equivalent expressions have the same value, or are equal to each other. An example would be: 5(4+2)=3(6=4). Both of the final answers are 30. This means that these two expressions are equivalent. This video explains equivalent expressions. http://www.youtube.com/watch?v=6pOWe74WUwA