the sum of the positive odd integers less than 100 is subtracted from the sum of positive even integers less or equal to 100 what is the resulting difference ? Sorry... (U__U) I"m very bad at word equations, can I also have some tips to make solving these equations easier ? Thank you
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You are watching: The sum of the first 100 positive odd numbers


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The typical way to do these type of problems is what kspcr did. A similar method:

Consider the odd numbers: 1, 3, 5, 7, 9, 11, . . ., 97, 99

Start pairing them off, as in:

1+99

3+97

5+95

7+93

and so on

You would have 25 pairs of...


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The typical way to do these type of problems is what kspcr did. A similar method:

Consider the odd numbers: 1, 3, 5, 7, 9, 11, . . ., 97, 99

Start pairing them off, as in:

1+99

3+97

5+95

7+93

and so on

You would have 25 pairs of numbers that all add to 100. Add all the pairs up, you get 2500.

Consider the same exact steps with the even numbers:

2+100

4+98

6+96

8+94

and so on.

You would get 25 pairs of numbers totaling 102. Adding those up, we get 2550. Subtracting the evens from the odds:

2550 - 2500 = 50

As a matter of fact, it"s been said that Gauss, a famous mathematician from years ago, was punished by his math teacher in elementary school for misbehavior. For his punishment, his teacher gave his the work, "Add all the numbers up from 1 to 10", thinking Gauss would add them all up individually, taking about 30 minutes to an hour. What Gauss did was something similar to what we did above and got done in about 3 minutes, leaving for the day.

The reason to do word problems is because they are applications of the number problems. There"s a number problem in there; you just need to get it out.Why ones like these just thrown out there for students to solve? It would get you using all your math knowledge. For instance, if you are covering quadratics in school, doing number problems with quadratics, then you get to the word problems, odds are the word problems are going to involve quadratics.But, in real life, you don"t always know what problems you are going to come up against. So, you need to be able to call on all of your knowledge. And, what did we use here? Finding a pattern, addition, and subtraction, all basic math skills.What does it have to do with everyday life? First, I will say I agree on the job odds are you will never get a problem like this. However, let me ask this? Football players lift weights. Let"s consider the bench press, where the football players lie on the back and lift weights upward with their arms. Why do this? Nowhere in a football game does their job call on lying on their back and lift metal weights upward. So why do bench press? Because it makes them stronger. And if they get stronger, they become better football players.

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That"s essentially the same thing going on in math classes. Yes, you may not get the exact same type of problems in real life that you get in math classes, exactly like the bench press isn"t the exact same movement they do in the games. However, you will get problems in real life that you have to solve, just like the football players will get in situations they need to use their strength. And just like how football players become better when they bench press, all people become better problem solvers "in real life" when they can become better problems solvers "in math class". Math classes work the brain for real life problems just like lifting weights work football players for their games.