Definition of 'Height'

Height: -The perpendicular distance from the base to the opposite side.
             -Common symbol is 'h'.

Definition of 'Base'

Base: -Is any side of a closed two-dimensional figure (or shape).
         -It's common symbol is 'b'.

How to find the Area in a Circle

As an example to show you step-by-step, we'll use r(adius)=12 cm. There is one formula to find the area.
1) A(rea of circle)=πr² (Always write the formula your using as your first line)
2)A=3.14 x (12²) (Write out the second line like so. It will usually specify whether or not you substitute π for 3.14, in this case it does. Put r² into brackets, meaning in the next line, you will do this first)
3)A=3.14 x 144 ('²' means to square. Meaning you have to multiply the number by itself not by 2, lots of people get confused by this. Your third line should look like this)
4)A=452.2 cm² (You then multiply 3.14 by your radius squared. There you have it! your answer! Don't forget to add what it's measured in plus squared)

Hope this helped you!  

How to find the Circumference

As an example to show you step-by-step, we'll use the number r(adius)=4.6 cm. I'll show you how to find the circumference if you have the radius.


1) C(ircumference)=2πr (This is the formula we use to find the circumference, always write this down first when beginning)
2) C=2 x π x 4.6 (Write out the second line like so but, substitute r for whatever your radius is)
3) C=6.28 x 4.6 (Multiply 2 x π (in most cases it will say to use 3.14 for π), you should get the answer of 6.28. Write that in the place of 2 x π like so)
4) C=28.8 cm (Multiply 6.28 x whatever your radius is and there you have it! the circumference. It will specify if you should round your answer or not, I've rounded the answer to the nearest tenth. Don't forget to include what it's measured in if it said)

I hope this helped you! 

Common terms in Circles

Diameter: Is the distance across a circle through it's circle.

Radius (or 'radii' for plural): Is the distance from the centre of a circle to its outer edge (sort of like a spoke in a wheel).

Circumference: Is the perimeter of a circle, or the distance around the circle.

Area: Is the inside of the perimeter (circumference), or what's inside the circle.

Number of The Day: Question 12.

Divide the number of the day by 3.55 and round to the nearest hundredth.
*As an example, we'll use the number 2364.578*

2364.578.
1 - Divide the number of the day by 3.55 (2364.578÷3.55=666.07830985915).
2 - We only need to know the whole number (666) and the tenths, hundredths and thousandths (0.078). So that leaves us with the number 666.078.
3 - The question states we have to then round to the nearest hundredth, which in this case, is the 7. To determine if it will stay as 7 or go onto 8, we need to use the next place value beside it (the thousandths). If the number that determines whether you round up or down is between 0-4, you round down. If the number is between 5-9, you round up. Since the thousandths place has an 8, we'll round the hundredth up. We end up with 666.08.
4 - We've done all the steps so the answer to this would be 666.08.

The Divisibility Rules.

Here are the divisibility rules for:
1 - Any whole number (examples: 890, 6531, 33325 etc..).
2 - Any whole number that ends with a 0, 2, 4, 6 and 8 (examples: 50, 9002, 5634, 1188).
3 - The sum of the whole number must have the factor of 3 (example: 1234. 1+2+3+4=10. 10 does not have the factor of 3).
4 - Any whole number that can be divisible by 2 twice (example: 240. 240÷2=120. 120÷2=60. 240 is divisible by 4).
5 - Any whole number that ends with 5 or 0 (examples: 3425, 100 etc..).
6 - The sum of the whole number must have the factor of 6/must be divisible by 2 and 3 (examples: 570. 5+7+0=12. 12 has the factor of 6/12. 12 is divisible by 2 and 3).
8 - Any whole number that can be divisible by 2 thrice (example: 624. 624÷2=312. 312÷2=156. 156÷2=78. 624 is divisible by 8).
9 - The sum of the whole number must have the factor of 9 (example: 6376. 6+3+7+6=22. 22 does not have the factor of 9).
10 - Any whole number ending in 0 (example: 10, 20, 30 etc..).
*These are the rules that we've gone through already*

Improper Fractions.

