Algebra-Math 101

When you think of a decimal that has 2 decimal places .05 think of $$Money$$

• • Think of these as money:

• • .50 = 1/2 Dollar or 50 cents

  • .25 = Quarter or 25 cents

  • .10 = Dime or 10 cents

  • .05 = Nickle or 5 cents

I always like to think of decimals as money because money is something we use every day.

• Now let's put these same decimals into a %

  • .50 = 1/2 a Dollar = 50% for a % you usually have 2 decimal places .50 = 50% = a half

  • .25 = 1/4 or a Quarter = 25%

  • .10 = 1/10 or a Dime = 10%

  • .05 = 5/100 or a Nickle = 5%

• Decimals to % = drop the . and add a %

  • .05 = 5%

  • .10 = 10%

  • .25 = 25%

  • .50 = 50%

You can see why 50 cents = 1/2 a dollar, 25 cents = 1/4 a dollar, etc.

The main thing is to have some numbers that are common sence to you. Money is common sence to me because we use it and think about it every day.

FOIL - First, Outside, Inside, Last

To watch a Khan Academy video on it https://www.youtube.com/watch?v=IWigvJcCAJ0

Quadratic Calculator (note if a denominator is a fraction then it is 3/7 =(7x-3) https://www.mathpapa.com/quadratic-formula/?q=2x%5E2-5x-3%3D0

To check your work with a Quad Equ Calculator http://www.math.com/students/calculators/source/quadratic.htm

When Foil doesn't work - or looks too hard - Dan Lamay has a great AC factoring video https://www.youtube.com/watch?v=8gpP4jkTVnA&feature=youtu.be

• GCF Learn Free.org- has videos for Computers, Reading, Math and more!!http://www.gcflearnfree.org/math

• Great Video on Decimals and Fractions in the Math section

• Education Portal - 18 FREE Courses http://education-portal.com/ Math, Calculus, English, Business, etc.

• Exponents - To the Power OF a Logarithm is how to solve for exponents of more than 2 (which is the square root)

• Logarithm - http://education-portal.com/academy/lesson/what-is-a-logarithm.html

• Calculators - Check your Answer http://www.expertmathtutoring.com/Factorize-Expand-Functions.php

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How long will it take a bus traveling 60 miles per hour to overtake a car traveling at 40 mph if the car had a 1.5 hour head start?

This is a good question, and actually one you think about every time you get into your car. When you have to drive any distance you may say to yourself. How long will it take to get me there? OK if you have to drive 100 miles and you are on the highway that has a speed limit of 50 miles per hour 100 miles divided by 50 miles per hour = 100/50 = 2 hours Now let's apply that same concept to our problem. We can break it up into the BUS and the CAR. The Bus travels at 60 miles per hour or 60mp, while the car travels at 40 miles per hour. You can say the Bus travels faster than the car 60mph to 40mph or 60/40 = 1 1/2 The BUS travels 1 1/2 times as fast as the car.

• The car has 1 1/2 hour head start = since the car travels at 40mph in 1 1/2 hours the car has traveled 40*1.5 = 60 miles

• The car has a 60 mile head start on the bus. When will the Bus catch up?

• When the bus begins the bus is a mile 0 and the car is at mile 60 let's make a grid/table to see this work:

so we know from the above that after 3 hours the faster bus has caught up with the slower car that got a 1 1/2 hour head start.

How do we put this in an equation???

• We use the Formula: Distance = Rate * Time or d=rt

• The car has a 1 1/2 hour head start, so we have to add the 1 1/2 or 1.5 extra hours to the travel

• time = t to t + 1.5 or if it is easier with fractions t = 3/2

• 60t = 40 (t + 1.5)

• 60t = 40t + 40(1.5)

• 60t = 40t + 60

• 20t = 60

• t = 60/20

• t=3 , time = 3, time = 3 hours, In three hours the faster Bus will catch up with the slower Car that got a 1.5 hour lead.

