Weighted Combination

In mathematics, a weighted combination refers to a way of combining two or more items with different weights or proportions. This concept is commonly used in various fields such as statistics, finance, and engineering.

Formula for Weighted Combination

The formula for finding the weighted combination of two items is:

Weighted Combination = (Weight of Item 1 * Value of Item 1) + (Weight of Item 2 * Value of Item 2)

Where:

Weight of Item 1, Weight of Item 2, ... = the proportion or importance assigned to each item
Value of Item 1, Value of Item 2, ... = the numerical value or quantity of each item

Example

Suppose you have a portfolio of stocks with the following weights and returns:

Stock A: Weight = 0.4, Return = 8%
Stock B: Weight = 0.6, Return = 5%

To find the weighted combination of the portfolio's returns, you can use the formula:

Weighted Combination = (0.4 * 8%) + (0.6 * 5%) = 3.2% + 3.0% = 6.2%

Study Guide

To understand and master the concept of weighted combination, here are some key steps to follow:

Understand the concept of weights: Learn how to assign proportional weights to different items based on their importance or significance.
Learn the formula: Memorize the formula for finding the weighted combination and understand each component of the formula.
Practice with examples: Work through several examples of weighted combinations to gain proficiency in applying the formula.
Real-world applications: Explore real-world scenarios where weighted combinations are used, such as in investment portfolios, statistical analysis, or engineering design.
Review and practice: Regularly review the concept and practice solving problems to reinforce your understanding.

By following these steps and practicing regularly, you can become proficient in working with weighted combinations and apply this concept effectively in various mathematical and practical contexts.

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The resources above cover the following skills:

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.

Weighted Combination

Formula for Weighted Combination

Example

Study Guide

[Weighted Combination] Related Worksheets and Study Guides:

◂Math Worksheets and Study Guides Seventh Grade. Algebraic Equations

The resources above cover the following skills: