Algebra I All-in-One For Dummies. Mary Jane Sterling

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The submarine was 60 feet below the surface when the skipper shouted, “Dive!” It went down another 40 feet. What is the submarine’s depth now?

      A. . Change from subtraction to addition. Change the 40 to its opposite, –40. Then use the addition rule. The submarine is now 100 feet below the surface.

      Q. Some kids are pretending that they’re on a reality-TV program and clinging to some footholds on a climbing wall. One team challenges the position of the opposing team’s player. “You were supposed to go down 3 feet, then up 8 feet, then down 4 feet. You shouldn’t be 1 foot higher than where you started!” The referee decides to check by having the player go backward, by making the player do the opposite, or subtracting the moves. What was the result?

      A. Putting a negative sign in front of each assigned move, you have: . The player ended up 1 foot lower than where they started, so they had moved correctly in the first place.

      And now here are some examples of subtracting signed numbers:

      Q. Solve:

      A. . The subtraction becomes addition, and the +4 becomes negative. Then, because you’re adding two signed numbers with the same sign, you find the sum and attach their common negative sign.

      Q. Solve:

      A. . The subtraction becomes addition, and the –5 becomes positive. When adding numbers with opposite signs, you find their difference. The 2 is positive because the +5 is farther from 0.

      

To subtract two signed numbers:

      27

      28

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      Multiplying Signed Numbers

      When you multiply two or more signed numbers, you just multiply them without worrying about the sign of the answer until the end. Then, to assign the sign, just count the number of negative signs in the problem. If the number of negative signs is an even number, the answer is positive. If the number of negative signs is odd, the answer is negative.

      

The product of two signed numbers:

      The product of more than two signed numbers:

        has a positive answer because there are an even number of negative factors.

        has a negative answer because there are an odd number of negative factors.

      

Q.

      A. Multiply the two factors without their signs, and you get 6. There are two negative signs in the problem, so the result is positive. The answer is +6.

      Q.

      A. There are three negative signs in the problem, so the result is negative. The product of the numbers (without their signs) is 24. The answer is –24.

      33

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      Dividing Signed Numbers

      The rules for assigning the sign of the answer when dividing signed numbers are exactly the same as those for multiplying signed numbers (see “Multiplying Signed Numbers” earlier in this chapter.) The rules do differ, though, because you have to divide, not multiply.

      

When you divide signed numbers, just count the number of negative signs in the problem — in the numerator, in the denominator, and perhaps in front of the problem. If you have an even number of negative signs, the answer is positive. If you have an odd number of negative signs, the answer is negative.

      

Q.

      A. There are two negative

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