Comparing and Ordering Fractions!!!

Hi, today we will be covering comparing and ordering fractions. First of all, what is this process? This process is or can be a few things. Sadly, you need another process in order for you to compare and order fractions. Specifically this process will be on how to make common denominators.

Here are ways to make common denominators

-multiplying both denominators 
-multiply/dividing numerator and the denominator
There are probably more but these are the methods I use

Multiplying both denominators

First of all, to get the common denominator using this method, you need to multiply both denominators together just like the title says. e.g. 

7/8   1/4                   
                       
4x8=32                    

Your new denominator is 32! Sadly, you're not done yet. You now have to multiply your numerators by the value which you used to multiply your denominators. e.g.

1    x 8          8                        7    x4             28
-            =     -                         -              =        -
4    x8          32                       8     x4             32

Multiplying/ dividing both the numerator and the Denominator

For this method, you only require to multiply/divide 1 of the fraction's numerator and denominator. e.g.

1 x2        2                2  divided by 2          1

-     =      -      or          -                           =      -

4  x2       8                8 divided by 2           4

Now that you know more about common denominators, we can begin the actual lesson!

 Comparing Fractions

First of all, comparing fractions is easy when you have the same denominator, but when there different it gets quite frustrating. Luckily, we have the common denominator method to help us! e.g.

Which is larger?  3/4   or   7/8   to turn 3/4 into a new fraction you multiply the numerator and denominator by 2 which makes 6/8. Turns out 7/8 is bigger!

ordering fractions 

Now to order fractions you need to make common denominators with all of them! but how? Well, look at the example and find out!

 1/4 1/2 2/6 2/3 All the denominators are factors of 12!!! So we need to make our denominator 12 using the second method listed! e.g.

1/4  4x3= 12   1x3=3  Our new fraction is 3/12!          1/2   2x6=12    1x6=6 our new fraction is 6/12

2/6  6x2=12    2x2=4   our new fraction is 4/12           2/3   3x4=12    2x4=8 our new fraction is 8/12

Now we can order them!!!

3/12 4/12 6/12 8/12  Don't forget to return them to their normal state!!

1/4, 2/6, 1/2, 2/3

Helpful videos!                                      Lowest Common Denominator!

                                                          Common Denominator By Justin Bieber LOL

       

Pattering: Variables, expressions, equations, coefficients, etc.

For pattering, you'll be using a lot of variables. What are variables? Variables are letters that represents a number.
Eg.1 If you had an equation like this: 5+7 You would replace the number(s) with a letter. Instead of 5+7, you could have x+7. x=5 or you could also have 5+y. In this case, y=7. You could also have x+y, meaning your x equals 5 and your y equals 7. You could choose whatever letters you want to represent a number, it does not always have to be an x or a y.
Variables could be used to represent whatever topic or idea the x and y axis has.
For patterning, you'll also be using expressions. What are expressions? An expression is a number sentence without an equal sign.
Eg.1 Instead of having 3+9=12, you'll only need to add, 3+9.
Another important word you need to remember are equations. What are equations? Equations are used to help show a number sentence. A number sentence is basically a math question that uses any type of math devices, such as multiplication, addition, subtraction, or division. These devices are used to help calculate or get the answer of a math question(number sentence). You would also have to add an equal sign =. An equation is the same thing as an expression but you have to add an equal sign with the answer of the math equation.
Eg.1 7+8=15 would be an equation because it uses a math symbol that is needed to complete a math equation. It has the addition sign + an it also has the equal sign =.
For expressions, a multiplication sentence(without the equal sign) is shown a different way.
Eg.1 Instead of 4x3, you could either show it as 4(3) or 3(4), it doesn't really matter what order you put it in. You could also put it as a coefficient.
If you are working with variables, you will need to use something called a  "coefficient". A coefficient is having a number go in front of a variable, this is used especially when you are multiplying, expressions, or equations.
Eg.1 6x3 is your expression. Let's say the 3 will be an x for our variable. We would have 6xx. This will get confusing because you don''t know if you're using a variable "x" or if you're using the multiplication sign. The rule to expressions or equations are to never show the multiplication sign unless you are using an x as a variable. It'll get confusing. This is when you use your coefficients. Instead of 6xx, you will only need to put 6x. (x=3) This shows that you are multiplying "x" 6 times. In this case, "x" is 3. You are multiplying 6 three times. Or you could do it the other way, 3x(x=6).
NOTE: Mrs. Boughton prefers you to put coefficients instead of putting it in brackets.
If we use graphs in class, make sure you label the graph chart. You need to label the x and y axis. The x axis is labelled going left and right(horizontally) and the y axis is labelled up and down(vertically). The x axis is usually labelled as the "Term #" for patterning. The y axis is usually labelled as whatever amount of shapes, toothpicks, or whatever type you are using for patterning.
There will be times when some of the worksheets will ask you for the value of the nth figure using words, numbers, and symbols. It just means to describe what you are doing.
Eg.1 There are three steps to completely answer the nth figure.
The equation using variables. 6x7=42. You'll need to have a variable for each number. In order to do that, you need to write down what number you want to change and write the number you want to replace the number with. If I wanted 6 to be a, I have to put "Let 6 be a." and if I wanted 7 to be h, I have to put "Let 7 be h" to let people know that this letter is the number you want it to be. You would also need to write down what is happening in your expression or equation. 6x7(Let 6 be n). 7n= 42 would be the equation you would need. You have to describe the equation. For example, "I am multiplying 7 by n(which is 6) and it all equals to 42.
To wrap up this up, make sure you figure out whatever pattern you need to answer.