I've just read and upvoted Negative Exponents, an introduction. I was writing a comment to add my notes, until I realized that maybe a post could be fine. Maybe not. I don't know. Teaching is a hard thing and different explanations of the same topic could reach different people. Thus, here we go. I'm not saying something different, I'm just saying it differently, with another angle, so to speak.
Unfortunately, Steemit does NOT support math!
I want to show how you give meaning to b0 and b-n (being n a positive integer) — negative exponents — only taking into account notation. Notation is something conventional, yet it must be meaningful and consistent. In his previous post, Exponents, an introduction, @mathworksheets correctly wrote
In simple words, exponents are the shorter way to write the repeated multiplication
To understand the negative exponents students need to understand the positive exponents. If there is the repeated multiplication of a number then we can use positive exponents to write it into shorter form. Please see my previous post on exponents for details.
Please note that Negative exponent has nothing to do with the positive or negative sign of the base but it ONLY FLIPS THE BASE. Now what I mean by flip the base?
Simple, "if you see a negative exponent (power) in the numerator then flip the base to the denominator and write the exponent as positive or if you see the negative exponent in the denominator then flip the base to the numerator and write the exponent as positive".
I have been teaching math for a couple of months and I've learned that teaching is hard work! I have had the benefit of loving math and enjoying new intellectual challenges.
What happens when a child has no interest in math? You end up having to make things really fun. The lesson becomes an excercise in finding what the student enjoys and building a bridge between that passion and some mathematical concept.
I had the added challenge of being in classrooms that were next door to students who were testing all day and needed a silent environment.
The best I could do was create math lessons on folding paper. Folding paper is pretty silent, and you end up with a tactile result and the pride of procuding something in the class hour.
Rules of Exponents: There are 4 basic exponent rules. Students in grade 7 and beyond need to be familiar with these rules and should be able to apply these rules when dealing with problems involving exponents.
Zero Exponent Rule or Power Zero Rule: This is a very very basic rule to remember as most often overlooked by students and which cost them lot of marks in their math quizzes and exams. The rule is that "If any number raised to the power of zero then its value is equal to one".
For example; consider the problem, 2º which is read as two raised to the power
So I did some math... if someone makes a Mr. Fusion... and you use one can of beer... the potential energy...
E=MC^2 so… we assume 371.38g of beer (I took the weight of 12 fluid ounces of water and did some guestimation since beer isn't pure water)
7.9775e+3 kilotons of TNT
7.9775 megatons of TNT
3.16362398 x 10^13 BTU
9.27166665 × 10^9 kwh or 7.97753345 × 10^12 kilocalories
Which is 9,271,666,650 kwh where the U.S. used an estimated 3.741 trillion kWh in 2009. So .002% of the U.S. energy consumption for 2009. Now... that's 1.243350979e+10 horsepower hours.
It’s also 9,271.66665 jigawatts Marty
So I was thinking about what such a device as the Mr. Fusion would mean as far as power for space travel...
SpaceX's Falcon 9 rocket carries 395,700kg of fuel (119,100 Kilograms of Rock
I wrote an article on combining like terms in algebra long ago and want to share. We need to know the basic algebra, such as variables, coefficients, algebraic expressions and polynomials to be able do it. In this representation I am going to explain how to combine like terms in a polynomial or an algebraic expression.
Like terms in a polynomial contain the same variable. For example “3a” and “6a” are the like terms because both terms contain the same variable “a”. On the other hand “3a” and “6b” are not the like terms as they contain the different variables “a” and “b
Functions are the key to understand algebra and pursue math in grade 7th and higher. Most often the algebraic equations generate functions.
We created an algebraic expression in a previous post where Arthur's Earnings were $60 plus number of lawns mowed by him.
In other words we can say that Arthur's Earnings are dependent on number of lawns he mows during a day.
Further we can say that Arthur's Earnings are a function of Number of Lawns Mowed by him.
Let's clear the above by starting from a very basi
In simple words, exponents are the shorter way to write the repeated multiplication of a number.
Let’s clear the above sentence by doing the following example:
Consider we have the following repeated multiplication of ‘2s”
2 x 2 x 2
We can write it using exponents as shown below:
2 x 2 x 2 = 2³
The number which is repeated in multiplication becomes the “BASE” of and “number of times” it got repeated becomes the “EXPONENT” or “POWER” of the “BASE”.
2³ is read as “2 to the power 3” or “2 raised to the power of 3”
I'm a 36 year old father of 2. I have a 6 year old girl and a 5 year old boy. I consider myself a relatively intelligent human being capable of solving a pretty standard math problem...even without using my calculator! 😜
Since my children started school I have had to deal with Common Core. Now I don't know if you all have had the pleasure of being a student during the start of this wonderful learning experience or have had to help your own children with this glorious product of what the US government thinks is the
world standard of learning , but if you have been a victim; I feel your pain.
Now like I said, I have 5&6 year olds & when I attempt to help them with their homework I feel like I'm reading Chinese! When 2+2 equals banana and takes 10 steps and they need to show how they got the answer **AND EVEN IF ITS WRONG BUT THEY SHOW HOW THEY GOT TO T
Algebraic expressions are the mathematical relations explaining a general trend in a changing activity. For example, consider adding two pound of sugar to a bucket of sugar which already contains some sugar in it.
Do we know how much sugar is already in the bucket? No.
Do we know how much more sugar got added? Yes.
How much sugar in the bucket now? We don't know. But we do know one fact with certainty that now the sugar is 2 pounds more.
So the unknown is "how much sugar was there in the bucket already". Isn't it? Let's use a lower case letter to represent this unknown.
Consider the sugar already in the bucket = s
Now we have added another 2 pou
Divisible means a number completely divide another number and gives zero remainder. We can tell very easily that if 2 or 3 or 5 will completely divide a given number without doing the long division.
Below are the Divisibility Rules (tests) starting at the test for divisibility by 2 and ending at test for divisibility by 10:
Algebraic Expressions and Equations
We created an algebraic equations in two variables using a very simple example from a daily life activity in my previous post. If you missed that post please click the link below to see it.
In that example we created a simple algebraic equation as below:
Arthur’s Earnings = 60 + 25 x number of lawns mowed
In above equation, there are two variable (changing or unknown activities). One is Arthur’s earnings and the other is number of lawns mowed by him. We used lower case letters to represent these variables as shown below:
Arthur’s Earnings = e
Number of lawns mowed = n
Then our equation became
Before starting to teach decimals and fractions I always suggest the following:
"Keep one and only one thing in mind, which is what?"
Yes, always keep the number "1" in your mind. This is the key and will open the doors to all the secrets hidden inside the decimal and fractions world.
We can call “1” as
WHOLE or can call it “ONES”. Everything starts from
1 and contain
1 in it. I mean all the numbers independent of how big or how small, can’t exist without the numb
Let's begin ALGEBRA!!
Not hard, chosen from our day to day life activities but given the weird names to these activities by mathematicians.
So there are some basic concepts in algebra such as variables, coefficients, constants and algebraic expressions.
Next; what these all basic algebraic concepts are and what they have to do in our daily lives?
Let's do the following example from a daily life situation to understand all of the above terms in algebra:
Consider every weekend, Arthur; a grade 9 student starts to help his brother in his landscaping business. Every time Arthur goes with his brother for work, bro