GED Math: Simplifying Algebra Expressions Disributive Property

I have found that one of the most difficult math concepts for GED students to understand and grasp is the concept of combining like terms, expecially those involving the Disributive Property.

I am beginning to understand that unless the learner has an almost perfect understanding of adding, subtracting, multiplying, and dividing integers (positive & negative), the process of simplifying expressions, along with the Distributive Property, is very difficult.

Students also need to have their basic math facts memorized. Many will come in understanding and knowing the basic facts of adding and subtracting. But when asked to multiply and divide.... that can be more challenging. Have them practice their facts, outside of class, using worksheets.

Even with a good grasp of integers and basic math facts, most students will need to take the concepts of the distributive property, combining like terms, and solving expressions one step at a time.

One important method is to teach a "small learning concept" and then give them a LOT of practice. For example, I taught the distribute property and went through about 7 examples. I then followed up with a worksheet containing 20 more examples! Although it seems like alot, and perhaps you might think way too much..... my students want the extra practice.

Once they understand the Distributive Property, I will then proceed and teach the combining of like terms. Here again, it will take a LOT of examples..... followed by a worksheet.

Sally wants to bake cookies and the recipe calls for 2 1/2 cups of flour. She looks in her pantry and finds that she only has 1 1/4 cup. How much flour does Sally still need?

a. 2 1/2 + 1 1/4
b. 2 1/2 - 1 1/4
c. 2 1/2 x 1 1/4
d. 1 1/4 - 2 1/2

answer: b

Check out www.WorksheetsDirect.com for other great math worksheets!

Susan is planning on attending college. The tuition including room and board is $15, 423.00 for the school year. If she receives $9, 420.00 in assistance, how much does she still need to pay? What percentage of the total cost will she need to pay?

Solution: This problem is asking for two answers. To answer the first question, you need to take the total tuition and subtract the assistance. $15, 423.00 - $9420.00 = $6003.00

Susan will need to pay $6003.00.

To answer the second question (what percentage of the total tuition will Susan pay), you need to translate it into a question, then solve.

$6003.00 is what percentage of $15, 423.00?

$6003.00 = Wp x $15, 423.00

$6003.00 ÷ $15, 423.00 = 0.3892 which is 38.92%

Susan will need to come up with almost 40% of the cost of tuition.

GED Math: Basic Math Facts

The arithmetic facts (addition, subtraction, multiplication, division) are the building blocks of math. Knowing your basic facts well..... creates the foundation needed to succeed in learning GED Math.

Free math flashcard download.


**The answer to an addition problem is the SUM.

**The answer to a multiplication problem is called the PRODUCT.

Learn the fact families of addition and subtraction together.

3 + 4 = 7
4 + 3 = 7

7 - 3 = 4
7 - 4 = 3

Learn the fact families of multiplication and division together.

4 x 5 = 20
5 x 4 = 20

20 ÷ 5 = 4
20 ÷ 4 = 5

GED Math: Place Value

In what place is the digit 3 in 12, 346? hundreds

In what place is the digit 9 in 934, 501? hundred-thousands

In what place is the digit 8 in 948, 203? thousands

What is the value of the digit 3 in 12, 346? 3 x 100 = 300

What is the value of the digit 9 in 934, 501? 9 x 100,000 = 900,000

What is the value of the digit 8 in 948, 203? 8 x 1,000 = 8,000

GED Math: Whole Number Place Value

Every whole number is made up of digits. The number 36 has two digits and the number 316 has three digits.

The position of each digit determines its place value.


↑ten-thousands
↑ thousands
↑ ↑ hundreds
↑ ↑ ↑ tens
↑ ↑ ↑ ↑ ones
6 9, 2 0 3

The 6 is in the ten-thousands place. 6 x 10,000
The 9 is in the thousands place. 9 x 1000

The 2 is in the hundreds place. It has a place value of 2 x 100.
The 0 is in the tens place. It has a place value of 0 x 10.
The 3 is in the ones spot. It has a place value of 3 x 1

60,000 + 9000 + 200+ 3 = 69, 203

GED Math: Whole Number Identification

Which of the following are whole numbers?

0, 5.5, 8, 12, 31 2/3, 203, and 2.01

Solution: 0, 8, 12, and 203

GED Math: Whole Numbers

Whole numbers are written with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Think of a whole number as a number that can be divided by another number with no remainder.

Examples of whole numbers: 2, 16, 29, 216

Examples of numbers that are Not whole numbers: 3.2, 8 1/2

Susan is sewing curtains for her sister Maria. Each set of curtains takes 8 1/2 yards of material. If Susan has 60 yards of materials, how many full sets of curtains can Susan sew?

Solution: 60 ÷ 8 1/2 = 60 ÷ 8.5 = 7.06

So... Susan can make 7 full sets of curtains.

The sum of three consectutive numbers is 69. What are they?

