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Math 010 – Lots of math. October 2, 2013. Announcements. If you were absent last class, sign up for a conference time. This is required and worth 8 quiz grades! Check your RIC e-mail Quiz today will be on today’s material. Recap from Monday: Rounding. - PowerPoint PPT Presentation
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Math 010 – Lots of mathOctober 2, 2013
AnnouncementsIf you were absent last class, sign up for a conference time. This is required and worth 8 quiz grades!
Check your RIC e-mail
Quiz today will be on today’s material
Recap from Monday: RoundingFind the digit in the place you are trying
to round to. This will be the last digit.This digit will either stay the same, or
round up. To figure out which, look at the digit to the right.5 or greater: round up4 or less: round down (stay the same)
If you need to round up a 9, change it to a 0 and increase the digit to the left by 1.
Rounding examplesRound $4.256 to the nearest cent, that is the
nearest hundredth.So our last digit will be in the hundredths
place.Will the 5 round up or down?6 ≥ 5, so $4.256 to the nearest cent is $4.26
Round 3.71 to the nearest tenth.So our last digit will be in the tenths place.Will the 7 round up or down?1 < 5, so 3.71 to the nearest tenth is 3.7
Rounding up from a 9Round 2.495 to the nearest hundredth.
Last digit will be in the hundredths place.Does the 9 round up or down?9 becomes a zero. Increase the tenths place by
1.2.50 = 2.5
Round 6.9997 to the nearest thousandth.Round up the 9, look at digits beforeTip: 6.999 + 0.001 = 7.000 = 7
Does rounding a decimal keep the number the same, or change it?The purpose of rounding is to get an
approximation of a number.We want an approximation when we don’t need
the exact value, just something close.π = 3.14159265….. but we round to the
nearest hundredth and say π ≈ 3.14, or “Pi is about 3.14.”
We don’t know what π is exactly, so we have to round.
So technically, the value of the decimal does change.
3.6 - Complex Fractions (Fractions inside fractions)
Do you remember what the fraction bar means?
A fraction bar means division.
Working from the inside outFirst need to perform the operations inside
the numerator and the denominator
Then it becomes a simpler complex fraction
Now it becomes a fraction division problem
numerator denominator
3.6 - Taking the square of a fractionWhat is Squared means multiplied by itself.So, = “One half of one half is one fourth”What is ? =
4.6 – Graphing Inequalities
Meanings of inequalities
(A) The minimum value of x is -2, and x is less than 3.
(B) x is between -4 and 2.(C) The minimum value of x is -2.(D) x is less than 3.
5.1 Properties of Real Numbers
Commutative Property of Additiona + b = b + a
Commutative Property of Multiplicationab = ba
Associative Property of Addition(a + b) + c = a + (b + c) = a + b + c =
(a + b + c)Associative Property of Multiplication
(ab)c = a(bc) = abc = (abc)
5.1 - More Properties (p. 308)Addition Property of Zero
Any number plus zero is that number. 8 + 0 = 8Multiplication Property of Zero
Any number times zero is zero. -9(0) = 0Multiplication Property of One
Any number times one is that number. 5(1) = 5Inverse Property of Addition
a + (-a) = 0Inverse Property of Multiplication
a= 1
Now let’s do some algebra.
Don’t get scared/angry! We can use our properties here.
3x(y)(4) + 2x + 5y – 7x
Using the multiplication propertiesRule of thumb: Constants (numbers) go before variables (letters).
5 (4x) = (5 4)x = 20x∙ ∙(5y)(3y) = 5 y 3 y = 5 3 y y = (5 3)(y ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙
y) = 15-9 (6y) = (-9 6)y = -54y∙ ∙(7x)(-5y) = (7)(-5)(x)(y) = -35xy(-20)(-c) = (-20)(-1c) = (-20 -1)(c) = 20c∙(-8)(-x) = (-8)(-1x) = (-8 -1)x = 8x∙
Using the addition properties-4t + 9 + 4t = -4t + 4t + 9 = (-4t + 4t) + 9 = 0 + 9 =
9
5 + 8y + (-8y) = 5 + 0 = 5
-5y + 5y + 7 = -5y + 5y + 7 = 0 + 7 = 7
-3z + 8 + 3z = -3z + 3z + 8 = 0 + 8 = 8
The Distributive PropertyUsed to remove parentheses from a variable
expressiona(b + c) = ab + ac
2(3 + 5) = 2(8) = 162(3) + 2(5) = 6 + 10 = 16
3(5a + 4) = 3(5a) + 3(4) = 15a + 12-4(2a + 3) = -4(2a) + -4(3) = -8a + (-12) =
-8a -12-5(-4a – 2) = -5(-4a) – (-5)(2) = 20a + 106(5c – 12) = 6(5c) – 6(12) = 30c - 72
5.2 – Simplest Form: TermsA term of a variable expression is one of the addends.
Terms are added together. has four terms. What are they?
, , , and The constant in each term is called the coefficientWhat is the coefficient of each term in ?4, -3, 1, -9The first three terms are variable terms9 is a constant term
Simplify by adding like termsWhat is 3x + 2x?Think about cats – or something else3 cats plus 2 cats is 5 catsSo, 3x + 2x = 5xMatch terms that have the same variable
part
10y - 5y = 5y3xy - 4xy = -1xy = -xyConstant terms also add together5 + 9 = 14
Simplify: 6a + 7 - 9a + 3It helps a lot to rewrite subtracted terms as addition of
a negative term. This way they can move around freely.6a + 7 + (-9a) + 3
Next, rearrange terms so like terms are together.6a + (-9a) + 7 + 3
Now, add like terms.-3a + 10
Simplify: 9y - 3z - 12y + 3z + 2Can change to 9y + (-3z) + (-12y) + 3z + 2
Group like terms: 9y + (-12y) + (-3z) + 3z + 2
Add like terms: -3y + 0z + 2
-3y + 2
Simplify:
Rewrite:
Group like terms:
Add like terms:
Simplify with Distributive ppty5x + 2(x + 1)Distribute:5x + 2x + 2Like terms already together, so add
them:7x + 2
One more of these9n – 3(2n – 1)Distribute:9n – 3(2n) – 3(-1) = 9n – 6n – (-3) = 9n – 6n +
3Add like terms: 3n + 3Keeping track of negative signs is important
Topics to know so far for the EXAMComplex fractionsTaking the square of
fractionsDecimals – order
relationConvert decimals to
fractionsRounding decimalsSet up decimal
addition, subtraction, multiplication
Solve equations with
decimalsSquare rootsGraphing inequalitiesWhat inequalities
meanSimplifying
expressions with all properties
Need help? E-mail me or stop by office before class
Quiz #7Show work & answers on a sheet of paper.
You can leave when you’re done.
1) Evaluate 2) What is one-third squared?3) Simplify: 3(2a + 4b)4) Simplify: x + 2x + 3 + 45) How well did you understand today’s
lesson?