When we compare numbers, we are looking at their relative values and determining which is greater, less than, or equal to the other. This is an important concept in mathematics and is used in various mathematical operations and problem-solving situations.

When comparing whole numbers, we use the following symbols:

- Greater than:
**>** - Less than:
**<** - Equal to:
**=**

For example, when comparing the numbers 7 and 4:

7 **>** 4 (7 is greater than 4)

4 **<** 7 (4 is less than 7)

7 **>** 7 (7 is equal to 7)

When comparing decimals, we follow the same principles as with whole numbers. We compare the digits place by place, starting from the leftmost digit.

For example, when comparing 3.25 and 3.5:

3.25 **<** 3.5 (3.25 is less than 3.5)

When comparing fractions, we can either convert them to a common denominator or use other strategies such as finding a common numerator. For example, when comparing 1/4 and 2/5:

1/4 **<** 2/5 (1/4 is less than 2/5)

To effectively compare numbers, it's important to remember the following key points:

- Use the appropriate comparison symbols:
**>**,**<**,**=** - For decimals and fractions, compare digit by digit, starting from the leftmost place value
- When comparing fractions, consider finding a common denominator or numerator to facilitate the comparison
- Practice comparing numbers through various exercises and problems to reinforce the concept

By mastering the skill of comparing numbers, you'll be better equipped to tackle more complex mathematical problems and operations.

.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.