ABOVE: Examples of improper fractions.

An improper fraction is a fraction that has a greater numerator than the denominator.

Mathematical Variables.

A variable is a letter that represents an unknown number. (CLICK HERE for some more thorough explanations on variables).

Basically, it could be any letter, A through Z. Like Y, X, P, J or O.

Also, here is a video:

I found that the said video was easy to understand and helpful.

Mathematical Expression.

An expression is any single number or variable, or a combination of operations such as subtraction (-), addition (+), multiplication (x) or division (÷) involving numbers and variables.

Here are a few examples: 3+2=5, x+10=21, y=x-4.

Here is a print-out that focuses on Algebraic Expressions: CLICK HERE.

Ordering Decimals.

I found this YouTube video on how to order decimals and I found this very helpful and easy to interpret.
Check it out!

Divisibility Rules for 8.

All numbers must be divisible by 2 thrice.
ex: 8 = 2x2x2
24÷2=12 / 12÷2=6 / 6÷2=3.
24 is divisible by 8.

Pg. 146-147 [Review], Question 5.

You should know what fractions look like/how much they are equal to.

The easiest way to represent a fraction is to draw a pie.

This is the pie I used to help me answer these questions. It's divided into eighths.

For B you'll have to convert your fraction into percent. You can do this 2 ways [for both you'll either have to divide or multiply, and whatever you do to the top you MUST do it to the bottom/vice versa]:

The first way to do this is take the denominator and try to make it into 100 [multiply it by whatever number will make it into a 100, or divide if the denominator is more than 100]. Again, what you do to the top you must to the bottom [vice versa]! if you do this correctly, you then take the numerator and add a percent sign to it [ex: 10%]. Show your work!

The second way to do this if your denominator cannot be multiplied or divided evenly is to first convert it into a decimal [see How to do C] after that you multiply the denominator by 100 [percents are always out of 100], then the numerator by 100 and you will get your answer [which may have since you couldn't multiply/divide it evenly]. Take the numerator add a percent sign to it. Show your work!

For C you'll have to convert your fraction into a decimal. There is one way to do this. Remember, what you do to the top you do to the bottom! always! it's a MUST! [vice versa].

All you have to do is take your denominator and divide it by itself [ex: if the denominator is an 8 then you must divide it by 8]. You should get a 1 and always a 1 [decimals are always out of 1!]. 'What you do to the top you must do it to the bottom [vice versa]' divide the numerator by it's denominator! [ex: The denominator is 8 and the numerator is 3. So you divide 3 by 8.]. There, now you have your decimal! [ex: 0.375 over 1].

Using Bar Notation.

Question 8, Pg. 138.

You only use Bar Notation if the decimal repeats and goes on forever.

As you see in Part C it is 0.1877777..., you wouldn't use the Bar Notation on the whole decimal [0.187] you would only use it over the 7 because that's the only number that repeats.

Order of Operations.

How to answer today's BEDMAS question step by step:

4x3+12÷2.

1. Do the Brackets - There are no brackets.

2. Do the Exponents - There are no exponents.

3. Do the Division - There is division [12÷2=6]. Underneath, rewrite 4x3+6.

4. Do the Multiplication - There is multiplication [4x3=12]. Underneath, rewrite 12+6.

5. Do the Addition and/or Subtraction [#6] - There is no addition or subtraction in today's BEDMAS question but, you would solve the first operation that comes first, left to right [example: 4+3-6x2. You would do addition first since it shows up first].

7. Add up the remaining numbers since there is nothing else to solve. Cube/square your answer [18].

Note: For Division and Multiplication you would do the first operation that shows up, just like Addition and Subtraction. Example: 2x3+6÷4. You would first solve the multiplication since it shows up first [left to right].

Check out this site on how to perform the Order of Operations/solve BEDMAS questions with easy to understand instructions and practice.

^ Here's a video that also teaches you how to use the Order of Operations/solve BEDMAS questions. ^