Whole Numbers Study Guide: GED Math

Whole Numbers and Their Place Value

Whole numbers are the counting numbers and zero: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,…Whole numbers are also sometimes called digits.

Each digit has a specific value. The position, or place, of a digit in a number written in standard form determines the value the digit represents.

The number 543,210 has a 5 in the hundred thousands place, a 4 in the ten thousands place, a 3 in the thousands place, a 2 in the hundreds place, a 1 in the tens place, and a 0 in the ones place.

The expanded form of a number is the sum (addition) of its various place values: 500,000 + 40,000 + 3,000 + 200 + 10 + 0.

Rounding Whole Numbers

On the GED, you may be asked to estimate your answer, which means to find an approximate answer. You can estimate by using rounded numbers. Numbers can be rounded to different place values. For example, to round to the nearest ten means to find the closest number having all zeros to the right of the tens place.

When the digit 5, 6, 7, 8, or 9 appears to the right of the place you are rounding to, round up. When the digit 0, 1, 2, 3, or 4 appears to the right of the place you are rounding to, round down.

Whole Number Addition and Subtraction

Addition is used when you need to combine amounts. The answer in an addition problem is called the sum or total.

It is helpful to stack the numbers in a column when adding. Be sure to line up the place-value columns and to work from right to left, starting with the ones column.

Example

20 + 529 + 24 =

First, 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:

Now, add the tens column, including the regrouped 1.

Finally, add the hundreds column. Because there is only one value, write the 5 in the answer.

Subtraction is used when you want 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. The answer in subtraction is called the difference.

Example

Find the difference between 36 and 75.

Start with the ones column. Because 5 is less than the number being subtracted (6), regroup or borrow a 10 from the tens column, leaving 6 tens. Add the regrouped amount to the ones column. Now, determine 15 – 6 in the ones column.

Regrouping 1 ten from the tens column left 6 tens. Subtract 3 from 6, and write the result in the tens column of your answer.

Whole Number Multiplication and Division

In multiplication, you combine the same amount multiple times. In some cases, multiplication can be used instead of addition. For example, instead of adding 60 four times, 60 + 60 + 60 + 60, you could simply multiply 60 by 4. If a problem asks you to find the product of two or more numbers, you should multiply.

Example

Find the product of 12 and 16.

Line up the place value as you write up the problem in columns. Multiply the ones of the top number by the ones of the bottom number: 2 × 6 = 12. Write the 2 in the ones place in the first partial product. Regroup the 10.

Multiply the tens place in the top number by 6: 6 × 1 = 6. Then add the regrouped amount: 6 + 1 = 7. Write the 7 in the tens column of the partial product.

Now multiply by the tens place of 16. Write a placeholder 0 in the ones place in the second partial product, because you're really multiplying the top number by 10. Then multiply the top number by 1: 1 × 2 = 2. Write 2 in the partial product next to the zero. Multiply 1 by the top number in the tens place: 1 × 1 = 1. Your total second partial product is 120.

Add 72 and 120. Your answer is 192.

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.

Example

Find the quotient of 72 divided by 3.

Set up a long division problem with 3 as the divisor and 72 as the dividend:

What times 3 equals 7, or a whole number closest to 7? 3 × 2 = 6, so this is your best choice. Write a 2 over the 7 in the dividend. 7 – 6 = 1, which is the remainder. Bring down the 2.

What times 3 equals 12? 3 × 4 = 12. Write a 4 over the 2 in the dividend.

The quotient of 72 divided by 3 is 24.

Practice problems for these concepts can be found at:

Numbers and Operations Practice Problems: GED Math