TABE Level D Math: Decimals

Decimals are like fractions. They are a way of representing part of a whole.

For example, the decimal number 6.2 is equal to the mixed number (six and two-tenths).

The decimal number 3.14 is equal to the mixed number (three and fourteen hundredths).

Digits to the left of the decimal point make up the whole number part.

Digits to the right of the decimal point make up the fractional part.

In decimals, the denominators of the fractional parts are always 10, 100, 1000, etc.

Whole numbers are decimals with zeros to the right of the decimal point.

For example, the decimal numbers 4.0, 4.00, 4.000, etc. are all the same number as the whole number 4.

Money is written in decimal form. The digits to the left of the decimal give you the dollars.

The two digits to the right of the decimal give you the cents.

Cents represent parts of a dollar. For example, $3.25 is 3 dollars and 25 cents, or dollars.
On the TABE D you will be expected to be able to add, subtract, multiply, and divide decimals.

Adding and Subtracting Decimals
If a problem adding or subtracting decimals is written in vertical form, all you have to do is make sure the decimal points are lined up, and then add or subtract as you would with whole numbers.

Examples:

If one decimal has more places to the right than the other, just fill in the blanks with zeros.
Examples:

In most of the TABE D problems, decimals problems are written in horizontal form to save space: 1.23 + 4.56 instead of

You should rewrite all problems in vertical form and line up the decimal point before adding or subtracting. Write one number above the other. If you’re adding, it doesn’t matter which number is on top. If you’re subtracting, the number that is being subtracted (the smaller one) goes on the bottom.

Practice Adding and Subtracting Decimals

1. 1.8 + 2.6

2. 6.75 − 3.38

3. 12.32 + 3.41

4. 17.24 − 8.58

5. 5.2 + 3.11

6. 7.1 − 6.06

Multiplying Decimals
Multiply decimals the same way you would whole numbers. Then count the total number of places to the right of the decimal point in both numbers. Count that many spaces from the right side of the answer and place a decimal point there.

Examples:

Multiplication problems are also written in horizontal form on the TABE-D. As before, you should re-write them in vertical form before attempting to do the calculations.

Practice Multiplying Decimals

1. 8 × 3.21

2. 2.7 × 3.6

3. .503 × 1.2

4. 18.6 × 8.5

5. 1.03 × 26

6. 17 × .124

Dividing Decimals
The dividend of a division problem is the number being divided up. The divisor is the number that does the dividing.

The answer is called the quotient. For example, in the division problem is the dividend, 5 is the divisor, and 2 is the quotient.

This problem can also be written or .
All three forms could appear on the TABE D. You should always rewrite the problem in form before you work it out.
When dividing decimals, it doesn’t matter what kind of number the dividend is. You need to look at two cases for the divisor.

Case 1. The divisor is not a decimal. In this case, divide as you would with whole numbers, but place a decimal in the quotient in the same location as it is in the dividend.
Examples:

Case 2. The divisor is a decimal. In this case, move the decimal to the right to make the divisor a whole number. Then move the decimal in the dividend the same number of places to the right. If the dividend is a whole number, or if it has fewer places to the right of the decimal point, write in zeros until you have the correct number of places.
Examples:

Practice Dividing Decimals

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Answers: Practice Adding and Subtracting Decimals

1. 4.4

2. 3.37

3. 15.73

4. 8.66

5. 8.31

6. 1.04

Answers: Practice Multiplying Decimals

1. 25.68

2. 9.72

3. .6036

4. 158.1

5. .2678

6. 2.108