Ch 5: Understanding Fractions & Mixed Numbers
About This Chapter
FTCE Middle Grades Math: Fractions - Chapter Summary
Make sure you're prepared to find solutions to problems involving fractions by studying this chapter. Doing so could help you answer questions on fractions when you take the FTCE Middle Grades Math exam. These video lessons will walk you through the steps involved in:
- Building, reducing, comparing and ordering fractions
- Finding the least common denominator
- Defining equivalent fractions
- Converting improper fractions to mixed numbers
- Adding and subtracting like and unlike fractions
- Multiplying and dividing mixed numbers and fractions
- Working with fractions and mixed numbers
- Solving complex fractions
Each lesson features a qualified instructor who shows you how to perform these computations. You can put what you know into practice with the quizzes associated with each lesson as well as the chapter test.
1. Arithmetic with Whole Numbers
Arithmetic with whole numbers includes the four operations of addition, subtraction, multiplication, and division. Explore these four operations and examples of how they are used in everyday life.
2. Arithmetic Calculations with Signed Numbers
Signed numbers are integers that are often used with mathematical operation signs to solve arithmetic calculations. Learn how to add, subtract, multiply, and divide integers in arithmetic calculations through a series of examples.
3. 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.
4. 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.
5. 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.
6. What are Equivalent Fractions? - Definition & Examples
Equivalent fractions use different numbers to represent the same part of a whole, such as 2/16 and 1/8. Explore the definition and examples of equivalent fractions, and learn how to test for equivalency. Understand the roles of multiplication and division in computing equivalent fractions, and recognize how equivalent fractions can be used in addition and subtraction.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
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Other Chapters
Other chapters within the College Preparatory Mathematics: Help and Review course
- Math Foundations: Help and Review
- Problem Solving & Reasoning Skills
- Percents in Math Basics
- Decimals & Fractions Overview
- Linear Equations: Help and Review
- Solving and Graphing Inequalities: Help and Review
- Graphing and Factoring Quadratic Equations: Help and Review
- Complex and Imaginary Numbers: Help and Review
- Properties of Exponents: Help and Review
- Praxis I Math: Square Roots
- Properties of Polynomial Functions: Help and Review
- Simplifying and Solving Rational Expressions: Help and Review
- Praxis I Math: Algebraic Expressions
- Properties of Functions: Help and Review
- Logarithms and Exponential Equations: Help and Review
- Data & Estimation
- Logic in Math: Help and Review
- Sets: Help and Review
- Basic Probability and Statistics: Help and Review
- Praxis I Math: Basic Statistics and Probability
- Geometric Laws & Proofs
- Grade Level Math Vocabulary: Help and Review
- MTEL Middle School Math/Science: History of Geometry
- MTEL Middle School Math/Science: Geometric Properties & Theorems
- MTEL Middle School Math/Science: Principles of Geometry
- MTEL Middle School Math/Science: Algebraic Applications in Geometry
- MTEL Middle School Math/Science: Using Trigonometric Functions
- MTEL Middle School Math/Science: Trigonometric Identities
- MTEL Middle School Math/Science: Trigonometric Applications
- Praxis I Math: Ratio and Proportions
- Praxis I Math: Congruence and Similarity
- Praxis I Math: Geometric Measurement and Dimension