Education.com
Try
Brainzy
Try
Plus

# Adding, Subtracting, Multiplying, and Dividing Decimals Study Guide: GED Math (page 3)

By
Updated on Mar 23, 2011

Practice problems for these concepts can be found at:

Fractions and Decimals Practice Problems: GED Math

Step 1   Write the numbers so that the decimal points are lined up.

Step 2   Make all the decimals have the same number of digits to the right of the decimal point by adding trailing zeros to the ends of shorter decimals.

Step 3   Write the decimal point in the answer so that it lines up with the decimal points in the problem.

Step 4   Add the decimals just as you would if you were adding whole numbers.

Example

9.23 + 6.02 + 1.1 =

Write the numbers so that the decimal points are lined up:

Make all the decimals have the same number of digits to the right of the decimal point by adding a trailing zero to the end of the shorter decimal:

Write the decimal point in the answer so that it lines up with the decimal points in the problem:

To add a whole number and a decimal together, you would follow the same steps.

Example

12 + 5.013 =

Write the numbers so that the decimal points are lined up. Insert a decimal point to the right of the whole number:

Make all the decimals have the same number of digits to the right of the decimal point by adding trailing zeros to the end of the shorter decimal:

Write the decimal point in the answer so that it lines up with the decimal points in the problem:

Add the decimals just as you would if you were adding whole numbers to find your solution:

Setting decimals up for subtraction is very similar to the setup when adding them. To subtract decimals, use the following steps:

Step 1   Write the numbers so that the decimal points are lined up. Insert a decimal point to the right of any whole number.

Step 2   Make all the decimals have the same number of digits to the right of the decimal point by adding trailing zeros to the ends of shorter decimals.

Step 3   Write the decimal point in the answer so that it lines up with the decimal points in the problem.

Step 4   Subtract the decimals just as you would if you were subtracting whole numbers.

Example

11 – 5.2 =

Write the numbers so that the decimal points are lined up:

Make all the decimals have the same number of digits to the right of the decimal point by adding a trailing zero to the end of the shorter decimal:

Write the decimal point in the answer so that it lines up with the decimal points in the problem:

Subtract the decimals, and don't forget to borrow to arrive at the final answer:

### Multiplying Decimals

If you can multiply whole numbers, then you can multiply decimals. The main thing to watch out for is the placement of the decimal point. Placing the decimal point in your answer is just a matter of counting place values.

When multiplying with decimals, multiply as you would for whole numbers, and ignore the decimal points until after the product is found. After performing the multiplication, count the number of digits after the decimal points (to the right of the decimal point) in both factors being multiplied. This count is the number of decimal places (to the right of the decimal point) that will be in the answer. Start at the rightmost side of the product (the answer) and count to the left the number of digits (the number of digits to the right of the decimal point in both terms) in order to place the decimal point.

Example

2.48 × 1.7 =

Multiply, ignoring the decimal points: 248 × 17 = 4,216.

Determine the digits to the right of the decimal points in the factors: 4, 8, and 7. Starting to the right of the 6 in the answer, move three digits to the left: 4.216.

### Dividing Decimals

To divide with decimal numbers, first change the problem to division by a whole number. It may be necessary to move the decimal point in the divisor (the number you are dividing by) to make it a whole number. Move the decimal in the dividend (the number you are dividing into) the same number of places, and copy the new decimal placeholder straight up into the quotient (the answer to the division problem). Once the decimal point is placed, divide as you normally would with long division.

Example

3.26 ÷ 0.02 =

Solve using long division. First move the decimal point two places to the right in each number:

### Decimal Operations: Multiplying or Dividing by the Powers of 10

The decimal number system is based on the powers of 10. This makes multiplication and division by 10, 100, 1,000,… a matter of moving the decimal point the number of places dictated by the number of zeros in 10, 100, or 1,000. This is because once you add or remove the zeros, you are essentially multiplying or dividing by 1.

To multiply a number by 10, move the decimal point one place to the right.
To multiply a number by 100, move the decimal point two places to the right.
To multiply a number by 1,000, move the decimal point three places to the right.
To divide a number by 10, move the decimal point one place to the left.
To divide a number by 100, move the decimal point two places to the left.
To divide a number by 1,000, move the decimal point three places to the left.

Practice problems for these concepts can be found at:

Fractions and Decimals Practice Problems: GED Math