47 -14i
You can work this out in the straight-forward way, or you can recognize that (6-i) is a common factor. In the latter case, you have ...
... = (6-i)(5 + 3-i)
... = (6 -i)(8 -i)
This product of binomials is found in the usual way. Each term of one factor is multiplied by each term of the other factor and the results summed. Of course, i = √-1, so i² = -1.
... = 6·8 -6i -8i +i²
... = 48 -14i -1
... =
_____
A suitable graphing calculator will work these complex number problems easily.
Answer to the first question: 7/10ths of a mile
Explaination: When adding fractions, you need to have a common denominator. Since dividing 3/10 by 2 to get a denominator of 5 makes 3 a decimal, it's easier to multiply 2/5 by 2 to get a denominator of 10. You do the same to the top that you do to the bottom: . From there, just add 4/10 and 3/10 to get the answer: 7/10ths of a mile.
Answer to the second question: Daniel read three (3/10) more books
Explaination: Since you can't evenly multiply 5 or 2 to get the opposite number, it's easier to multiply to the lowest common multiple. The easiest way to find that is to multiply both denominators (5*2=10). You'll have to multiply the numerator by the same amount you multipled the denominator by. For Daniel, that would mean: . For Edgar, that would mean:
. So, Daniel read 3 more books than Edgar.
Answer to the third question: 2/4 mile (or 1/2 a mile)
Explaination: 2/8 can be simplified, by dividing the top and bottom by 2, resulting in 1/4. Since both fractions have the same denominator (/4), you can add them to get 2/4ths. This can be simplified further to half (1/2) a mile.
