Variable Expression

A variable expression is a mathematical expression that contains one or more variables, along with numbers and operations. Variables are symbols that represent unknown or changing values. Variable expressions can be used to represent relationships and solve problems in mathematics.

Parts of a Variable Expression

Variable expressions consist of the following parts:

Variables: Symbols (such as x, y, a, b, etc.) that represent unknown or changing values.
Numbers: Constant values that are known and do not change.
Operations: Mathematical operations such as addition, subtraction, multiplication, and division.

Examples of Variable Expressions

Here are some examples of variable expressions:

2x + 5
3y - 8
4a + 2b
5x² - 3x + 7

How to Evaluate Variable Expressions

To evaluate a variable expression, you substitute specific values for the variables and then perform the operations to find the resulting value. For example, if the expression is 2x + 5 and x = 3, you would substitute 3 for x and then perform the operations to get the value of the expression.

Practice Problems

Now, let's try some practice problems to reinforce the concepts:

1. Evaluate the expression 4a + 3b when a = 2 and b = 5.

Answer: 4(2) + 3(5) = 8 + 15 = 23

2. Evaluate the expression 7x - 2y when x = 4 and y = 3.

Answer: 7(4) - 2(3) = 28 - 6 = 22

3. If the expression 3n + 2 represents the total cost of n items, find the total cost when n = 6.

Answer: 3(6) + 2 = 18 + 2 = 20

Remember to always substitute the given values for the variables and then perform the operations step by step to evaluate the expressions.

Hope this helps!

◂Math Worksheets and Study Guides Sixth Grade. Simple Proportions

The resources above cover the following skills:

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.

Grade 6 Curriculum Focal Points (NCTM)

Number and Operations: Connecting ratio and rate to multiplication and division

Students use simple reasoning about multiplication and division to solve ratio and rate problems (e.g., 'If 5 items cost $3.75 and all items are the same price, then I can find the cost of 12 items by first dividing $3.75 by 5 to find out how much one item costs and then multiplying the cost of a single item by 12'). By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative sizes of quantities, students extend whole number multiplication and division to ratios and rates. Thus, they expand the repertoire of problems that they can solve by using multiplication and division, and they build on their understanding of fractions to understand ratios. Students solve a wide variety of problems involving ratios and rates.