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
  

Latest revision as of 02:38, 15 May 2021

Problem

What is the value of \[1-(-2)-3-(-4)-5-(-6)?\]

$\textbf{(A)}\ -20 \qquad\textbf{(B)}\ -3 \qquad\textbf{(C)}\  3 \qquad\textbf{(D)}\ 5 \qquad\textbf{(E)}\ 21$

Solution 1

We know that when we subtract negative numbers, $a-(-b)=a+b$.

The equation becomes $1+2-3+4-5+6 = \boxed{\textbf{(D)}\ 5}$ ~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 $a-(-b)$, that will equal $a+b$ as the opposite/negative of a negative is a positive. Thus, $1-(-2)-3-(-4)-5-(-6)=1+2-3+4-5+6$. We can group together a few terms to make our computation a bit simpler. $1+(2-3)+4+(-5+6)= 1+(-1)+4+1=\boxed{\textbf{(D) }5}$.

~BakedPotato66

Video Solution

Check It Out! :) Education, the Study of Everything (wow!) https://www.youtube.com/watch?v=NpDVTLSi-Ik


https://youtu.be/Gkm5rU5MlOU

~IceMatrix


https://youtu.be/-wciFhP5h3I

~savannahsolver


https://www.youtube.com/watch?v=GNPAgQ8fSP0&t=1s

~AlexExplains

See Also

2020 AMC 10B (ProblemsAnswer KeyResources)
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

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