In mathematics, the term "product" refers to the result of multiplying two or more numbers or quantities together. It is a fundamental concept in arithmetic and algebra, and understanding how to find the product of numbers is essential for solving various mathematical problems.

To find the product of two numbers, you simply multiply them together. For example, the product of 3 and 4 is 3 x 4 = 12. This can be extended to finding the product of more than two numbers by multiplying them all together. For example, the product of 2, 3, and 5 is 2 x 3 x 5 = 30.

In mathematical notation, the product of two numbers a and b is often denoted using the multiplication symbol "×" or by placing the numbers next to each other. For example, the product of a and b can be written as a × b or simply ab.

There are several important properties of products that are useful to understand:

**Commutative Property:**The product of two numbers is the same regardless of the order in which the numbers are multiplied. In other words, a × b = b × a.**Associative Property:**When multiplying three or more numbers, the product is the same regardless of how the numbers are grouped. In other words, (a × b) × c = a × (b × c).**Identity Property:**The product of any number and 1 is the number itself. In other words, a × 1 = a.**Distributive Property:**The product of a number and the sum (or difference) of two other numbers is equal to the sum (or difference) of the products of the number and each of the other two numbers. In other words, a × (b + c) = a × b + a × c.

Here are some examples to illustrate the concept of finding the product:

- The product of 7 and 8 is: 7 × 8 = 56.
- The product of 12, 3, and 4 is: 12 × 3 × 4 = 144.
- The product of 5 and 1 is: 5 × 1 = 5.

When studying the concept of product in mathematics, it's important to focus on the following key points:

- Understanding how to find the product of two or more numbers.
- Recognizing the notation used to represent products.
- Being familiar with the properties of products, such as the commutative, associative, identity, and distributive properties.
- Practicing solving problems that involve finding products, both with and without the use of a calculator.

By mastering the concept of product and its properties, you will be better equipped to handle various mathematical problems and applications that involve multiplication.

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.