Decimal’s are all around us!

We have been using decimal’s all of our lives and don’t even realize it. An average person can use decimals in these five ways in their daily life.

1.      Money

2.      Weight

3.      Landscaping

4.      Measurements

5.      Medicine Dose

While we use these 5 things on a daily basis we never really think about the decimal. It is simply common knowledge that the decimal is there. The only time we really think about the decimal is when we are adding, subtracting, multiplying, and dividing decimals. 

Let’s look at what a decimal is and how to add, subtract, multiply and divide decimals. 

Decimal A decimal is a number that is written with a decimal point in it.  For example: 6.2, 15.65 and 0.023 are decimals. The value of the digits is based on the number ten.

Adding Decimal Adding decimals is very much like adding whole numbers. One important thing to remember when adding decimals is to line up all the decimal points in a column!  If the numbers you are adding do not have the same number of digits to the right of the decimal point, you still have to line up the decimal points before adding.

Subtracting Decimal Subtracting decimals is very much like subtracting whole numbers. One important thing to remember when subtracting decimals is to line up all the decimal points in a column! If the numbers you are subtracting do not have the same number of digits to the right of the decimal point, you still have to line up the decimal points before subtracting.

  

Multiplying Decimals Multiplying decimals is very much like multiplying whole numbers - the major difference is that after you have finished multiplying all the terms while ignoring the decimal points, you have to add up how many decimal places there are in the factors, and put that many decimal places in the answer.

Dividing Decimals Dividing decimals is very much like dividing whole numbers - the major difference is that before you start dividing, you have to multiply the divisor by a power of 10 in order to make it a whole number. Multiply the dividend by the same power of ten then put a decimal point in the answer directly above the new decimal point in the dividend.  The rest of the division problem is just like dividing integers.

Sets using the Venn Diagrams

When I  first was introduced to sets and whole numbers, I had no clue what I was doing. It was not until a couple of years ago when I had to take a math class to finish up my A.A. degree that I finally understood the concept of sets and whole numbers. It was Venn diagram with universal set that helped me understand the concept. 

A few things that a person needs to understand when dealing with sets and whole numbers are: What is a set, one-to-one correspondence and the difference between equal and equivalent sets:

A set is any collection or objects or ideas that can be listed or described.  For example, the set of boy names contains the names Tom, Tucker, and Doug. In mathematical shorthand, we list the objects in a set within braces :{ Tom, Tucker, Doug}.

Sets A and B have one-to-one correspondence if and only if each element of A is paired with exactly one element of B and each element of B is paired with exactly one element of A. 

A = {m, n, o, p, q}

B = {w, x, y, z, a}

 The different between equal sets and equivalent set. A= {1,2,3,4,5,6} and B = {1,2,3,4,5,6} A and B above are equal sets because all their elements are precisely the same. C= {a,b,c,d,e,f} and D= {3,4,5,6,7,8} C and D are equivalent sets because the number of elements in both the sets is the same i.e.6. 

How we come to the part that talks about Venn diagrams with universal sets. The relationship of a set to its universal set leads to an important definition of the complement of a set:

The complement of a set A, written A, consists of all of the elements in U that are not in A.

Here is the math problem from my math class that made set with whole number using a Venn diagram with universal sets that made me understand the concept of sets and whole numbers. I believe it was the use of a real-life situation that helped me understand. 

A winter resort took a poll of its 350 visitors to see which activities people enjoyed. The results were as follows: 178 liked ski, 154 liked to snowboard, 57 liked to ice skate, 49 liked to ski and snowboard, 15 liked to ski and ice skate, 2 liked to snowboard and ice skate, and 2 liked all three activities. Complete the Venn diagram below and determine the cardinality for each region

First step: The first step to filling in the four inner circles is to look at the numbers with and/all. Where the three circles meet this is where you will put all (2)

Second Step: Now that you have your all filled in, to find the next three you will subtract all from the and. Example: to find how many like both snowboarding and ice skating you would take 2 (all) from 2 giving you 0, 2-2=0. To find skiing and ice skating you subtract 15 and 2 to give you 13, 15-2=13. Follow the same for ski and snowboarding, 49-2=47

Third step: to find the individual sport lovers you will subtract 13,2,47 (the inner circles) from those that like the individual sport. Example: Skiing =178 people liked skiing, so 178-13-2-47= 116 people who just like skiing. Follow this step for the other two circles. 

Fourth step: Add all circles (including inner) to find how many people took the survey. Subtract the number from the number of visitors polled to find how many didn’t apply. Example: 116+105+42+13+2+47=325(people who took the poll.) 350-325=25 (people who didn’t apply) This number goes outside the circles into the universe.  

This is a great introduction video on Venn Diagrams.

Understanding Integers

Understanding integers has now become a math standard for students starting as young a 3^rd grade.  An Integer is a number on a number line that goes on forever. Whole numbers greater than zero are positive integers. These numbers are to the right of zero. Whole numbers less than zero are negative integers. These are to the left of zero. There is a good video that explains what are integers is.

An integer is a positive and negative number that is commonly used to give meaning to all sort of real-world situations form body weight, sports, music charts, stock market and many more. As you can see an integer is an important part of life. 

Here are some basic operations one needs to know when dealing with integers.

OPERATIONS WITH INTEGERS

Addition When addends have the same sign, add. Use that sign when you write the sum. 6 + 9 = 15 -10 + -20 = -30 When addends have different signs, subtract. Use the sign of the greater addends -5 + 3 = -2 46 + -12 = -34	Subtraction To subtract an integer, add its opposite. The opposite of 12 is -12 4 -12 = 4 + -12 = -8 9- (-12) = 9 + 12 = 21 The opposite is -15 is 15 1-(-15) = 1 + 15 =16 -20-(-15) =-20 + 15 = -5
Multiplication When the factors have the same sign, the product is positive. 7 x 8 = 56 -15 x -5 = 75 When the factors have different signs, the product is negative. -5 x 4 = -20 3 x -11 = -33	Division When the dividend and the divisor have the same sign, the quotient is positive. 36 / 6 = 6 -150 / -5 = 30 When the dividend and the divisor have different sign, the quotient is negative. 28 / -2 = -14 250 / 10 = -25

When looking into integers, I found that there are many different websites that deal with Integers, Absolute Value & Operations with Integers. This activity includes finding absolute value of integers, comparing integers, and addition, subtraction, multiplication and division of integers.