algebraic expressions and equations convert units of measurements formulas solving inequalities...
TRANSCRIPT
Algebraic Expressions and Equations
Convert units of measurements
Formulas
Solving Inequalities
Problem Solving
Proportions Review
A car can travel 300 miles on 15 gallons of gas. How many gallons of gas are needed to travel 50 miles?
I can text 100 words in 4 minutes. How many minutes will it take me to text a message that has 1500 words?
P.56 # 1
p. 57 # 4 & 5
Convert between Metric and US
The SI unit is the international accepted model of measurement in the world. However, it is not utilized in the US.
p. 58 Charts the measurements and conversions.
a) Length
b) Capacity/Volume
c) Mass
Steps to change ……
Example 1: If a person is 140 centimeters tall, how many inches tall are they? (Round to two decimal places)
Know
Measurement given
Measurement desired
Example 2: Capacity/Volume
If Bill drank 4 quarts of water, how many liters is that?
Given 1 liter (L) = 1.057 quarts (qt) Plan:
Temperature
You have decided to go to Canada for the weekend and the meteorologist describes a brisk 4oC. Should you wear shorts or head back to Orlando?
Hint: F = 9/5 c + 32 or C = 5/9(F – 32)
Formulas
A list of formulas to remember and know
Shapes: rectangle (perimeter) P = 2L + 2W
Rectangle (area) A = lw
Triangle (area) A = ½ bh
Cylinder (Volume) V = πr2h
Money: Sale = Original – discount
Interest = (Principal)(Interest Rate)(Time)
Manipulating Formulas
Solving in terms (explicitly) for a variable refers to isolating the variable in question.
Example: solve for w
A = lw to get w by itself we need to remove the l
A/l =lw/l Then divide/cancel the variable.
A/l = w
Practice
Solve for h given V = πr2h What is the arithmetic relationship between pi,
r and h? How do we undo the operation Solve
p. 66 and 67 #1, 4, 7,9
Inequalities
Symbol Terms/Words
< is less than
< is less than or equal to
no more than
> Is greater than
> is greater than or equal to
at least
Graphing Inequalities
X < 3 means all numbers that are smaller than 3 but does not include 3
Y > -1 all numbers greater than –1 and including –1
P.69
Solving Inequalities
The objective in algebra is always to isolate or define the unknown variable.
To solve for an inequality we need to move the numerical value to one side of the inequality and the variable to the other side.
Solving compound inequalities
Solve the same as one inequality, but apply the steps for both sides
-5< x + 4 < 14
p.72 Example 3p.73-74
Applications
READ, READ, READ Circle/highlight the question What are key words (underline, highlight,
circle) Determine plan to solve the problem Test or solve Check the numerical result with the question.
Does it make sense?
A pair of jeans is priced at $50, but is on sale for 25% off. What is the sale price of the jeans? What do we want to solve for? What does the first number represent? What is the second number? How to approach or solve? Does the answer describe what is asked for?
What amount should I invest at 5% simple interest to yield $200 in interest in 8 years? I = PRT What is the unknown variable in the problem?