Ch 1 - Whole Numbers and Operations Basic to solving all math problems is a good, strong foundation in whole number math facts, mainly the addition facts and multiplication tables. Addition Table/Facts

Multiplication Table

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Addition In some addition problems you will have to regroup, or carry. This means that the column that you have added together becomes more than 9. For anything in the tens, you will carry a 1 to the next column left of the one you are working on. For anything in the twenties, you will carry a 2, etc. Example:

Regroup 1 1

5 6 2

4 5

+ 1 2 8

Answer 7 3 5 Subtraction In some subtraction problems you will have to do regrouping, or borrowing. This means that the top of the column that you are subtracting from doesn’t have a large enough number to subtract. You will have to borrow from the next column to the left and reduce that digit by 1. Example:

Regrouping - 2nd time

10

Regrouping - 1st time

1 0 16

2 1 6

- 8 7

Answer 1 2 9

Multiplication In multiplying problems you will have to regroup. When multiplying by a multi-digit number you will start by using the ones digit in the second number and multiply all the numbers in the top number individually. Then you will cross off the ones place for the bottom number and place a zero in the ones place below and proceed as you did with the ones digit with the tens digit of the bottom number. If the bottom number is 3+ digits repeat the procedure just mentioned adding a zero for each place crossed off. Example:

Regroup - using 3

Regroup - using 1

Regroup - using 8

1 2 1

5 1 3 2

x 3 1 8

Regroup 1 1

4 1 0 5 6

5 1 3 2 0

+ 1 5 3 9 6 0 0

Answer 1 6 3 1 9 7 6

Division The DIVISOR is the number that you are dividing by. The DIVIDEND is the number you are dividing into. Division will include multiplication and subtraction. Example: 3049 æ 6

Answer 0 5 0 8 R 1

6 3 0 4 9

6x0 -0

3 0

6x5 -3 0

0 4

6x0 -0

4 9

6x8 -4 8

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Problem Solving 5 Steps in solving word problems:

1. Understand what the question is asking. a. Read the problem thoroughly and then determine exactly what the

question is asking. 2. Organize data and identify information necessary to solve the problem.

a. Choose only the information needed to solve the problem. As in real life, there is often more information than you need. Once in a while there may not be enough information to solve the problem. Select numbers with their unit labels.

3. Select a problem-solving strategy using mathematical operations. a. After you have determined the question and identified the necessary

information, you will select a problem-solving strategy. Each problem will contain key words or concepts that will help you decide what to do. Many times, your intuition will help you determine which arithmetic operation to choose. This intuition comes from both your personal experience and your understanding of math concepts. Remember, there are only four operations from which to choose: addition, subtraction, multiplication, and division.

4. Set up the problem, estimate, and then compute the exact answer. a. After choosing the operation, set up the problem. Next, estimate an

answer using compatible, rounded numbers. For some problems an estimate can be the final answer, as when a question asks for an approximate or rounded value. At other times, you can use the estimate to check whether you have chosen the right setup and whether your answer makes sense. The estimate can help you check to make sure you entered the numbers and symbols correctly on the calculator.

b. After estimating the answer, solve the problem using the exact information and operations you’ve set up. Do the computations carefully and accurately.

5. Check the reasonableness of the answer. a. The final step in solving any problem is to evaluate your answer. Does

your solution answer the question? Is your answer a sensible one? Is your calculation close to your estimate?

Multistep Problems Many of the problems you see on the Mathematics Test will take more than one calculation to solve.

Personalizing a Problem If you have trouble restating a problem, reread it several times. Think about how you might solve a similar problem in your own life. Many of the problems on the GED Test will involve questions about practical, everyday situations. Restating the Problem Using Words, Sketches, or Diagrams It often helps to restate the problem by organizing the information in a way that puts the problem in your own words. You might actually talk to yourself. As you do this, jot down notes, sketches, or diagrams that help you organize your thoughts.