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GED Math: Quantitative, Arithmetic & Algebraic Problem Solving9 chapters | 66 lessons

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Lesson Transcript

Instructor:
*Betsy Chesnutt*

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Decimals are used to represent parts of a whole and are very useful in many types of measurements and calculations. In this lesson, learn how to add, subtract, multiply, and divide decimals.

Imagine that you threw a party for your friends and bought 5 pizzas, each with 10 slices. After the party, you look in the boxes and see that one box has 2 slices left, one has 3 slices left, one only has 1 slice left, and two boxes have 4 slices left. How many pizzas total do you have left over? You could write each of these numbers as a fraction of a pizza, but fractions are not that easy to add. Instead, you can convert the fractions to decimals, which are much easier to work with.

Just like fractions, we use decimal numbers to represent parts of a whole, and they can be added, subtracted, multiplied, and divided using simple rules. We'll come back to the problem of the leftover pizza in a minute, but first let's look at the rules for performing these mathematical operations with decimals.

When adding or subtracting two numbers with decimals, you want to remember one important rule: always line up the decimals before doing anything else! If you can remember to do that first, then the rest of the problem will be easy.

For example, suppose you want to add the numbers 12.8 and 9.602. Even though 12.8 has one digit after the decimal while 9.602 has 3 digits, we can still add these numbers together. To add them, you need to write them in **vertical** format with one underneath the other, being careful to line up the decimals.

Easy, right? To finish this problem, you need to add zeros to the shorter number so that each number has the same number of digits after the decimal. Then simply add each column of numbers.

So, the sum of 12.8 and 9.602 is 22.402.

Going back to the problem of the leftover pizza, we can now also determine exactly how many pizzas you have left over.

First, determine how much pizza was left in each box:

Box 1: 2/10 = 0.2 pizzas

Box 2: 3/10 = 0.3 pizzas

Box 3: 1/10 = 0.1 pizzas

Box 4: 4/10 = 0.4 pizzas

Box 5: 4/10 = 0.4 pizzas

Now add all these decimals together to get the total amount of pizza:

0.2 + 0.3 + 0.1 + 0.4 + 0.4 = 1.4 pizzas left over

Subtraction is done exactly the same way, except you would subtract the two columns of numbers instead of adding them. Don't forget: line up the decimals. Let's now subtract 9.602 from 12.8.

Multiplying with decimals is even easier than adding or subtracting because you don't have to worry about lining up the decimals. To multiply two numbers that contain decimals, first just multiply them and ignore the decimal point altogether. Then count the total number of digits after the decimal point in both numbers. The answer will have that same number of digits after the decimal point, so you can then count over from the right that many digits and put the decimal point in the right place.

Taking those same two numbers, 12.8 and 9.602, let's see what you would get if you multiplied them together.

Division with numbers containing decimals is the probably the trickiest operation to perform. To divide two numbers, you need to carefully follow these four steps:

1. First, look at the divisor, the number that is doing the dividing. If it contains a decimal, you first need to move the decimal over until it becomes a whole number.

2. Move the decimal in the dividend - the number that is being divided - the exact same number of places as you did in the divisor (even if that means it is still a decimal).

3. Divide just like you would if you had two whole numbers.

4. Place the decimal point in the answer just above the decimal point in the dividend.

To add or subtract numbers containing decimals, first set up the problem vertically, being careful to line up the decimals. Then add or subtract each column of numbers to get the final answer.

To multiply numbers containing decimals, first multiply the two numbers in the same way you would if there were no decimals. Then, count the number of digits after the decimal in both of the original numbers and place the decimal in the answer so that it has this same number of digits after the decimal.

To divide numbers containing decimals, first move the decimal in the divisor over until it becomes a whole number and then move the decimal in the dividend over the same number of digits. Then, divide it as you would if there were two whole numbers and place the decimal in the answer directly above the decimal in the dividend.

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GED Math: Quantitative, Arithmetic & Algebraic Problem Solving9 chapters | 66 lessons

- Decimal Basics: Rounding, Ordering & Zeros
- Performing Operations with Decimals 4:36
- Changing Between Improper Fraction and Mixed Number Form 4:55
- How to Raise and Reduce Fractions 6:17
- Practice with Fraction and Mixed Number Arithmetic 7:50
- Changing Between Decimals and Fractions 7:17
- Using the Number Line to Compare Decimals, Fractions, and Whole Numbers 6:46
- Go to GED Math: Decimals & Fractions

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