example how to simplify integer expressions
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Answers:The easiest way to work it is to assign two variables. Let F = the cost of a football Let B = the cost of a basketball "A football and a basketball cost $65.00" means: F + B = 65 "A football costs $5.00 more than 1/2 of the basketball" means: F = 5 + B/2 We can rewrite the first equation by subtracting F from both sides: B = 65 - F This lets us substitute "65 - F" in place of B in the second equation: F = 5 + (65 - F)/2 Multiply both sides by 2: 2F = 10 + (65 - F) Simplify: 2F = 75 - F Add F to both sides: 3F = 75 Divide by 3: F = 25 So a football costs $25 Sanity check: If a football is $25, then a basketball should be $65.00 - $25.00 = $40.00 Using 25 for F and 40 for B, does our second equation still work? Yes. 25 does equal 40/2 + 5.
Answers:When simplifying any equation remember this: Please Excuse My Dear Aunt Sally Parentheses, Exponents, Multiplication, Division, Addition, Subtraction This is the order of simplification so for you first example the first thing to do is to get rid of the parentheses by distributing the 4 to both numbers inside. -12z + 4z -36 + 30 + z there are no exponents so you can skip that step, also there is no mult. or div. so the next thing to simplify is add/ sub. Remember, you can only combine like terms so no mixing up numbers with variables. All items with a "z" we can combine together. -12z +4z +z = -7z now all you have left is the +30 and -36 which you then combine together to get -6. now we cannot combine the last two tems so just put them together and get -7z -6. some teachers do not like the first term to be negative so to change that it would be 7z+6 all right now given these rules see if you can figure the next one on your own
Answers:-4x / 3xy^2 = -4 / 3y^2 [Because the x in the denominator (bottom bit) cancells with the x in the numerator (top bit) But that's all that can be done with it. As for the rules if you google for them you'll find them Here's a powerpoint version thats pretty good: http://www.ltscotland.org.uk/Images/therulesofindices_tcm4-123386.ppt It doesn't give the rule for fractional exponents because thats in another presentation which wasn't listed and I'm too lazy to try and find it but this rule might help: (a^m)^n = a^(mn) is used to help evaluate terms with fractional exponents a^(p/q) means the qth root of a^p So a^(p/q) means (a^p)^(1/q) but to simplify stuff its probably better to think of it as meaning [a^(1/q)]^p because this is easier to evaluate without having to use a calculator. When you have a fraction raised to an exponent the exponent refers to both the numerator and the denominator of the fraction For example (8/27)^(2/3) = [8^(2/3)] / [27^(2/3)] = [8^(1/3)]^2 / [27^(1/3)]^2 = 2^2 / 3^2 = 4 / 9 Not sure if that'll help ... hope it does.
Answers:You can use Boolean Algebra for this and what is called Karnaugh Mapping. http://en.wikipedia.org/wiki/Karnaugh_map The purpose of the karnaugh map is to reduce or simply the amount of logic gates needed in a circuit.