Solution: 22, 23, 24

First Integer: x
Second Integer: x + 1
Third Integer: x + 2

(x) + (x + 1) + (x + 2) = 69
3x + 3 = 69
3x + 3 - 3 = 69 - 3
3x = 66
(3x)/3 = 66/3
x = 22

Lukas is planning on putting fencing around his rectangular yard. If his yard measures 205 ft. by 100 ft, and there is a gap of 30 ft for the driveway and front lawn, how many feet of fencing would Lukas need to complete his project?

Solution: 2(205) + 2 (100) - 30 = 410 + 200 - 30 = 580 ft.

Sarah picked up 3 pizzas and cut each of the pizzas into 6 equal slices. If she has five friends over and they are all equally hungry.... how many slices will each of them get? Will there be any left over?

Answer: If there are 3 pizzas cut into six slices.... this gives a total of 18 slices. Five friends plus Sarah makes 6 hungry people. Each person will get 3 slices with 0 left over. Sure hope she ordered extra large pizzas!

What is the perimeter of a perfect square with an area of 36 square inches?

Solution: First, use the formula for area to determine what the length of the square's side.

Area = side squared ..... With an area of 36, each side of the square is 6 inches.

Once you have found the length of the square's side, use the formula for the square's perimeter.

Perimeter = side x 4

Perimeter = 6 in. x 4

Perimeter = 24 inches

What is the volume of a rectangular solid whose length is 10 in., width is 8 in, and height is 4 in. ?

Answer: Before you answer the problem you need to know the formula. The formula for volume of a rectangular solid is V = length x width x height.

10 in. x 8 in. x 4 in. = 320 cubic inches

GED Math: Integers

Simplify the following:

-9 + 3x + 7 + (-x) + 5 +7x =

Solution: 7 + 9x

GED Math: Geometry

Susan is planning to replace the carpet in her living room. Her living room measures 15ft long and 10 feet wide. How many square feet of carpet will she need? Also, at $3.99 a square foot, how much will it cost her?

Solution: Use the formula Area = length x width. 15ft x 10 ft = 150 square feet. At $3.99 per square foot, it will cost Susan $598.50.

GED Math Algebra: Solving Equations

Solve the following equation when x = -3

x^2 + 10 - 3x + 2x =

Solution: 9 +10 - (-9) + (-6) = 22

GED Math Algebra: Evaluating equations

Evaluate the following when y = 6 and x = 2

6 - y + 3(2 + x) =

Solution: 6 - 6 + 3(2+2) = 12

Mrs. Smith is serving punch at her daugher's graduation party. She is planning on having 75 people attend and was told that she should average 16 oz. of punch per person. How much punch should she make?

Solution: 75 x 16 = 1200 ounces of punch; 1200 ÷ 128 (128 ounces in a gallon) = 9 gallons, 1 quart, 1 pint

Simplify the following:

(y^2)( y^3) =

Solution: (y · y)(y · y · y) = y^5

Susan went to the clothing store and bought a sweater. The sweater was originally priced at $50. What would the cost of the sweater be at 25% off and 5.5% sales tax?

Step one: Find the cost of the sweater. $50 x .75 = $37.50

Step two: Find the sales tax. $37.50 x 0.055 = $2.06

Step three: Add the cost of the sweater and sales tax together. $ 37.50 + $2.06 = $39.56

Simplify the following:

(7 + 6)(-3 + 9) - 3(2)=

Answer: 72

Evaluate the following when x= 7 and y=5.

3(x - y) + 17 =

Answer: 23

What is.....

-9 + 10 -(-5) +5 - (6)

Answer: 5

Natasha averaged $15.50 a day for 5 days in groceries. How much altogether did she spend?


Answer: $15.50 x 5 = $77.50

Sally took 4 math tests and received an 86, 92, 90, and 78. If she is hoping to average an 90, what score does she need to receive on her fifth test?

Answer: Sally will not be able to average a 90 unless she is able to get extra credit. She would need a 104 on her fifth test.

How many hamburgers can you get from 98 pounds of hamburger if each hamburger is 1/4 lb.

Answer: 392 hamburgers

Sally is twice as old as her sister Anna, and Anna is ten years younger than her brother Sam. If Sam is 12, how old is Sally and Anna?

Answer: You must find the variable expressions; Sam: x, Anna: x-10, Sally: 2(x-10)

x=12

Sam is 12 years old.
Anna is 2 years old.
Sally is 4 years old

Samantha spent $256 to rent a car for four days. The cost of the car was the same for each day. How much was the daily cost, including a 5.5% sales tax?

Answer: $67.52

This year the Smith family has been on a very tight budget and has finally put together a monthly budget. If their monthly food bill is $550 and their annual combined income is $47, 500, what percentage of their income is set aside for food?

Answer: First, you need to find out how much the Smith family spends each year on food. $550 x 12 months equals $6600.

Next, you need to divide $6600 by $47, 500 which equals 0.13894.

Finally, convert the decimal to a percent by moving the decimal point two places to the right.

Your answer: The Smith family spends 13.89 % or about 14% of their annual income on food.