Back To Course

GED Math: Quantitative, Arithmetic & Algebraic Problem Solving10 chapters | 73 lessons | 7 flashcard sets

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

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.

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
2 in chapter 4 of the course:

Back To Course

GED Math: Quantitative, Arithmetic & Algebraic Problem Solving10 chapters | 73 lessons | 7 flashcard sets

- 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

- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Computer Science 203: Defensive Security
- JavaScript Language Basics
- Forms & JavaScript
- JavaScript & HTML
- Error Handling, Debugging & Events in JavaScript
- HTML Elements & Lists
- What is the PHR Exam?
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP
- MEGA Exam Registration Information
- MEGA & MoGEA Prep Product Comparison
- PERT Prep Product Comparison

- Human Experience in Texts: Literary Features & Analysis
- System Calls: Function, Importance & Categories
- Multilingualism: Definition & Role in Education
- Supporting Adaptive Skills in Preschool
- Networking Components in Commercial Networks
- Managing Cybersecurity Risks through User Training, Awareness & Accountability
- Practical Application for C Programming: Recursive Functions
- Quiz & Worksheet - Stative Verbs
- Quiz & Worksheet - Significance of the Ganges River
- Quiz & Worksheet - Behavioral Theory & Learning Environments
- Quiz & Worksheet - Raising Reading Rate & Accuracy
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Positive Behavior Support | PBIS Tips for Teachers
- 9th Grade Math Worksheets & Printables

- NY Regents Exam - Earth Science: Test Prep & Practice
- MTEL Speech (44): Practice & Study Guide
- Creating Proactive Customer Service
- Middle School Physical Science: Help and Review
- Information Systems: Tutoring Solution
- Common Core Math Grade 8 - Geometry: Pythagorean Theorem
- ILTS Biology: Weather & Storms
- Quiz & Worksheet - Salome by Oscar Wilde
- Quiz & Worksheet - Brain Mapping Methods
- Quiz & Worksheet - Premotor Cortex
- Quiz & Worksheet - FBD & Balanced Force Calculations
- Quiz & Worksheet - Determining if String is Integer

- Major Subfields of Psychology
- Gregor Mendel: Biography, Facts & Timeline
- SBEC Technology Application Standards for Teachers
- Next Generation Science Standards for Middle School
- Homeschooling in South Dakota
- 2nd Grade Word Walls
- Best Psychology Books for Beginners
- Nevada State Science Standards
- How to Pass the Social Studies GED Test
- What is the FTCE General Knowledge Test?
- What Is The Difference Between NGSS & CCSS?
- How to Study for US History

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject