# Ch 3: High School Algebra: Decimals and Fractions

### About This Chapter

## High School Algebra I: Decimals and Fractions - Chapter Summary

Learn the basics of working with decimals and fractions with the lessons in this chapter. A knowledgeable instructor will show you how to add, subtract, multiply and divide fractions and decimals. You'll also learn to incorporate whole and mixed numbers. After completing this chapter, you should be able to:

- Define decimal place value
- Compare and order decimals and fractions
- Solve equations and word problems using decimals and fractions
- Use estimation
- Build and reduce fractions
- Understand fraction and mixed number arithmetic

Video | Objective |
---|---|

What Is a Decimal Place Value? | Understand the definition of decimal place value. |

Comparing and Ordering Decimals | Get to know the process of comparing and ordering decimals. |

Adding and Subtracting Decimals | Learn how to add and subtract decimals. |

Multiplying and Dividing Decimals | Review multiplying and dividing decimals, including multiples of 10. |

How to Estimate in Math | Explore the process of estimating decimals to solve math problems. |

How to Build and Reduce Fractions | Understand how to build and reduce fractions. |

How to Find Least Common Denominators | Learn to find the least common denominator. |

Comparing and Ordering Fractions | Review the process of comparing and ordering fractions. |

Changing Between Improper Fraction and Mixed Number Form | Become familiar with changing between improper fraction form and mixed number form. |

How to Add and Subtract Like Fractions and Mixed Numbers | Get to know how to add and subtract like fractions and mixed numbers. |

How to Add and Subtract Unlike Fractions and Mixed Numbers | Explore the process of adding and subtracting unlike fractions and mixed numbers. |

Multiplying Fractions and Mixed Numbers | Understand how to multiply fractions and mixed numbers. |

Dividing Fractions and Mixed Numbers | Take a look at dividing fractions and mixed numbers. |

Practice with Fraction and Mixed Number Arithmetic | Review fraction and mixed number arithmetic. |

Estimation Problems Using Fractions | Learn to work estimation problems using fractions. |

Solving Problems Using Fractions and Mixed Numbers | Identifying the process of solving problems with fractions and mixed numbers. |

How to Solve Complex Fractions | Understand methods of solving complex fractions |

Addition, Subtraction, Multiplication and Division with Decimal Notation | Take a look at adding, subtracting, multiplying and dividing with decimal notation. |

Using the Number Line to Compare Decimals, Fractions and Whole Numbers | Learn how the number line can be used to compare decimals, fractions and whole numbers. |

How to Simplify Word Problems with Fractions Using Whole Numbers | Review the process of using whole numbers to restate a word problem containing fractions. |

### 1. What is a Decimal Place Value?

In mathematics, decimals provide a shorthand method for writing mixed numbers and fractions to the powers of ten. Learn about decimals and decimal place values, and understand how to read decimals. Recognize that the placement of decimals matters tremendously, so it is vital to ensure the decimal is in the correct place.

### 2. Comparing and Ordering Decimals

In mathematics, a decimal is a number that includes a whole number and a fraction separated by a decimal point. Learn to recognize numbers that are decimals, and explore how to use decimals to count. Understand how to compare decimals and put them in order from the least decimal to the greatest.

### 3. Addition, Subtraction, Multiplication, and Division with Decimal Notation

The syntax rules in expressing decimals are known collectively as decimal notation and allow for consistency in calculations. Explore the notation in addition and subtraction and learn the rules for multiplication and division as well.

### 4. Adding and Subtracting Decimals: Examples & Word Problems

Certain steps, like the alignment of the digits in an equation, are very important when adding and subtracting using decimals. Learn about adding and subtracting using decimals through a series of examples, including practice word problems.

### 5. Multiplying and Dividing Decimals: Examples & Word Problems

When multiplying and dividing decimal numbers, there are rules about what to do with the decimal point. Learn how to multiply and divide decimal numbers, and practice with real-world word problem examples.

### 6. How to Estimate with Decimals to Solve Math Problems

In order to estimate with decimals, they must be rounded to the nearest whole number. This process makes it easier to solve math problems. Study three word problems that are all about estimating decimals.

### 7. How to Build and Reduce Fractions

In mathematics, fractions are numerical quantities used to represent something that is a portion of a whole, such as a piece of pie that is 1/8, or one of eight pieces, of an entire pie. Learn what fractions are and recognize the difference between the numerator and denominator. Explore how to build and then how to reduce fractions, and understand the role of the greatest common factor (GCF) in this process.

### 8. How to Find Least Common Denominators

Finding the least common denominator requires calculating the least common multiple of two or more denominators. Learn the definition of multiples, explore how to use them to find the least common denominator, and understand the examples.

### 9. Comparing and Ordering Fractions

When comparing and ordering fractions, you need to have a common denominator. Learn how to find the common denominator and understand how to compare and order fractions.

### 10. Changing Between Improper Fraction and Mixed Number Form

In mathematics, an improper fraction has a denominator that is smaller than its numerator, and a mixed number is composed of an integer paired with a proper fraction. Practice examples to learn how to change between the forms for improper fractions and mixed numbers. Understand when each form is appropriate and should be used over the alternate form.

### 11. How to Add and Subtract Like Fractions and Mixed Numbers

After determining a common denominator in a problem with mixed numbers and fractions, adding and subtracting fractions and mixed numbers requires two more steps. Learn how to add and subtract like fractions and mixed numbers, and review examples.

### 12. How to Add and Subtract Unlike Fractions and Mixed Numbers

Some of the most commonly seen forms of fractions are unlike fractions and mixed numbers. Learn to add and subtract unlike fractions and mixed numbers by reviewing how fractions are handled then explore these processes using real-life examples.

### 13. Multiplying Fractions and Mixed Numbers

Fractions can be multiplied, even when presented as mixed numbers, where an integer accompanies a fraction. Demonstrate understanding through solving examples in dollars, and practicing multiplying fractions and mixed numbers.

### 14. Dividing Fractions and Mixed Numbers

Fractions can be divided even when presented as mixed numbers, which is where an integer accompanies a fraction. Practice the division of fractions and mixed numbers in a series of practical scenarios.

### 15. Practice with Fraction and Mixed Number Arithmetic

In mathematics, arithmetic studies and manipulates numbers using addition, subtraction, multiplication, and division. Learn how to use these operations on fractions and mixed numbers, and gain additional understanding by doing practice problems that use the operation of mixed number arithmetic.

### 16. Estimation Problems using Fractions

In mathematics, estimation is the process of calculating the approximate value of something. Learn how to use fractions to work estimation problems. Understand when close counts and do practice problems to gain more understanding of estimating.

### 17. Solving Problems using Fractions and Mixed Numbers

From understanding a recipe to deciding the winner of a competition, fractions have many uses in solving everyday problems. Learn how to use fractions and mixed numbers, including comparisons, addition, subtraction, multiplication, and division to solve problems.

### 18. How to Solve Complex Fractions

Complex fractions are fractions that contain fractions in the numerator, denominator, or both. Learn the two methods used to manage and solve complex fractions by simplifying the problem.

### 19. Using the Number Line to Compare Decimals, Fractions, and Whole Numbers

A number line is a line constructed with numbers that are plotted in order and at regular intervals. Learn how to use a number line to compare decimals, fractions, and whole numbers.

### 20. How to Simplify Word Problems with Fractions Using Whole Numbers

Simplifying word problems with fractions using whole numbers first requires labeling all of the important pieces provided. Learn more about equations that use fractions in word problems and how to multiply by the least common denominator to remove the fractions and solve the equation using whole numbers.

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### Other Chapters

Other chapters within the Remedial Algebra I course

- High School Algebra: Basic Arithmetic
- High School Algebra: Solving Math Word Problems
- High School Algebra: Percent Notation
- High School Algebra: Real Numbers
- High School Algebra: Exponents and Exponential Expressions
- High School Algebra: Radical Expressions
- High School Algebra: Algebraic Expressions and Equations
- High School Algebra: Properties of Functions
- High School Algebra: Matrices and Absolute Value
- High School Algebra: Working With Inequalities
- High School Algebra: Properties of Exponents
- High School Algebra: Complex and Imaginary Numbers
- High School Algebra: Algebraic Distribution
- High School Algebra: Linear Equations
- High School Algebra: Factoring
- High School Algebra: Graphing and Factoring Quadratic Equations
- High School Algebra: Properties of Polynomial Functions
- High School Algebra: Rational Expressions
- High School Algebra: Cubic Equations
- High School Algebra: Quadratic Equations
- High School Algebra: Measurement and Geometry
- High School Algebra: Calculations, Ratios, Percent & Proportions
- High School Algebra: Data, Statistics, and Probability
- High School Algebra: Well-Known Equations