Two numbers have a product of 8 …
a•b = 8 …
… [Two numbers have a] sum of 9 …
a + b = 9 …
Yes. When we multiply numbers, the result is called their 'product'. When we add numbers, the result is called their 'sum'.Correct set up?
Now, how do you go about solving those equations?
Now, how do you go about solving those equations?
There is no need to ask us if you set it up right. Just solve it and see if it is correct. Seriously, that is how you learn math. Of course 8*1=8 and 8+1=9. I am sure that you know that. Please try it for yourself.My concern is always the set up.
I will be back to show my work.
There is no need to ask us if you set it up right. Just solve it and see if it is correct. Seriously, that is how you learn math. Of course 8*1=8 and 8+1=9. I am sure that you know that. Please try it for yourself.
Algebra is good and thinking is even better (and more fun). You should always spend a couple of seconds to see if the answer is obvious. Two numbers that multiply out to 8 and add up to 9 can be done in your head if you try. Seeing things is a mathematical growth. It really is! Students and teachers always tell me that I am wrong about having students see the answer without doing any work. Thinking is always good. Hopefully the other helpers will comment, if not ask them.Here it goes:
a•b = 8...Equation A
a + b = 9...Equation B
Solve B for either a or b.
a + b = 9
a = 9 - b
Plug into A.
(9 - b)b = 8
9b - b^2 = 8
b^2 - 9b + 8 = 0
Solving for b, I got b = 1 and b = 8.
Now I plug the two values found for b into EITHER A or B to find a.
I will use ab = 8.
Let b = 1.
a(1) = 8
a = 8
Let b = 8.
a(8) = 8
a = 8/8
a = 1
Answer: The two numbers are 1 and 8.
Yes?
True, but after you asked if you had the correct setup.I posted the complete solution.
Yes, indeed, whenever numbers are easily manipulated mentally. Of course, in exercises like the one in this thread, students would need to have memorized the multiplication table, before gaining the number sense needed to "see" those patterns.… Seeing things is a mathematical growth … having students see the answer without doing [work on paper] …
Algebra is good and thinking is even better (and more fun). You should always spend a couple of seconds to see if the answer is obvious. Two numbers that multiply out to 8 and add up to 9 can be done in your head if you try. Seeing things is a mathematical growth. It really is! Students and teachers always tell me that I am wrong about having students see the answer without doing any work. Thinking is always good. Hopefully the other helpers will comment, if not ask them.
Yes, indeed, whenever numbers are easily manipulated mentally. Of course, in exercises like the one in this thread, students would need to have memorized the multiplication table, before gaining the number sense needed to "see" those patterns.
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