Graphing Inequalities

Today we began inequalities.  An inequality says that two quantities are not equal. Click on inequality for more explanation.

We learned how to write an inequality to represent a situation such as:

Situation:  My classroom can hold no more than 30 students.
Inequality:   s < 30   The number of students can be less than or equal to 30.

Situation:  The waiting room has at least 15 people in it.
Inequality:   p > 15    The number of people in the waiting room is 15 or more people.

We also learned how to graph inequalities.  If the inequality is < or > then you would use an open circle because the solution does not include the value.  If the inequality is < or > then you would use a closed circle because the solution does include the value.

Here are some examples.

Tuesday we will solve 1-step inequalities and graph the solutions.

Images used from Google images.

Week of Oct. 13th

We have now completed 7 weeks of school, that is hard to believe.  This week we will learn about 1-step inequalities and 2-step equations.  Last week we began with 1-step equations with addition and subtraction then multiplication and division.  This week we will put both steps together.

Monday and Tuesday:  1-Step Inequalities
- We will begin by learning how to graph inequalities and then we will solve them.

Wednesday and Thursday:  Solve 2-Step Equations
- We will put our knowledge of 1-step equations with add/subtract and multiply/divide and put them together.

Friday:  Right now the plan is to create equations and inequalities from word problems and solve them.  This plan may change.


Bonus Question of the Week:
A physical therapist earns $87,000 annually. The therapist owes 6.2% of her earned wages for social security tax. She also owes 1.45% of her earned wages for Medicare tax.

What are the physical therapist's total payroll deductions for social security tax and for Medicare tax for the year?

Copy the problem, solve, and turn in by Friday, Oct. 17th for 10 extra bonus points.

Solving 1-Step Equations

In order understand 1-step equations you need to understand four vocabulary words:
Variable, Constant, Expression, and Equation.  Click on the word for its definition.

1-Step Equations are equations that require only one step to solve.  For all equations we have one goal in mind and that is to get the variable by itself.  For an equation involving addition you add the opposite of the number with the variable to get the variable by itself.  If the equation involves subtraction you LCO the problem and then add the opposite.  For equations involving multiplication and division you don't add the opposite but you do the opposite.

Examples:

Addition:
          x + 5 = 9
x + 5 + (-5) = 9 + (-5)    Add the opposite
                x = 4

Subtraction:
             m - 8 = -4
        m + (-8) = -4     LCO
  m + (-8) + 8 = -4 + 8     Add the opposite
                   m = 4

Multiplication:
       4g = 12

      4g  =  12     Since you have a multiply by 4 you do a divide by 4 to get the variable by itself.
       4        4
         g = 3

Division:
       h  = -7
       5

 (5)  h  = -7 (5)   Since you have a divide by 5 you do a multiply by 5 to get the variable by itself.
       5

        h = -35

October 3, 2014 - Sales Tax, Discount, and Tip

Thursday, we discussed how to find percent of a number, today we learned how to apply what we learned.

Sales Tax - a percentage of the total purchase that is added to your purchase.  In Huntsville our tax rate is 8.25% of your purchase.

Example:
Ms. Acton spent $205.60 at Target. If the sales tax is 6%, what was her final bill?

The first thing you do is determine the percent question being asked:

What is 6% of $205.60?

.06 x $205.60 = 12.336  We round this amount to the nearest cent, $12.34 and add that amount to the amount Ms. Acton spent.

$205.60 + $12.34 = $217.94

Her final bill was $217.94.

Discount - a percentage of the total purchase that is subtracted from your purchase.

Example:
Macy's is having a one-day 35% off special. If Sara bought $124.50 worth of items, what would the final bill total after applying the discount of 35%?

So what is the percent question:  What is 35% of $124.50?

0.35 x $124.50 = 43.575 = $43.58 is the amount of discount.  You subtract this amount from $124.50.

$124.50 - $43.58 = $80.92   Sara's final bill is $80.92.