So when you compare what you got t equal to and what our common since grid at the top of the page they are the same. I hope this helps you to think about math problems in real life and how you set them up in a math problem. It takes practice to make this process internal. Purple Math has other Distance or d=rt problems, distance = speed * time http://www.purplemath.com/modules/distance.htm

Ratio

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Linear Algebra - Open Source Text Book: A First Course in Linear Algebra http://linear.ups.edu/html/fcla.html

Rate of Growth or Rate of Decay

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You are looking for GROWTH, and to find Growth you have to use Exponents - that was what they were created for.

If you are looking to estimate the growth of a population, germs in a Petri dish, or how much interest you will make - you need exponents.

Here is a great web site that explains the Exponential Growth & Exponential Decay http://www.regentsprep.org/regents/math/algebra/ae7/expdecayl.htm

Now you have to take your data and break it down so it will fit into this formula

The population of Disneyland was 2.3 billion, one hundred years ago.

Currently, the population is 3.2 billion.

Exponential Growth forumla is: y=a(1+r)^x

where:

a = initial amount before measuring growth/decay = 2.3

r = growth/decay rate (often a percent) = What we are solving for

x = number of time intervals that have passed = 100

y = Final Growth ................................ = 3.2

let's plug the numbers in:

y=a(1+r)^x

3.2 = 2.3(1+r)^100

it is easier if you have a calculator that can do logs

if not you can use this

Growth Calculator http://www.miniwebtool.com/exponential-growth-calculator

Logarithm Calculator http://www.rapidtables.com/calc/math/Log_Calculator.htm

Now that we know the Rate of Growth , we can calculate

What will this population be 100 years from now.

we use the same formula

Exponential Growth forumla is: y=a(1+r)^x

where:

a = initial amount before measuring growth/decay

r = growth/decay rate (often a percent)

x = number of time intervals that have passed

y = Final Growth

Notice at the bottom of the calculator - it has a link to the

Exponential Decay Formula

You can use this to find the answer - but then you have to find HOW you got that

Exponential Decay is essentially the same formula except you SUBTRACT the Rate

y=a(1-r)^x

This is the formula you need to use for the second half of your question.

I like Khan Academy to explain concepts here are his videos on Decay & Growth https://www.khanacademy.org/math/trigonometry/exponential_and_logarithmic_func/exp_growth_decay/v/word-problem-solving--exponential-growth-and-decay

Celcius and Fahrenheit

http://www.manuelsweb.com/temp.htm

°F = °C x 9/5 + 32

°C = (°F - 32) x 5/9

Order of Operations

... Math is Fun website has a nice layout explaining this, with Great Examples! https://www.mathsisfun.com/operation-order-pemdas.html

The rules are:

• P - Do thing in Parentheses first

• E - Exponents, Powers, Roots next

• MD -Multiply or Divide

• AS - Then Add or Subtract ... Left to Right

• Referred to as PEMDAS

Here is one example ... but the above link has lots more. Plus there are times when you can work one-on-one with an eTutor and we can work together - right on the white board. My hours this semester are Tues 8am-10:30am Check the schedule any Math eTutor can help you with Order of Operation.

• Right: 4 + 6 x 3 = ? Rule: Do multiplication before Addition 6 x 3 = 18 + 4 = 22 <-- Right

• Wrong: 4 + 6 x 3 = ? Didn't apply rules just went from L to R 4 + 6 = 10 x 3 = 30 <-- Wrong

You can also watch many great videos explaining Order of Operations from Khan Academy https://www.youtube.com/watch?v=ClYdw4d4OmA and PEMDA https://www.youtube.com/watch?v=piIcRV2dx7E

LeeAnn's Tutoring

http://ehs.ccsuvt.org/academics/math/mrs-smith/algebra-1-200/

Parabolas

Khan Academy Video https://www.khanacademy.org/math/algebra/quadratics/parabolas-intro-alg1/v/parabolas-intro

Parabola Calculator https://www.symbolab.com/solver/parabola-equation-calculator/2x%5E%7B2%5E%7B%20%7D%7D%20-1