A fraction represents a part of a whole. It consists 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 in the whole.

There are different types of fractions:

**Proper Fraction:**A fraction where the numerator is less than the denominator (e.g., 1/2).**Improper Fraction:**A fraction where the numerator is greater than or equal to the denominator (e.g., 5/3).**Mixed Number:**A whole number combined with a fraction (e.g., 2 1/4).

Equivalent fractions are different fractions that represent the same part of a whole. They have the same value but may look different. To find equivalent fractions, you can multiply or divide the numerator and denominator by the same number.

There are four basic operations with fractions:

**Addition:**To add fractions, find a common denominator, add the numerators, and keep the denominator the same.**Subtraction:**To subtract fractions, find a common denominator, subtract the numerators, and keep the denominator the same.**Multiplication:**To multiply fractions, simply multiply the numerators together and the denominators together.**Division:**To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

Now that you've learned about fractions, let's practice with some problems:

Convert the following improper fraction to a mixed number: 7/3.

**Answer:** 7/3 = 2 1/3

Add the following fractions: 1/4 + 1/3.

**Answer:** 1/4 + 1/3 = 7/12

Multiply the following fractions: 2/5 * 3/4.

**Answer:** 2/5 * 3/4 = 6/20 = 3/10

Divide the following fractions: 2/3 ÷ 4/5.

**Answer:** 2/3 ÷ 4/5 = 5/6

Remember, fractions are a fundamental concept in mathematics, and understanding them is crucial for many math topics. Practice different types of fractions and operations to strengthen your skills!

.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.