get the additive identity. So
A. The additive inverse of 5 is –5. If you add –5 to the expression, you have
Q. Use a multiplicative identity to change the expression
A. Because the term
Notice how the distributive function works for you here!
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29 Use an additive identity to change the expression
30 Use a multiplicative identity to change the term –7x to one with only the variable factor.
31 Use a multiplicative identity to change the expression
Working with Factorial
The nonbinary operation called factorial is important in problems involving probability, counting items, and, of course, is a basic function used in algebra. When you see n!, you know to take the number n and multiply it by every natural number smaller than it is:
The number n must be a whole number. This means that 1! is rather redundant. There’s no natural number smaller, so
A particular challenge when working with factorials is to reduce fractions containing those functions. Basically, you find the common factors in the factorials in the numerator and denominator, eliminate them, and determine what’s left.
A. If these were just the two numbers 4 and 3, you would either leave it as is, because 4 and 3 don’t have any common factors other than 1, or you would write this as a mixed number. It’s different with factorials. Rewrite the fraction after expanding the factorial values.
Q. What is
A. Write out the factorials and reduce the fraction.
Q. What is
A. The value of
Q. What is
A. “Yikes!”, you say. I have to write out the product of all the numbers from 100 down to 1 and then from 97 down to 1? “No,” is the answer. You can take a shortcut. In the numerator, instead of writing from 97 down to 1, just use 97!. Here’s how it works:
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Applying the Greatest Integer Function
The greatest integer function is one of the nonbinary functions that is frequently used in algebra and its applications. This function is a method of rounding numbers. When you “round” a number to its nearest integer or tenth or thousandth or thousand, and so on, you move up or down to get to the closer value. With the greatest integer function, it doesn’t matter how close, it matters in which direction.
When rounding numbers, you determine what digits need to be dropped and whether the target place value or number goes up by 1 or stays the same.
Suppose you want to round
