Monday, November 10, 2014

GED Math Factorials, Permutation, Combinations | Videos

I recently helped a student with their GED math, and in particular GED math and factorials.  Until she showed me the section on factorials, I had no idea that concept along with permutations are important to understand.  To be even clearer, it was in the GED Science section of the GED learning video.

example of factorials


The learner was completely confused, and even though she read through and listened to the video, she still had no idea what the difference was between factorials, permutations, and combinations.  She also was baffled as to how they might relate to her in the "real world".

Being the teacher I am, I decided to Google these terms and search for any website that might offer a simple explanation.

exampe of finding combinations


I did find one... and that was Kahn Academy.  All the other websites had examples and explanations, but they were, in my opinion, still too complicated.  I was looking for a simple and easy way to try to break down the difference so that my students, who were preparing for their GED math test, might have a better understanding.

Having found, not one, but several videos on factorials, permutations, and combinations gave me a sense of relief.  I now have a resource for my students.  There are also several samples worked out through videos. 

As a teacher, watching those videos, I now have a better understanding of how to teach the difference.

I would highly suggest that if you are teaching your students these GED math concepts, you go to Kahn Academy and view these videos.

They helped me tremendously.... and I am anxious to meet with my student in a few days to share what I have learned.

You might be thinking... just TELL me... what IS factorials, permutations, and combinations!  In all honesty, I am still learning myself.  What I can tell you is once you view the videos.... perhaps even once or twice..... you will have a great understanding!  I also think that you will then be able to, in simple math language, explain to your learners, not only the difference but also give them examples.

Check out videos on factorials, permutations, and combinations!

Wednesday, October 08, 2014

Finding the Least Common Denominator of Three Fractions

The least common denominator of two or more fractions is the smallest number that can be divided evenly by each of the fractions' denominators.  You can determine the LCM (least common multiple)  by finding multiples of the denominators of the fractions.

Find the least common denominator of the following fractions:  5/12, 7/36, and 3/8.

8, 16, 24, 36
12, 24, 36
36

The least common denominator is 36.

Tuesday, October 07, 2014

Least Common Multiple

Find the least common denominator of 6, 8, 12.

6, 12, 18, 24
8, 16, 24
12, 24

The least common multiple is 24.

Monday, October 06, 2014

Help With GED Math Problems: Finding Lowest Common Denominator for Fractions

Building the LCD or lowest common denominators for two or more fractions can be challenging.  But it is an important skill for knowing how to add and subtract fractions and one that anyone studying their GED math test will need to know.

First step:  Take each denominator and factor to product of prime numbers.
Second step:  Build the lowest common denominator by using each factor with the greatest exponent.

What is the lowest common denominator for the following fractions: 7/12, 7/15, 19/30?  Use the product of prime factor method.

12 = 2 x 2 x 3 or 2^2 x 3
15 = 3 x 5
30 = 2 x 3 x 5

Build the lowest common denominator by using each factor (i.e. 2^2) with the greatest exponents.

If I were demonstrating the concept of building lowest common denominators to students, it would go something like this, " Let's start with the denominator twelve.  The denominator 12 needs at least two twos and a three.  The denominator fifteen needs a three, but because we have one from the twelve... we do not need to write another one.  However, the denominator twelve needs a five, so we need to add a five.  The denominator thirty needs a two... which we have so we do not need to add one. It also needs a three and a five, but because we already have both, again we do not need to add.  We have now build our LCD and all we need to do is multiply the factors together. So 2 x 2 x 3 x 5 = 60.  The LCD of 12, 15, and 30 is 60.

LCD = 2 x 2 x 3 x 5 = 60

Friday, October 03, 2014

Lowest Common Denominator

Find the lowest common denominator for the following fractions:  1/2, 1/4, 1/5

2, 4, 6, 8, 10, 12, 14, 16, 18, 20
4, 8, 12, 16, 20
5, 10, 15, 20

Because 20 is the first common multiple of 2, 4, and 5..... it is the lowest common denominator or LCD.

Wednesday, July 30, 2014

GED Math Test Prep: Area of Rectangle

GED Skill: Area of rectangles

You have decided to put carpet in your 10ft by 15 ft. living room. What is the area of carpet needed?

Answer: 10ft x 15ft = 150 cubic feet

GED Math Test Prep: Simplify the equation 3x + 7y - 2z + 3 - 6x - 5z +15

Simplify the following equation.

3x + 7y - 2z + 3 - 6x - 5z +15

Step 1:  Using the associative property, rearrange the terms of the equation so that "like" terms are next to each other.

3x - 6x - 2z - 5z + 7y + 3 + 15

Step 2:  Combine like terms.

-3x - 7z + 7y + 18

Monday, May 12, 2014

Using the Product Rule with Exponents

When you multiply constants (variables) that have the same base, you add the exponents... but keep the base unchanged.

For example:

x^2c · x^3 = x^(2+3) = x^5
(x · x) (x · x · x) = x^5

"X" squared times "X" cubed equals "X" to the fifth power.



Try a few more.

