Rational numbers are numbers that can be expressed as the quotient or fraction p/q of two integers, where q is not equal to 0. In other words, a rational number is any number that can be written in the form p/q, where p and q are integers and q is not zero.

- 2/3
- -5/7
- 1 (can be expressed as 1/1)
- -3 (can be expressed as -3/1)

**Closure Property:**The sum, difference, or product of any two rational numbers is also a rational number.**Commutative Property:**For addition and multiplication, the order of the rational numbers does not matter.**Associative Property:**For addition and multiplication, the grouping of rational numbers does not matter.**Identity Property:**The sum of any rational number and 0 is the rational number itself.**Inverse Property:**Every rational number has an additive inverse (its negative) and a multiplicative inverse (reciprocal).

Rational numbers can be operated on using the following operations:

**Addition:**To add two rational numbers, find a common denominator, add the numerators, and simplify if necessary.**Subtraction:**To subtract two rational numbers, find a common denominator, subtract the numerators, and simplify if necessary.**Multiplication:**To multiply two rational numbers, multiply the numerators and denominators separately, and simplify if necessary.**Division:**To divide two rational numbers, multiply the first number by the reciprocal of the second number.

When studying rational numbers, make sure to understand the concept of fractions and how to perform operations with fractions. Practice finding common denominators and simplifying fractions. Familiarize yourself with the properties of rational numbers and how they apply to different operations. Additionally, work on word problems involving rational numbers to apply your knowledge in real-life situations.

Remember to always check your work and simplify your answers whenever possible.

Feel free to ask if you have any more questions or need further clarification on rational numbers!

.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.