MHB What Are the Solutions to These Basic Arithmetic Problems?

  • Thread starter Thread starter beefy
  • Start date Start date
  • Tags Tags
    Arithmetic
AI Thread Summary
The discussion focuses on solving basic arithmetic problems using the order of operations (PEMDAS). Participants clarify the need for precise notation, particularly regarding expressions like 4(-2) to the 2nd degree, which can be interpreted in multiple ways. The calculations for specific problems, such as 8(6-5) + 10 and 598% divided by 26%, are explored, emphasizing the importance of understanding percentages as relative to a base. Misplaced elements in the expressions, like the "3" in the second line, are noted as potential sources of confusion. Overall, the conversation highlights the necessity of clear mathematical communication for accurate problem-solving.
beefy
Messages
1
Reaction score
0
8(6-5) +10 equal?4(-2)to the 2nd degree plus 8 (-2) + 3(-2) + 6 equal?
3
(1/3) (9) equals?

598%/ 26% what is answer?
 
Last edited:
Mathematics news on Phys.org
beefy said:
8(6-5) +10 equal?4(-2)to the 2nd degree plus 8 (-2) + 3(-2) + 6 equal?
3
(1/3) (9) equals?

598%/ 26% what is answer?

1) 8(6-5)+10= ?

This is a basic use of the order of operations or PEMDAS as it is commonly taught. You should start by simplifying inside the parentheses, then multiply and lastly add. What do you get?

2) I'm not exactly sure what is being taken to the 2nd degree. You need to be very precise with parenthesis! 4(-2) to the 2nd degree could mean [math]\left( 4(-2) \right)^2[/math] or [math]4 \times (-2)^2[/math] Which one is it? For the second part of this, +8(-2)+3(-2)+6, multiply first then add or subtract.

3) You wrote this:

4(-2)to the 2nd degree plus 8 (-2) + 3(-2) + 6 equal?
3
(1/3) (9) equals?

On the second line, where does that "3" belong? Is that part of a problem or number 3?

4) 598%/26%

Let's say that we have 100 apples. Then 598% of those apples is 5.98*100. Similarly 26% of those 100 apples is 0.26*100. Once we find those and divide what do you get?
 
beefy said:
8(6-5) +10 equal?
8(1)+ 10= 18, of course. I think I learned that kind of arithmetic in third or fourth grade.
4(-2)to the 2nd degree plus 8 (-2) + 3(-2) + 6 equal?
Assuming the "2nd degree" refers only to the "(-2)", that is 4(4)+ 8(-2)+ 3(-2)+ 6= 16- 16- 6+ 6= 0.

3
(1/3) (9) equals?
That "3" is misplaced. Assuming you meant (1/3)3(9), that is (1/27)(9)= 1/9.

598%/ 26% what is answer?
Percentages are NOT numbers and standard arithmetic operations are not defined on percentages. You can interpret percentages as meaning percentages of a specific base, so converting to numbers. That is what Jameson did but that is just one possible interpretation of the question- which is, itself, meaningless.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...

Similar threads

Replies
7
Views
2K
Replies
24
Views
3K
Replies
20
Views
2K
Replies
3
Views
1K
Replies
30
Views
3K
Replies
7
Views
2K
Back
Top