1)  p^5 · p^4 =
2)  2t^2 · 3t^4
3)  r^2 · 2^3 · r^5
4)  3x^2 · 2x^5 · x^4
5)  (p^2)(3p^4)(3p^2)


Answers:

1)  p^9
2)  6t^6
3)  2r^10
4)  6r^11
5)  9p^8

Thursday, May 08, 2014

Simplify and Solve Using the Addition Principal of Equality

4 ( 8 - 15) + (-10) =  x - 7




Answer:
4 ( 8 - 15) + (-10) =  x - 7
32 - 60 + (-10) = x - 7
-28 + (-10) = x - 7
-38 = x - 7
-38 + 7 = x -7 + 7
-31 = x + 0
-31 = x

Wednesday, May 07, 2014

Solving Equations Using the Addition Principle of Equality

Can you find the error in the following problem?


5² + (4 - 8) = x + 15
25 + 4 = x + 15
29 = x + 15
29 + (-15) =  x + 15 + (-15)
14 = x + 0
14 = x

Tuesday, May 06, 2014

Practice Solving Simple Equations Using the Addition Property of Equality

It is important to practice the addition property of equality.  See below and solve five simple equations using the addition property of equality.

Practice Problem #1
x - 11 = 41

Practice Problem #2
x - 17 = -35

Practice Problem #3
84 = 40 + x

Practice Problem #4
45 = -15 + x

Practice Problem #5
-21 = -52 + x


Answers:

Practice Problem #1
x - 11 = 41
x - 11 + 11 = 41 + 11
x + 0 = 52
x = 52

check

52 - 11 = 41
41 = 41

Practice Problem #2
x - 17 = -35
x - 17 + 17 = -35 + 17
x + 0 = -18
x = -18

check

-18 - 17 = -35
-35 = -35

Practice Problem #3
84 = 40 + x
84 + ( - 40) = 40 + (-40) + x
44 =  0 + x
44 = x

check
84 = 40 + 44
84 = 84

Practice Problem #4
45 = -15 + x
45 + 15 = -15 + 15 + x
60 = 0 + x
60 = x

check
45 = -15 + 60
45 =  45


Practice Problem #5
-21 = -52 + x
-21 + 52 = -52 + 52 + x
31 = 0 + x
31 = x

check
-21 = -52 + 31
-21 = -21

Monday, May 05, 2014

Solving Equations Using the Addition Property of Equality


The addition principle of equality states that if a = b, then a + c = b + c.
When you solve equations using this addition principle of equality, you need to use the additive inverse property.  In other words, you must add the same number to both sides of an equation. 
Example #1:
x - 5 = 10
x - 5 + 5 = 10 + 5   We add the opposite of (-5) to both sides of the equation.
x + 0 = 15                We simplify     -5 + 5 = 0.
x = 15                       The solution is x = 15
 
To check the answer, simply substitute 15 in for x, in the original equation and solve.
15 - 5 = 10
10 = 10
 
Example #2:
x + 12 = -5
x + 12 + (- 12) = -5 + (- 12)   We add the opposite of (+12) to both sides of the equation.
x + 0 = -17                    We simplify +12 - 12 = 0.
x = -17                           The solution is x = -17
Check our answer.
(-17) + 12 = -5
-5 = -5

Friday, April 11, 2014

Practice Percent Word Problem

A car which is normally priced at $25,437 is marked down 10%.  How much would Karen save if she purchased the car at the sale price?

Answer:  $2543.70

(Spanish translation coming soon...)

Tuesday, March 11, 2014

Practice Translating Algebraic Words Into Expressions: (Spanish & English)

1.  Twenty-one more than a number is 51. What is the number?

Veinte y uno más que el número es 51. ¿Cuál es el número?



2.  Thirty-seven less than a number is 45. Find the number.

Treinta y siete menos que el número es 45. Encuentre el número.

Answers:
1.  30
2.  82

Monday, March 10, 2014

Practice Translating Algebraic Words Into Expressions: (Spanish & English)

1.  The sum of a number and 50 is 73. Find the number.

La suma del número y 50 es 73. Encuentre el número.

2.  Thirty-one more than a number is 69. What is the number?

Treinta y uno más que el número es 69. ¿Cuál es el número?

3.  A number decreased by 46 is 20. Find the number.

El número que está reducido por 46 es 20. Encuentre el número.

Answers:
1.  23
2.  38
3.  66

Friday, March 07, 2014

Practice Translating Algebraic Words Into Expressions: (Spanish & English)

1.  The sum of a number and 28 is 74. Find the number.

La suma del número y 28 es 74. Encuentre el número.


2. Thirty-nine more than a number is 72. What is the number?

Treinta y nueve más que el número es 72. ¿Cuál es el número?

3.  Eighteen less than a number is 48. Find the number.
Dieciocho menos que el número es 48. Encuentre el número.
 
Answers:
1.  46
2.  33
3.  66
 

 

Thursday, March 06, 2014

Practice Translating Algebraic Words Into Expressions: (Spanish & English)

1.  A number increased by 21 is 52. Find the number.

El número que está aumentado por 21 es 52. Encuentre el número.


