Number Relations: GED Test Prep
A good grasp of the building blocks of math will be essential for your success on the GED Mathematics Exam. This article covers the basics of mathematical operations and their sequence, variables, integers, fractions, decimals, and square and cube roots.
Basic problem solving in mathematics is rooted in whole number math facts—mainly addition facts and multiplication tables. If you are unsure of any of these facts, now is the time to review. Make sure to memorize any parts of this review that you find troublesome. Your ability to work with numbers depends on how quickly and accurately you can do simple mathematical computations.
Addition and Subtraction
Addition is used to combine amounts. The answer in an addition problem is called the sum, or the total. It is helpful to stack the numbers in a column when adding. Be sure to line up the place-value columns and work from right to left, starting with the ones column.
Add 40 + 129 + 24.
- Align the numbers you want to add on the ones column. Because it is necessary to work from right to left, begin to add starting with the ones column. The ones column equals 13, so write the 3 in the ones column and regroup or "carry" the 1 to the tens column:
- Add the tens column, including the regrouped 1.
- Then add the hundreds column. Because there is only one value, write the 1 in the answer.
Subtraction is used to find the difference between amounts. Write the greater number on top, and align the amounts on the ones column. You may also need to regroup as you subtract.
If Kasima is 45 and Deja is 36, how many years older is Kasima?
- Find the difference in their ages by subtracting. Start with the ones column. Because 5 is less than the number being subtracted (6), regroup or "borrow" a ten from the tens column. Add the regrouped amount to the ones column. Now subtract 15 – 6 in the ones column.
- Regrouping 1 ten from the tens column left 3 tens. Subtract 3 – 3, and write the result in the tens column of your answer. Kasima is 9 years older than Deja. Check: 9 + 36 = 45.
Multiplication and Division
In multiplication, you combine the same amount multiple times. For example, instead of adding 30 three times, 30 + 30 + 30, you could simply multiply 30 by 3. If a problem asks you to find the product of two or more numbers, you should multiply.
Find the product of 34 and 54.
- Line up the place values as you write the problem in columns. Multiply the ones place of the top number by the ones place of the bottom number: 4 × 4 = 16.Write the 6 in the ones place in the first partial product. Regroup the 10.
- Multiply the tens place in the top number by 4: 4 × 3 = 12. Then, add the regrouped amount 12 + 1 = 13.Write the 3 in the tens column and the 1 in the hundreds column of the partial product.
- Now multiply by the tens place of 54.Write a placeholder 0 in the ones place in the second partial product, because you're really multiplying the top number by 50. Then multiply the top number by 5: 5 × 4 = 20.Write 0 in the partial product and regroup the 2.Multiply 5 × 3 = 15. Add the regrouped 2: 15 + 2 = 17.
- Add the partial products to find the total product: 136 + 1,700 = 1,836.
In division, the answer is called the quotient. The number you are dividing by is called the divisor and the number being divided is the dividend. The operation of division is finding how many equal parts an amount can be divided into.
At a bake sale, 3 children sold their baked goods for a total of $54. If they share the money equally, how much money should each child receive?
- Divide the total amount ($54) by the number of ways the money is to be split (3).Work from left to right. How many times does 3 go into 5? Write the answer, 1, directly above the 5 in the dividend. Because 3 × 1 = 3, write 3 under the 5 and subtract 5 – 3 = 2.
- Continue dividing. Bring down the 4 from the ones place in the dividend. How many times does 3 go into 24? Write the answer, 8, directly above the 4 in the dividend. Because 3 × 8 = 24, write 24 below the other 24 and subtract 24 – 24 = 0.
- If you get a number other than 0 after your last subtraction, this number is your remainder.
9 divided by 4.
The answer is 2 R1.
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