By Bob Miller
A is for Algebra-and that's the grade you'll pull if you happen to use Bob Miller's uncomplicated consultant to the maths path each college-bound child needs to take
With 8 books and greater than 30 years of hard-core lecture room adventure, Bob Miller is the pissed off student's ally. He breaks down the complexities of each challenge into easy-to-understand items that any math-phobe can understand-and this absolutely up-to-date moment version of Bob Miller's Algebra for the Clueless covers every thing a you must comprehend to excel in Algebra I and II.
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Extra resources for Bob Miller's Algebra for the Clueless (Clueless Series)
S U B T R AC T I O N Next is subtraction. We sort of avoided the definition of subtraction, but now we need it. Integers Plus More 27 DEFINITION Subtraction: a − b = a + (−b) 6 − (+8) = 6 + (−8) = −2 Important: There are only two real subtraction problems: + + −7 − (−3) = −7 − (− 3) = −7 + (+3) = −4 What we are doing is changing all subtraction problems to addition problems. A number followed by a minus sign followed by a number in parentheses with a − sign in front of it. + − 8 − ( +2) = 8 − ( + 2) = +8 + (−2) = 6 A number followed by a minus sign followed by a number in parentheses with a + sign in front.
1 From 0 to −1 is down 1. −1 (+2)(+3) = +6 (+1)(+3) = +3 (0)(+3) = 0 (−1)(+3) = −3 −3 Answer goes down 3. −3 Answer goes down 3. −3 Product is −3, down 3. We just showed that a minus times a plus is a minus. By the commutative law, a plus times a minus is a minus. One more pattern: −1 −1 −1 (+2)(−3) = −6 (+1)(−3) = −3 +3 Answer goes from −6 to −3. Uppp 3!!!! +3 Answer from −3 to 0, again up 3. +3 From 0 to −1, down 1. Answer up 3. (0)(−3) = 0 (−1)(−3) = +3 We just showed that a minus times a minus is a plus.
ANSWER −17 EXAMPLE 8— −9 + 6 or 6−9 Signs are different. Subtract 9 − 6 = 3. The larger number without the sign is 9. The sign of 9 is −. ANSWER −3 EXAMPLE 9— 8 − 4 − 9 + 3 + 5 − 7 − 10 Add all the positives, 8 + 3 + 5 = 16. Add all the negatives, −4 − 9 − 7 − 10 = −30. Thennnn 16 − 30 = −14. EXAMPLE 10— 4a − 5b − 7a − 7b Add like terms: 4a − 7a = −3a; −5b − 7b = −12b. ANSWER −3a − 12b Just like the last chapter!!!! S U B T R AC T I O N Next is subtraction. We sort of avoided the definition of subtraction, but now we need it.
Bob Miller's Algebra for the Clueless (Clueless Series) by Bob Miller