2.  Twenty-five more than a number is 68. What is the number?

Veinte y cinco más que el número es 68. ¿Cuál es el número?


3.  Forty-two more than a number is 58. What is the number?

Cuarenta y dos más que el número es 58. ¿Cuál es el número?

Answers:
1.  31
2.  43
3. 16

Wednesday, March 05, 2014

Practice Translating Algebraic Words Into Expressions: (Spanish & English)

1.  Twenty more than a number is 42. What is the number?

Veinte más que el número es 42. ¿Cuál es el número?
 

2.  Forty-three more than a number is 85. What is the number?

Cuarenta y tres más que el número es 85. ¿Cuál es el número?

3.  Twenty-two more than a number is 62. What is the number?

Veinte y dos más que el número es 62. ¿Cuál es el número?


Answer:
1.  22
2.  42
3.  40

Tuesday, March 04, 2014

Practice Translating Algebraic Words Into Expressions: (Spanish & English)

1.  The sum of a number and 26 is 42. Find the number.

La suma del número y 26 es 42. Encuentre el número.


2.  Thirty more than a number is 51. What is the number?

Treinta más que el número es 51. ¿Cuál es el número?


3.  Fifteen more than a number is 47. What is the number?

Quince más que el número es 47. ¿Cuál es el número?


Answer:
1.  16
2.  21
3.  32

Practice Translating Algebraic Words Into Expressions: (Spanish & English)

1. One-half of a number is 13. Find the number.

Una media de un número es 13. Encuentre el número. 


2.  A number decreased by 29 is 39. Find the number.

Un número que está reducido por 29 es 39. Encuentre el número.


3.  The sum of a number and 39 is 56. Find the number.

La suma del número y 39 es 56. Encuentre el número.

Answer:
1.  26
2.  68
317

Tuesday, January 28, 2014

Practice Translating Algebraic Words Into Expressions: (Spanish & English)

1.  A number increased by eight is 14. Find the number.

El número que aumenta por ocho es 14. Encuentre el número.


2.  Three less than a number is 2. Find the number.

Tres menos que el número es dos. Encuentre el número.



Answers:
1.  6
2.  5

Monday, January 27, 2014

Translating Words Into Algebraic Expressions Examples: (Spanish & English)

1.  Six less than a number is 9. Find the number.

Seis menos que el número es nueve. Encuentre el número.



2.  Ten less than a number is 9. Find the number.

Diez menos que el número es nueve. Encuentre el número.



3.  A number increased by seven is 12. Find the number.

El número que aumenta por siete es 12. Encuentre el número.



Answers:
1.  15
2.  19
3.  5




Friday, January 24, 2014

Easy Tanslating Algebra Word Problems: (Spanish & English)

1.  Seven more than a number is 11. What is the number?

Siete más que el número es 11. Encuentre el número.


2.  The sum of a number and six is 16. Find the number.


La Suma del número y seis es 16. Encuentre el número.



3.  A number diminished by 9 is 3. Find the number.

El número que reduce por nueve es tres. Encuentre el número.



Answers:
1.  4
2.  10
3.  12

Thursday, January 23, 2014

Translating Words into Algebraic Expressions Simple: (Spanish & English)

1.  A number diminished by 2 is 7. Find the number.


El número que reduce por dos es siete. Encuentre el número.



2.  A number decreased by 7 is 8. Find the number.

El número que reduce por siete es ocho. Encuentre el número.


3.  A number increased by three is 13. Find the number.

El número que aumenta por tres es 13. Encuentre el número.



Answers:
1.  9
2.  15
3.  10

Wednesday, January 22, 2014

Translating Simple Number Word Problems: (Spanish & English)

1. Six less than a number is 5. Find the number.

Seis menos que el número es cinco. Encuentre el número.


2. Six less than a number is 7. Find the number.

Seis menos que el número es siete. Encuentre el número.



3.  The sum of a number and three is 11. Find the number.

La suma del número y tres es 11. Encuentre el número.


Answer:
1.  11
2.  13
3.  8

Tuesday, January 21, 2014

Translating Word Problems Simple: (Spanish & English)

1. One-third of a number is 1. Find the number.

Un tercer del número es uno. Encuentre el número.


2. A number increased by five is 13. Find the number.

El número que aumenta por cinco es 13. Encuentre el número.



3.  One-third of a number is 2. Find the number.

Un tercer del número es dos. Encuentre el número.



Answers:
1.  3
2.  8
3.  6

Monday, January 20, 2014

Translating Simple Algebra Word Problems: (Spanish & English)

1.  Two more than a number is 8. What is the number?

Dos más que el número es ocho. ¿Cuál es el número?


2.  Three more than a number is 5. What is the number?

Tres más que el número es cinco. ¿Cuál es el número?


3.  A number decreased by 2 is 5. Find the number.

El número que reduce por dos es cinco. Encuentre el número.


Answers:
1. 10
2.  8
3.  7