Exam notes: Geometry Lines

There are 3 geometry lines that we discussed in class. They are:

Parallel lines: Two lines that will never, never, EVER meet. Guaranteed. Here is a picture of what it looks like:


Perpendicular lines: These are to lines that meet in an 90 degree angle. Here's what they look like:


Intersecting lines: These are just basically lines that meet. Here's what they look like:


This SITE will explain a bit more about the geometry lines

Exam notes: How to make Perpendicular bisectors

There are two ways to make perpendicular bisectors. One way is to make semi circles and the other way is to just measure.

Way 1:
1. take your compass, put the point at the end of the line segment and draw a semi-circle.
2. do the same thing to the other end of the line segment.
3. take the ruler, align it to the intersections of the 2 semi-circles and draw a line.
4. label the bisector.

the end result should look like this:


Way 2:
1. take your ruler and measure the line segment.
2. find the center of the line and make a mark, then draw a straight line
3. label it.

Follow this Link for a video on more how to make a perpendicular bisector.

Exam Notes: How to find out mean, median, mode, range and outlier?

MEAN (AVERAGE)- You find out the mean by adding up all the numbers and dividing them by the number of numbers you added.
e.g 1 +2 + 3+ 4 + 5 = 15/5 = 3 <-- the mean is 3, you get it?

MODE- You find out the mode by looking for the number(s) that occurs more often.
e.g 1, 1, 2, 2, 2, 2, 3, 5 <--- 2 is the mode because it happens more often than any of the numbers.

MEDIAN- You find out the median by PUTTING THE NUMBERS IN ORDER FIRST,  then you put a finger on the first number and one on the last number and make them go closer, the number that your fingers land on is the median. But if you don't land in any middle number, find out the mean of the two numbers your fingers land on. The mean of the two of those numbers is the median.
e.g 1, 2, 4, 6, 8, 16, 20 <--- the median is 6 because it is the middle number.

Range- To find the range, you must find the smallest number and the largest number and subtract them.
e.g 5, 6,12, 90: 90 - 5 = 85 <--- the range is 85.

Outlier- To find the outlier(s), you just have to locate the number that doesn't fit in.
e.g 5, 20,21,23, 90 <-- the outliers are 5 and 90 because they don't fit in with the 20s.

Use this information wisely.

Exam notes: Integer Subtracting tips (without calculators)

I am going to show you tips on how to make subtracting integers easier.

First of all, I would list questions that you have to solve in the end of the blog:

1.) 19 - 79 = ?
2.) 95 - (-54) = ?
3.) (-98) - (-94) = ?
4.) (-78) - 85 = ?

Now, to solve these, it's going to be hard because of the large numbers right? So, we can use this strategy: opposite operations. The way that the opposite operations strategy works is that you switch the sign of the number on the right and the operation.
e.g.  3 - (-4) can be converted to 3 + 4 so that finding the answer is easy, instead of wasting time trying to use integer chips (which is another strategy).

So now you understand how to use the opposite operations here's a list on the possibilities:
a) (-) - (-) = (-) + (+)
b) (-) - (+) = (-) + (-)
c) (+) - (+) = (+) + (-)
d) (+) - (-) = (+) + (+)

Now I hope you got it! AND DON'T FORGET TO ANSWER THOSE QUESTIONS! Except for you Mr. Isfeld.

Exam Notes: Formulas for a Circle

There are 2 formulas to find the circumference of a circle. There is one formula to find the Area.
These are the formulas:

Circumference:
1.) C=πd (Circumference is equal to Pi times the diameter.)
2.) C=2πr (Circumference is equal to 2 times Pi times the radius.)


Area:
1.) (Area is equal to pi times the radius squared)

E.g.  Find the Circumference and the Area of a circle that has a radius of 5.

Circumference:
C=2πr
C=2x3.14x5
C=3.14x10
C=31.4 


Area:
A=πrr
A=3.14x5x5
A=3.14x25
A=78.5

I hope you learned something.

What's a Common Denominator?

A common denominator is a common multiple of the denominators of a set of fractions.

E.g. What is the common denominator of 3 and 6 ?

= 6

Solution:

Find the Multiples :

3: 3, 6

6: 6, 12

A wee test for ye:

What is the common denominator of 11 and 12?

How to add Mixed Numbers

What is a mixed number? - a mixed number is a number made up of a whole number and a fraction.

E.g. 1 1/2, 2 3/2 <-- WRONG!!

Instructions:

1. Deal with the fractions first. If they have a common denominator, go ahead. But if they have a different denominator, find a common denominator.

