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

Автор: Mary Jane Sterling

Издательство: John Wiley & Sons Limited

Жанр: Математика

Серия:

isbn: 9781119843061

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СКАЧАТЬ rel="nofollow" href="#fb3_img_img_578b8401-4a42-579d-8113-bdf81463aad4.png" alt="math"/>. This is by definition. The value of 0! is designated as being 1. This result doesn’t really fit the rule for computing the factorial, but the mathematicians who first described the factorial operation designated that 0! is equal to 1 so that it worked with their formulas involving permutations, combinations, and probability.

      Getting the most for your math with the greatest integer

      You may have never used the greatest integer function before, but you’ve certainly been its victim. Utility and phone companies and sales tax schedules use this function to get rid of fractional values. Do the fractions get dropped off? Why, of course not. The amount is rounded up to the next greatest integer.

      

The greatest integer function takes any real number that isn’t an integer and changes it to the greatest integer it exceeds. If the number is already an integer, then it stays the same.

      The symbol for the greatest integer function is a set of brackets, math. You put your number in question in the brackets, evaluate it, and out pops the answer.

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Q. Find the absolute value: math

      A. math. The distance from –4 to 0 is 4 units.

      Q. Evaluate: math

      A. math. You perform the operation inside the absolute value bars before evaluating.

      Q. Evaluate 3!

      A. math

      Q. Evaluate 6!

      A. math

      Q. Evaluate: math

      A. math. The number 6 is the biggest integer that is not larger than math.

      Q. Evaluate: math

      A. math. Just picture the number line. The number –3.87 is to the right of –4, so the greatest integer not exceeding –3.87 is –4. In fact, a good way to compute the greatest integer is to picture the value’s position on the number line and slide back to the closest integer to the left — if the value isn’t already an integer.

      15yourturn Determine which is greater: math or 3!

      16 Determine which is greater: math or math.

      17 Determine which is greater: 5! or math.

      What is a binary operation? A bicycle has two wheels. A biannual term lasts two years. And a binary operation requires two numbers. These operations are performed on two numbers — one written before the operation symbol and one after. Addition and subtraction are pretty familiar, but the multiplication and division symbols come in several varieties.

      Adding signed numbers

      If you’re on an elevator in a building that has four floors above the ground floor and five floors below ground level, you can have a grand time riding the elevator all day, pushing buttons, and actually “operating” with signed numbers. If you want to go up five floors from the third sub-basement, you end up on the second floor above ground level.

      You’re probably too young to remember this, but people actually used to get paid to be elevator operators and push buttons all day. I wonder if these people had to understand algebra first.

      Adding like to like: Same-signed numbers

      When your first-grade teacher taught you that math, 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:

math