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 GuideDisplaying data Worksheet/Answer key

Displaying data Worksheet/Answer key

Displaying data Worksheet/Answer key

Displaying data Worksheet/Answer keyOrganizing & Displaying Data

Data Analysis and Probability (NCTM)

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

Select and use appropriate statistical methods to analyze data.

Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.

Develop and evaluate inferences and predictions that are based on data.

Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit.

Grade 8 Curriculum Focal Points (NCTM)

Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets

Students use descriptive statistics, including mean, median, and range, to summarize and compare data sets, and they organize and display data to pose and answer questions. They compare the information provided by the mean and the median and investigate the different effects that changes in data values have on these measures of center. They understand that a measure of center alone does not thoroughly describe a data set because very different data sets can share the same measure of center. Students select the mean or the median as the appropriate measure of center for a given purpose.

Connections to the Grade 8 Focal Points (NCTM)

Data Analysis: Building on their work in previous grades to organize and display data to pose and answer questions, students now see numerical data as an aggregate, which they can often summarize with one or several numbers. In addition to the median, students determine the 25th and 75th percentiles (1st and 3rd quartiles) to obtain information about the spread of data. They may use box-and-whisker plots to convey this information. Students make scatterplots to display bivariate data, and they informally estimate lines of best fit to make and test conjectures.