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.

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?