Читать книгу Algebra I All-in-One For Dummies - Mary Jane Sterling, Mary Sterling Jane - Страница 50

When your first-grade teacher taught you that , they probably didn’t tell you that this was just one part of the whole big addition story. They didn’t mention that adding one positive number to another positive number is really a special case. If they had told you this big-story stuff — that you can add positive and negative numbers together or add any combination of positive and negative numbers together — you might have packed up your little school bag and sack lunch and left the room right then and there.

Adding positive numbers to positive numbers is just a small part of the whole addition story, but it was enough to get you started at that time. This section gives you the big story — all the information you need to add numbers of any sign. The first thing to consider in adding signed numbers is to start with the easiest situation — when the numbers have the same sign. Look at what happens:

 You have three CDs and your friend gives you four new CDs:You now have seven CDs.

 You owed Jon $8 and had to borrow $2 more from him:Now you’re $10 in debt.

There’s a nice S rule for addition of positives to positives and negatives to negatives. See if you can say it quickly three times in a row: When the signs are the same, you find the sum, and the sign of the sum is the same as the signs. This rule holds when a and b represent any two real numbers:

I wish I had something as alliterative for all the rules, but this is math, not poetry!

Say you’re adding –3 and –2. The signs are the same; so you find the sum of 3 and 2, which is 5. The sign of this sum is the same as the signs of –3 and –2, so the sum is also a negative.

Here are some examples of finding the sums of same-signed numbers:

 : The signs are both positive, and so is the sum.

 : The sign of the sum is the same as the signs.

 : Because all the numbers are positive, add them and make the sum positive, too.

 : This time all the numbers are negative, so add them and give the sum a minus sign.

Adding same-signed numbers is a snap! (A little more alliteration for you.)