Gayathri J. answered 10/11/12
GMAT Math and Essay Coaching
Usually times is refered to the multiplication
Three times means Multiply by 3
Two A means 2A
so here, it means 3 * 2A
that is 6A
Brittany W.
asked 10/10/12three times two a
Gayathri J. answered 10/11/12
GMAT Math and Essay Coaching
Usually times is refered to the multiplication
Three times means Multiply by 3
Two A means 2A
so here, it means 3 * 2A
that is 6A
Jon C. answered 10/11/12
Former Math Curriculum Specialist
The way I think of this is realizing that its all multplication. So just stick all the corresponding parts (similar to like terms when adding, but this is multiplying) together and find their products.
3 times 2 a = 3•2a or (3)(2a) or 3(2a).... this could go on. For these problems, just multpily numbers with numbers and variable with variables. This is the quickest way to think about these problems.
3 and 2 have a product of 6. So the answer is 6a.
HERE ARE SOME EXAMPLES TO HELP YOU GET WHAT IM SAYING HERE:
1) 4 times 5xy = 20xy
2) 5t(6t2) = 30t3
3) 1/2(4a)15a = 30a2
Creston L. answered 10/10/12
Math/Science Tutor. Elementary-High School and College Freshmen.
3*2a can be written in many fasions, in particular I prefer to view it as 3(2a). In addition to the communitive property, you can also view this as a scalar multiplication, so that for any "x" where "u" and "v" are real numbers, u(vx)=(uv)x. This is a very handy way of looking at such problems, as it has many repurcussions later in mathematics. In the example provided "three times two a" 3(2a)=(3*2)a=(6)a=6a. You can prove this by working backwards with example problems. Begin, for example with 10a. We know that 2*5=10, so let us write it as (2*5)a=10a, then you can write this, via our axiom, as 2(5a) which is "two times five a." You will find that this axiom holds true for all sets of real numbers.
Christopher M. answered 10/10/12
Math, Science and Test prep tutor
3*2a
To solve this problem you need to use the communitive property of multiplcation which states for all real numbers a, b, and c a*b*c=b*c*a=c*a*b=b*a*c.....etc. The gist of this is multiplcation is not dependent on order, so
3*2a= 3*2*a= 6a
Rick N. answered 10/11/12
SAT, GMAT Preparation and General Subject Assistance
It's really simpler than all that jibberish. Just multiply 3X2, and remember to add the a at the end.
Rick N.
Jon,
I am with you on method. However, from experience, the proof is in the pudding. Getting the right answer is better than knowing how the system is designed. Sometimes intuition is a good way to go.
Not a pedagogue myself, but I have helped many kids with homework, and they usually respond better, and perform better, when things are made simple. That's why I don't teach Russian grammar until kids get a grasp on basic vocabulary.
10/11/12
Jon C.
I appreciate the response and you're making perfect sense. But I do believe there are situations where understanding WHY can save alot of time and headaches memorizing every little math trick, loophole, equation, etc.
Like with 3D geometry: I think its more important to know why the volume of a cylinder is V =(pi)r^2•h. If you break this down, first part is the area of a circle.... "h" represents how many circles are stacked onto each other....
But all in all, the teaching method here greatly depends on the students capability and willingness to learn rather than pass a test.... There will never be a simple or best way answer to any of these questions since everyone understand things differently. You need that one on one time, or just SPEAK UP IN CLASS!!!!
10/11/12
Rick N.
Yes, it alsways goes back to basics. So long as r and h are in the same units, and you don't forget to raise the power to accommodate the 3d dimension....all good...
10/11/12
Jon C.
Good eye Rick.
10/11/12
Rick N.
Always hated math teachers.... Look at some of the commentary on here about a simple problem.
10/11/12
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Jon C.
Clearly thats the shortcut... but why a student may ask. Why does that work like that? I've had students give me answers like " well three times two A means 3•A•A " OR " 3 times 2A = (3)(2)(1) = 6". These students may not be able remember "add the a at the end" because they don't know why they are doing it... my ten cents. Don't get me wrong, I'd do it your way, but when a student is first learning, they should be introduced to different methods until they find one that works for them, yours included and for many, that end all be all method.
Good answer Rick. I just don't think it would work for everyone.
10/11/12