How to solve 7th Grade Math Work with Positive and Negative Numbers?

The beginning of 7th grade math work in algebra start to get complicated when positive and negative numbers are mixed together. This is the start of 7th grade math work...getting complicated.

But, hopefully we should try to crack a few of those maths problem solving questions on positive and negative numbers.

What are Negative Numbers?

Numbers with minus signs infront of them are called negative numbers. Other numbers are positive. Sometimes positive numbers are written with a plus sign in front of them.

Nought is not positive or negative.

Numbers that are negative are less than zero. For example -2.5, -879, -0.173, -1/10 are all negative. 0, 3.5, 173, 0.0001 are not negative.

We can think of positive and negative numbers as if it were on a number scale.

Or simply the numbers on a thermometer.

… -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 …

Lets warm up and try these 7th grade math work for starters:(Answers are at the bottom of the page)

1.

a) Is 15°C warmer than -10°C?

b) Is 10°C warmer than -20°C?

c) Is -15°C warmer than -5°C?

d) Is -10°C colder than -2°C?

2.

a) Which is warmer, 40°C or -40°C?

b) Which is colder, -6°C or -8°C?

c) Which is colder -4°C or 0°C?

d) Which is warmer, -14°C or 5°C?

3.

Write the temperatures in order, coldest first.

a) 8°C, -45°C, 0°C, -14°C, -2°C
b) -2°C, 6°C, -3°C, 9°C, -1°C

Negative numbers are not just found on thermometers you know. They are all over the place.

For instance the lift in a building, what number is ground floor? Usually, it is 0. Going up will be all the positive numbers. First floor being number 1, second floor being number 2 etc.

What would be below 0? That would be the basement or the car-park, -1.

If you were on the third floor and wanted to go to the basement, -1.

How many floors do you go down? 4 floors?

Minus and a minus?

If we were to write this mathematically, in your 7th grade math work it would be 3 - - 1 = 4. If I were to say this in words, it would be 3 takeaway minus 1 equals 4. Or alternatively, we could say 3 minus minus 1 equals 4.

There is a rule when we have two negative numbers together. When I mean together, I literally mean together, just the way it is written above. It does not apply to something like -3-1. The answer to this would be -4.

So, the rule for when we have two negative numbers together is positive. We change the two minuses into a plus. We say a minus and a minus makes a plus. If you are the kind of person that needs to know where it has come from, lets take a closer look at the proof.

Proof

You will not need this for your 7th grade math work, but just in case you are wondering how to do it:

Lets takeaway some numbers from 3, lets say 4, 3, 2, 1, 0, -1, -2 etc.

3-4 = -1
3-3 = 0
3-2 = 1
3-1 = 2
3-0 = 3
3- -1= 4
3- -2= 5
.

.

.

And so on, spot the pattern?

Do you see the example from our lift, 3- -1?

We can carry on with these sums until infinity, but really the point is, a minus and a minus makes a plus.

Plus and a minus? Minus and a plus?

We can best describe this with an example then prove it later. Lets say, Mr Jones has a points system for his class 7p : Early 1 point, Just in time 0 point, late -2 point.

Zak is early on Monday, just in time on Tuesday, Wednesday and Thursday, and late on Friday. How many points does she have at the end of the week?

1+0+0+0+ -2
=1+ - 2
=1-2
=-1

In this example, on the second line we have a plus and a minus together. It could easily have been a minus and a plus if the question was worded differently.

This example appears to be straight forward, but trust me, this is the example most people in 7th grade math work either forget how to do or get confused on.

So when we have a plus and a minus together or vice versa, the rule is...we change it to a minus.

Proof

Can we prove this on the number scale? Lets take a look, we will add 1 to 3, 2, 1, 0, -1, -2, etc

1+ +3 = 4
1+ +2 = 3
1+ +1 = 2
1+ - 0 = 1
1+ - 1 = 0
1+ - 2 = -1
etc

Can you see the pattern in the answers?

Plus and a plus?

This one does not really need explaining, even to any 7th grade math work, but for those of you who are still not sure. When we have a plus and a plus sign together, its a plus, we add the numbers together. Your telling me, hey that's pretty obvious.

A couple of example's can be seen in the above proof. We get

1+ +1= 2, 1+ +2= 3 and so on.

Summary

There are four rules we have to learn, but in theory only have to learn two of them.

The four rules are:

• - and - = +
• - and + = -
• + and - = +
• + and + = +

The two we only have to remember is the first and the second (or third) example. The second and third example are the same. The signs are just reversed.

At this point, I should provide some questions and answers. That will follow shortly, in due course. But for now, I hope the information here has been of some use.

1. a) yes b) yes c) no d) yes

2. a) 40°C b) -8°C c) -4°C d) 5°C

3. a) -45°C, -14°C, -2°C, 0°C, 8°C

b) -3°C, -2°C, -1°C, 6°C, 9°C,

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