Tip (gratuity) - a percentage of your bill at a restaurant that you leave for the wait staff.

Example:

The Kerwoods went out to eat at Chille's. If there bill was $58.65 and they gave their server a 15% tip, how much did they pay altogether?

The question is What is 15% of $58.65?

0.15 x $58.65 = 8.7975 = $8.80 is the amount of tip the Kerwoods should leave.  Now the question asks how much did they pay all together?  So you need to add the bill total and the tip together.

$58.65 + $8.80 = $67.45 is the total amount spent by the Kerwood family at Chille's.

October 2, 2014 - Percent of a Number

Today, in class we learned how to calculate percent of a number.  This topic, in my opinion, is one of the most important topics a student can learn.  Percent of a number is calculated for us all the time:  sales tax, discount, a tip at a restaurant, interest rates etc.

Percent of a number questions come in the form of questions like:   What is 40% of 80?

I discuss with the students that this is a Language Arts style question.  We need to translate this into a mathematical question.

  What   is 40% of 80?         translate into
______ = 40%  x  80

The What is a blank, is means =, and of means multiply.  We are using calculators in class so they multiply 40% by 80.  There is only one problem, our calculator, the TI-83, does not have a percent key.  TI assumes that if you are smart enough to use their calculator you are smart enough to know how to type a percent into the calculator.  All you do is change the percent into a decimal by moving the decimal 2 places to the left.

_ 32    = .4 x 80

Here are a couple more examples.

What is 25% of 75?   -   .25 x 75 = 18.75
What is 15% of $120?     -     .15 x 120 = $18
What is 0.5% of 12?     -     0.005 x 12 = 0.06
What is 140% of 8?     -     1.4 x 8 = 11.2

Sept. 30, 2014 - Convert Fractions to Decimals to Percents

Tuesday, we added one more conversion, convert fractions to decimals and then to percents.  So what is a percent?  Percent is a comparison to 100.  We have already learned to convert a fraction to a decimal, divide the numerator by the denominator (top in bottom out).  To convert a terminating decimal to a fraction you say it correctly using place value and a repeating decimal you do the "9-Thing."

To convert a decimal to a percent you just move the decimal 2 places to the right and add a percent sign.

examples:
0.25 = 25%
1.5 = 150%

To convert a percent to a decimal you move the decimal 2 places to the left and take off the percent sign.

examples:
46% = 0.46
125% = 1.25

The hardest thing to remember is which way you move the decimal.  We think about Dr. Pepper to helps us remember.  Dr. Pepper means to change a decimal to a percent you move the decimal to the right D to P.  To convert a percent to a decimal you move the decimal to the left which is P to D.  You always move the decimal 2 places because there are 2 zeros on 100.

Students will have to give the missing values when given either the fraction, the decimal, or the percent.

    Fraction         Decimal            Percent   
      3/4                  .75                   75%  

     1  65/100        1.65                  165%  
     1  13/20  


        4/5                 0.8                   80%

Sept. 29, 2014 - Convert Decimals to Fractions

Monday, we learned to convert terminating and repeating decimals into fractions or mixed numbers.  First, let's have some definitions.

terminating decimals - decimals that stop. They do not repeat.  When dividing you have a remainder of 0.
examples:  0.25,  3.674

repeating decimals - decimals that repeat a number or series of numbers continually. To write a repeating decimal, you write the number or series of numbers that repeat one time and put a bar on top of the numbers that repeat.
                   __      __
examples:  0.5,   4.45

To convert a terminating decimal to a fraction you just say the decimal correctly using place value.

examples:
0.6 = 6/10 = 3/5
4.75 = 4  75/100 = 4  3/4

To convert a repeating decimal, where the entire decimal is repeating, you do what we call the "9-thing."
You put the decimal as the numerator and for each digit that is repeating in the decimal you put a 9 in the denominator.

examples:
  __
0.5 =    5/9
   __
0.63 =  63/99 = 7/11
   ___
5.363 = 5  363/999 = 5  121/333