Equations and Expressions

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The lessons included in the Equations and Expressions section of HelpingWithMath.com are summarized below. Additional related lessons will be added over time.

Work through these to help tutor your children. There are also a list of Equation and Expressions Worksheets listed towards the bottom of the page.

What you will find in this section

Multiplication as Comparison explains how to see multiplication as more than just an operation. It shows how two factors and their product can be viewed as a comparison.

 This lesson on the use of grouping symbols in expressions covers the precedence of parentheses, brackets, and braces. Determining Order of Operations follows on from the Grouping Symbols lesson and explores the order in which different parts of an expression are evaluated. The Writing Simple Expressions lesson shows how to use the order of operations rules to write simple expressions. It also introduces some basic relationships between numbers and operations within expressions. There are guidance and examples on writing inequalities and showing them on a number line. Take a look at directly proportional relationships and how the can be graphed and also represented algebraically using the equation y=mx. Includes real-life example covering currency exchange rates and time and distance relationships. A closer look at the slope of a line that is generated when proportional relationships are plotted on a X-Y grid. Includes illustrated examples and an explanation of how any two points on a line can be used to determine its slope. There are several different examples of how the formula for calculating slope is used. A more detailed examination of how the equation of a straight line can be given in slope intercept form with the benefits of that being an immediate identification of the y-intercept value and the slope of the line. Three different methods for solving simultaneous linear equations are illustrated and explained here. These methods can be worked on using the limitless questions available on this worksheet generator.

Try the Equations Worksheet Generator. It will provide a limitless number of simple equations. There are 4 types; e.g. 4x = 12, 5t + 8 = 33, 2r/7 = 4, 5n/3 - 7 = 8. You can decide on the number of questions and you can select combinations of the different types. There is also an option to require just x2, x5, and x10 multiplication facts for those that struggle with memorizing math facts.

Worksheet Generators

There are four worksheet generators that can be categorized in this Equations and Expressions section and they are listed and described below.

• The Equations Worksheet Generator provides a limitless number of simple equations. There are 4 types; e.g. 4x = 12, 5t + 8 = 33, 2r/7 = 4, 5n/3 - 7 = 8. You can decide on the number of questions and you can select combinations of the different types. There is also an option to require just x2, x5, and x10 multiplication facts for those that struggle with memorizing math facts.
• There is a Factoring/ Expanding Linear Expressions: Worksheet Generator that provides expressions in the form of 4a + 20 and 5b + 30c. There is an option for either factoring or expanding the expressions among other options. This is typically a 6th Grade-level worksheet.
• The Solving Simultaneous Equations Worksheet Generator provides pairs of linear equations e.g. 3x + 3y = 31 and 2x + 4y = 12 with the requirement to solve these to find the values of x and y. This is typically an 8th Grade-level worksheet.
• The Factoring Quadratic Expressions Worksheet Generator provides expressions such as
a2 + 8a + 15 for factoring e.g. to (a + 5)(a + 3). There are options to create different types of expression with varying degrees of difficulty for factoring. There is also an option to generate questions on expanding expressions. Note: Unlike most resources on HelpingWithMath.com, this is typically for students beyond the 8th Grade level.

The worksheet generators above are also listed along with many other types on the worksheet generator page.

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