2. Then deal with the whole numbers.

3. Finally, combine the fractions and the whole denominators.

4. And if you can, bring the fraction to its lowest terms

Here's a little test for you:

1 1/2 + 3 3/4 = ?

Figure it out

What is a Numerical Coefficient?

A Numerical Coefficient is a number that multiplies the variable.

E.g. numerical coefficient--> 2t <--variable

What is a Constant?

A Constant is a number that does not change and it increases or decreases the value of an expression.

What is a Variable?

A Variable is a letter that represents an unknown number.

E.g. X, A, N, B, etc.

MathLinks Homework booklet page 67 #14

Q: Desiree is buying boxes of chocolates for tables at a banquet. The people at each table will divide the chocolates equally. The tables seat 2, 3, 5, or 6 people. Which size of box will work on all the tables: 12 or 30? Show your thinking.

A: The box with 30 pieces of chocolates will work on all the tables.

S: 30 can be divided by 2: 30 ÷ 2 = 15

30 can be divided by 3: 30 ÷ 3 = 10

30 can be divided by 5: 30 ÷ 5 = 6

30 can be divided by 6: 30 ÷ 6 = 5

Legend: Q: Question

A: Answer

S: Solution

This post will help you with the MathLinks Homework booklet page 67 #14, Guaranteed....

Divisibility Rule for 2: If the number's last digit ends in an even number, then it can be divided by 2.

Example: 36 can be divided by 2 because the digit in the ones place (6) is an even number.

27 on the other hand, cannot be divided by 2 because the digit in the ones place (7) is an odd number.

Think and Answer: Is 127 350 divisible by 2?

Mathematics Glossary: Even number: a number that ends in 0, 2, 4, 6, 8

Ones: the digit that is right in front of a decimal (eg. 123, 3 is in the ones place)

Odd number: a number that ends in 1, 3, 5, 7, 9

MathLinks Textbook page 138 #10

Change each fraction to a repeating decimal,

then use the bar notification to show the repeating part.

a) 5/6 = ?

b) 2/3 = ?

c) 45/99 = ?

d) 7/11 = ?

The answers are:

a) 0.833333..... can be also 0.83 ( the line is over 3)

b)0.666666..... can be also 0.6 (the line is over 6)

c)0.454545..... can be also 0.45 (the line is over 45)

d)0.636363..... can be also 0.63 (the line is over 63)

The solutions are:

a) 6 divided by 6 and 5 divided by 6, which results to 83/1.

b) 3 divided by 3 and 2 divided by 3, which results to 6/1.

c) 99 divided by 99 and 45 divided by 99, which results to 45/1.

d) 11 divided by 11 and 7 divided by 11, which results to 63/1.

Check this site out if you need more information about repeating decimals.....

Converting Fractions and Decimals

Fractions are: Decimals are: Percents are:

whole numbers anything anything

whole numbers 1 100

e.g. 1, 3, 5, etc. e.g. 0.1, 0.5, 0.375 e.g. 60% = 60, 54.7%=54.7

2 4 3 1 1 1 100 100

Not 30%, 0.1 or 0.5 e.g. 6 = 6 = 6.0

3 1

Convert means change

e.g. Fractions to Decimals

1 = 0.5

2 1

Convert 3 to a decimal:

4

3 = .75

4 1 o.75 is a Terminating decimal

Convert 2 to a decimal:

3

2 = .6666.....

3 1 0.666666.........is a repeating decimal, another way to write this is:

_

0.6 (the line is supposed to be above the six)

check this site out!!! the site has a table that shows different results of converting a fraction to a decimal

Finding the Percent of a Number

Hello, I am going to show you how to find the percent of a number.

An example of a question would be like - 25% of 80 is ? Now to find the percent of a number, you must use a Ratio Table. The ratio table must look like a T-chart:

Example (this is not what it should look like):

(Percents will be below this)-->%<-------------->#<--(Numbers will be below this.)

Now to figure out the answer of the question:

1. You make a T-chart and on the % side, you write 100:

%<-------------->#

100

2. On the # side you write the number, for this question, it is 80:

%<-------------->#

100 80

3.to reach 25% you should start the easy way - divide 100 by 2 = 50%:

%--------------#

100-----------80

50------------

4. Do what you did on the percent side:

%--------------#

100-----------80

50------------40

5.Divide 50 by 2 = 25%:

%--------------#

100------------80

50-------------40

25-------------20

Now we know that 25% of 80 is 20. Another way we would've done it is 100 divided by 4:

%<------------->#

100-----------80

25------------20

And here is a video of another way of finding the Percent of a Number:

Hope you learned something new..!!