**Introduction to Fractions**

Fractions are a way of representing a part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). The numerator represents the number of parts we have, and the denominator represents the total number of parts that make up a whole.

**Types of Fractions**

**Proper Fractions**: When the numerator is less than the denominator, it is called a proper fraction. For example, 1/2, 3/4, and 5/8 are all proper fractions.**Improper Fractions**: When the numerator is greater than or equal to the denominator, it is called an improper fraction. For example, 5/4, 7/3, and 11/5 are all improper fractions.**Mixed Numbers**: A mixed number is a combination of a whole number and a fraction. For example, 2 1/3, 4 2/5, and 7 3/4 are all mixed numbers.

**Equivalent Fractions**

Equivalent fractions are different fractions that represent the same part of a whole. They have different numerators and denominators but the same overall value. For example, 1/2, 2/4, and 3/6 are all equivalent fractions.

**Adding and Subtracting Fractions**

When adding or subtracting fractions, the denominators must be the same. If they are not the same, you need to find a common denominator before performing the operation.

**Multiplying and Dividing Fractions**

When multiplying fractions, you simply multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. When dividing fractions, you multiply by the reciprocal of the second fraction (flip the fraction and then multiply).

**Study Guide**

**Understanding Fractions**: Make sure to understand the concept of fractions, including the numerator, denominator, and the relationship between the two.**Types of Fractions**: Familiarize yourself with proper fractions, improper fractions, and mixed numbers.**Equivalent Fractions**: Practice identifying and generating equivalent fractions for a given fraction.**Operations with Fractions**: Practice adding, subtracting, multiplying, and dividing fractions. Pay special attention to finding common denominators and simplifying the results.**Real-life Applications**: Explore real-life scenarios where fractions are used, such as in cooking, measuring, and sharing quantities.

Remember to practice regularly and seek help if you encounter difficulties with any of the concepts. Fractions are an important topic in mathematics and a solid understanding of them will be beneficial in many areas of life.

Study GuideDecimals/Fractions Activity LessonOrdering Decimals & Fractions Activity LessonPercent Grids Activity LessonFraction & Percent Circles Worksheet/Answer key

Decimals/Fractions Worksheet/Answer key

Decimals/Fractions Worksheet/Answer key

Decimals/Fractions Worksheet/Answer keyDecimals/Fractions Worksheet/Answer keyPercent Grids Vocabulary/Answer keyDecimals/Fractions

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Grade 4 Curriculum Focal Points (NCTM)

Number and Operations: Developing an understanding of decimals, including the connections between fractions and decimals

Students understand decimal notation as an extension of the base-ten system of writing whole numbers that is useful for representing more numbers, including numbers between 0 and 1, between 1 and 2, and so on. Students relate their understanding of fractions to reading and writing decimals that are greater than or less than 1, identifying equivalent decimals, comparing and ordering decimals, and estimating decimal or fractional amounts in problem solving. They connect equivalent fractions and decimals by comparing models to symbols and locating equivalent symbols on the number line.