I was in home tutoring a 6th grader in Kaimuki, part of Honolulu Hawaii. I taught her how to isolate a variable involving fractions. I thought I'd teach you how to solve these equations.
-y/6 -5 = 7 Is The Equation We're Going to Solved Together
The first thing you should know is it doesn't matter if it's -y or -6. They're interchangeable.
We need to solve for y so we need to get that on one side of the = and everything else on the other side.
What is PEMDAS?
PEMDAS represents the order of operations in mathematics.
Parentheses () Exponents ^ Multiplication * Division / Addition + Subtraction -
Please Excuse My Dear Aunt Sally
To Isolate The Variable We Will use SADMEP
The opposite of PEMDAS. I'm the only teacher/tutor I know of that ever gave it a name. So we started with subtraction and addition
DO NOT skip a step! Write the entire process out on paper.
-y/6 -5 = 7
Change the sign add a line
Here's a YouTube video that I used to show my 7th grade math class.
-y/6 -5 = 7
-y/6 + (-5) = 7
Make this equation plus a negative number frees us up to do things we can do with addition that we cannot do with subtraction.
According to SADMEP we need to zero out the -5
What's the opposite of -5? +5
So we add a positive 5 to both sides to keep the equation balanced. If you do something to one side of the equation you must do it to the otherside. For example
However 1+2 ≠ 1+2+1
We must balance out the equation by adding 1 to both sides
Thus Adding positive 5 to both sides of our equation keeps it balanced
-y/6 + (-5) +5= 7+5
Again, write this whole thing out DO NOT skip steps and do this in your head. I'm especially talking to some of my ADHD students
-y/6 = 12
Think Of The Fraction Line Like This
The fraction line is called the division bar. Think of that line as meaning divided by. So we now have
-y divided by 6 =12
So since we are dividing, we do the opposite to get rid of that 6. Now the first thing I'm going to do is change the equation slightly. Remember when I told it didn't matter where we placed the - sign in a fraction? We'll save a little step if we do this
-y/6 = 12 is the same as y/(-6)=12
So now, we need can isolate y not (-y). Therefore we deal with (-6)
Remember a negative times a negative is a positive and we want the solution to positive y. so
If we are dividing by (-6) we multiply each side by (-6)
When parentheses are next to a number you multiply.
The Secret Ninja Invisible 1
I used to tell my 7th grade math students there's a secret ninja invisible 1 in front of all variables. I'd also do a few martial arts moves as I said this to entertain the students and keep their attention.
thus y/(-6)(-6)=12(-6) is actually 1y/(6)(-6)=12(-6)
We can forget about the y for now and solve
Here's Another Tip About Fractions
It may be easier for you to look at this part of the equation like so
1/(-6) * (-6)/1
This is called a reciprocal. When you multiply the reciprocal of any number you get 1
I would say to my students for a final example what is if we multiply a million gazillion trillion by its reciprocal what do we get
A Variable Next to a Number Means Multiply
So what our equation now looks like is
y* 1/(-6) * (-6)/1=12(-6)
Since 1/(-6) * (-6)/1 = 1 and 12(-6) = -72
We are left with
y * 1 = -72
Let's Solve The Equation Step by Step
This is how I want you to write it out again without skipping any steps.
-y/6 -5 = 7
-y/6 +(-5) = 7
-y/6 +(-5)+5 = 7+5
-y/6 + 0 =12
Do It Yourselfers Who Don't Want to Hire Me or My Other Two Teachers I Have The Pleasure of Managing.
About The Author/Teacher/Tutor J. Richard Kirkham B.Sc.
J. Richard Kirkham is the only tutor in Honolulu Hawaii covering all of Oahu with ADHD specializing in ADHD. Mr. Kirkham is in such high demand he enlisted the help of two other professional educators.
Dr. Alice DePina
Dr. De Pina has 16 years of teaching a diverse population and varying educational platforms including Special Education and the Gifted Student Enrichment courses which makes her especially talented in student motivation.
When interviewed for a teaching position one response stood out to her,
“The example you provide for students makes the greatest impact on their self-confidence.”
Dr. D, as her students and now in home tutoring students here in Honolulu Hawaii call her, received her doctorate in Principals of Teaching and Learning in 2013.
Mr. Nathan Krahn
Who joins our ohana of teachers with a diverse background in Special Education, which taught Mr. Krahn, first hand, how to deal with frustration directed toward him, and Computer Science making him an expert in both computers and teaching. This makes him the perfect fit to in home tutor senior citizens and business owners in the use of computers, cell phones, tablets and software.
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I have to admit, even with the help of two wonderful educators and tutors our schedules are getting full.