A fraction represents a part of a whole. It consists of a numerator and a denominator, separated by a horizontal line. The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts that make up a whole.

There are several types of fractions, including:

**Proper fraction:**When the numerator is less than the denominator (e.g., 3/4).**Improper fraction:**When the numerator is greater than or equal to the denominator (e.g., 7/4).**Mixed number:**A whole number combined with a proper fraction (e.g., 1 3/4).**Equivalent fractions:**Fractions that represent the same part of a whole (e.g., 1/2 and 2/4).

Fractions can be added, subtracted, multiplied, and divided. The following are the basic operations with fractions:

When adding or subtracting fractions with the same denominator, simply add or subtract the numerators and keep the common denominator.

Example:To multiply fractions, multiply the numerators together and the denominators together.

Example:To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

Example:To compare fractions, find a common denominator and then compare the numerators. To order fractions, express them with the same denominator and then compare the numerators.

To convert a fraction to a decimal, divide the numerator by the denominator. To convert a fraction to a percentage, first convert it to a decimal and then multiply by 100.

1. Add the following fractions: ^{1}/_{3} + ^{2}/_{5} 2. Multiply the following fractions: ^{3}/_{4} * ^{2}/_{7} 3. Compare the following fractions: ^{2}/_{5} and ^{3}/_{8} 4. Convert ^{5}/_{6} to a decimal and then to a percentage.

Once you have worked through these problems, you should have a good understanding of the basic concepts and operations involving fractions. Feel free to reach out if you need further clarification or additional practice problems.

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

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

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.