In math, the concept of "equal to" refers to the relationship between two quantities that have the same value. The symbol used to denote equality is "=", and it is used to compare two expressions or values to determine if they are the same.

When we say that two quantities are equal, it means that they represent the same amount or value. For example, 5 = 5, which reads "5 is equal to 5," indicates that both 5s are representing the same quantity.

Equality is a fundamental concept in mathematics and is used in various operations such as addition, subtraction, multiplication, division, and equations.

Here are some examples of equality in math:

- 2 + 3 = 5
- 10 - 4 = 6
- 3 × 4 = 12
- 20 ÷ 5 = 4

When working with equality, it's important to understand the properties that govern the relationship between two equal quantities:

**Reflexive Property:**Any quantity is equal to itself. For example, a = a.**Symmetric Property:**If a = b, then b = a.**Transitive Property:**If a = b and b = c, then a = c.**Addition Property of Equality:**If a = b, then a + c = b + c.**Subtraction Property of Equality:**If a = b, then a - c = b - c.**Multiplication Property of Equality:**If a = b, then a × c = b × c.**Division Property of Equality:**If a = b and c ≠ 0, then a ÷ c = b ÷ c.

When studying the concept of "equal to," it's important to practice solving equations and understanding the properties of equality. Here are some key points to focus on:

- Practice writing and solving equations using the "=" symbol.
- Understand the reflexive, symmetric, and transitive properties of equality.
- Work on applying the addition, subtraction, multiplication, and division properties of equality when solving equations.
- Review real-life examples of equality to understand its practical applications.
- Complete practice problems to reinforce your understanding of equality in math.

By mastering the concept of "equal to" and its properties, you'll be well-equipped to tackle more advanced mathematical concepts and problem-solving tasks.

.Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

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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.