At some point a math student needs to move from learning algebra to doing algebra. Many techniques that students learn are designed to facilitate a person’s understanding and remembrance of algebraic processes and are not optimized for efficiency or speed. Adding a number to both sides of an equation or always using a least common denominator when adding fractional expressions are examples of the conflation of technique and reason for the technique combined into one rule.

But as students move into the next level math courses,precalculus and calculus, algebra becomes a just a tool for exploring new concepts. At this point a math learner should be thinking about the new ideas not algebraic processes. The second term of precalculus with its plethora of proportions, equations and identities is the place, I think, to make this jump. Therefore I will be modeling fast algebra techniques like those in the image below.

Fast Algebra Techniques

I have written about these matters before. See this post and this post and this post for other takes on fast algebra techniques.

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## About jrh794

I am a sixty-five year old math instructor at Southern Oregon University. I taught at the College of the Siskiyous in Weed California for twenty-six years. Prior to that I worked as a computer programmer, carpenter and in various other jobs. I graduated from Rice University in 1967 and have a MS in Operations Research from Stanford. In the past I have hand-built a stone house and taken long solo bicycle tours. Now I ride my mountain bike and play golf for recreation.

Dude .. Thanks a lot .. This has helped me .. As day after tomorrow I Am supposed attended my Maths Exam for 12 th Std. .. All I am poor in maths is Algebra .. This one went through my mind .. Thanks a lot .. I Appreciate

Amazing, but what is the official term for this technique?

You know like there are terms such as substituition and cross multiplication etc.

Thanks.

After much experience doing Algebra, these techniques come out. You will glean them after doing many many problems.

Thanks Helped Me Alot

Thank you so much I got it now:)

thanks for this site now I can solve algebra easiely

Good ideas! Simple and easy to explain

Is the very last one right?

Easy to understand and teach someone. Appreciate the hardwork