Difference between revisions of "2020 AMC 10B Problems/Problem 1"
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<math>\textbf{(A)}\ -20 \qquad\textbf{(B)}\ -3 \qquad\textbf{(C)}\ 3 \qquad\textbf{(D)}\ 5 \qquad\textbf{(E)}\ 21</math> | <math>\textbf{(A)}\ -20 \qquad\textbf{(B)}\ -3 \qquad\textbf{(C)}\ 3 \qquad\textbf{(D)}\ 5 \qquad\textbf{(E)}\ 21</math> | ||
| − | ==Solution== | + | ==Solution 1== |
We know that when we subtract negative numbers, <math>a-(-b)=a+b</math>. | We know that when we subtract negative numbers, <math>a-(-b)=a+b</math>. | ||
The equation becomes <math>1+2-3+4-5+6 = \boxed{\textbf{(D)}\ 5}</math> ~quacker88 | The equation becomes <math>1+2-3+4-5+6 = \boxed{\textbf{(D)}\ 5}</math> ~quacker88 | ||
| − | ==Solution== | + | ==Solution 2== |
We know that when we subtract negative numbers, a-(-b), this will equal a+b, because a negative of a negative is a positive. Because we know this, we can rewrite the expression as 1+2-3+4-5+6. Now, we can simplify this expression. You will get 5. So, you will choose D. - BrightPorcupine | We know that when we subtract negative numbers, a-(-b), this will equal a+b, because a negative of a negative is a positive. Because we know this, we can rewrite the expression as 1+2-3+4-5+6. Now, we can simplify this expression. You will get 5. So, you will choose D. - BrightPorcupine | ||
Revision as of 01:38, 15 May 2021
Problem
What is the value of
![\[1-(-2)-3-(-4)-5-(-6)?\]](http://latex.artofproblemsolving.com/9/4/c/94cdfebdc087637cc5450da458e0db822c81da88.png)
Solution 1
We know that when we subtract negative numbers, 
.
The equation becomes 
~quacker88
Solution 2
We know that when we subtract negative numbers, a-(-b), this will equal a+b, because a negative of a negative is a positive. Because we know this, we can rewrite the expression as 1+2-3+4-5+6. Now, we can simplify this expression. You will get 5. So, you will choose D. - BrightPorcupine
Solution 3
Like Solution 1, we know that when we subtract 
, that will equal 
as the opposite/negative of a negative is a positive. Thus, 
. We can group together a few terms to make our computation a bit simpler. 
.
~BakedPotato66
Video Solution
Check It Out! :) Education, the Study of Everything (wow!) https://www.youtube.com/watch?v=NpDVTLSi-Ik
~IceMatrix
~savannahsolver
https://www.youtube.com/watch?v=GNPAgQ8fSP0&t=1s
~AlexExplains
See Also
| 2020 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
