Explain your thought process without performing actual computations.
How do you know that 3 negative29 is smaller than 2 negative29?
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I am unsure if you want us to explain how we'd do this because you need help, or because it's a homework assignment. If it's the second, here's what I suggest you do. Solve the problem with only numbers, writing out every single step. In this case, you add -29 + -29 and get an answer. Then add -29 + -29 + -29 and get an answer. I don't think your teacher will just accept that there are three -29s in one case and two in another, since it says to use computations.
Think of it as a number line. Every time you have a -29 you are going farther away from zero (to the right). So if you go that distance away from zero three times, you are going to go farther than if you go that distance only two times. Since farther to the right on a number line means smaller your first number is smaller.
I would agree with the number line method. A negative number is smaller than a positive. The closer one is to zero, when dealing with negative numbers, the larger the number is. Therefore, 3 negatives would be further away from zero making the 2 negatives closer to zero.
I have always been one to work math differently. If it does not make sense it is the process I use and may not make sense.
I also agree with the number line idea. Personally, I'm a very visual learner. I would often draw sketches beside my computations and equations to help me understand the problem. You might want to actually draw out a number line when you come across another problem like this. As posts 3 and 4 point out, the farther a number is to the right of zero, the smaller it will be. It will certainly make the correct answer easier to see and understand.
To figure this out without calculations requires the realization that negative 39 is further away from zero in a diminishing direction, probably more correctly stated "as a diminishing quantity." As positive 39 is further away from zero in an increasing direction, or as an increasing quantity, so is negative 39 further away in a diminishing direction, or as a diminishing quantity.
I would think of it as 3(-1) and 2(-1)... working with smaller numbers is always easier... so since -3 is smaller than -2, then 3(-29) should be smaller than 2(-29). i think the number line method works fine as well :)
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