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Pre-Algebra

Math Review of Applications of Percents

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Overview Percents are based on the decimal system and have many useful applications in business, sales, and finance. Other applications of percents include percent increase and decrease. Estimating Percentages Many of the most useful applications of percents involve estimating and calculating percentages for sales tax and tips at a restaurant. Suppose the sales tax is…

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Math Review of Inequalities with More than One Step

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Overview If an inequality contains more than one operation, it will take more than one step to solve it. Suppose that in order to solve an inequality, both multiplication and addition statements need to be undone by using the multiplicative and additive inverses. As with other inequalities that take one step, the variable will have…

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Math Review of Inequalities

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Overview While equations are statements that two quantities are equal, inequalities state that quantities are not equal. One side of the expression might be greater than the other side, or one side of the expression may be less. Correct solutions for variables encompass more than one number. Inequalities Inequalities include symbols such as greater than…

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Math Review of Percents

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Overview Percents are special types of ratios that compare the number to 100. Similar to any ratio, a percent can be expressed as a fraction. Since percents compare to 100, they can also be expressed in decimal form. Fractions to Percents Percent or the percent sign (%) means “per 100,” so 5% means the same…

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Math Review of Rates, Ratios, and Proportions

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Overview A rate compares 2 quantities that have different types of units, such as kilometers per hour or miles per gallon. A ratio compares quantities with the same type of units by dividing the quantity in the numerator by the quantity in the denominator, as in a fraction. A proportion states that 2 ratios are…

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Math Review of Two-Step and Multi-Step Equations

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Overview Not all equations can be solved in one step. Many take several steps to solve, but the principles of solving one-step equations can be applied. Use the order of operations to simplify the equation; math properties to combine like terms; then apply inverses to isolate the variable on one side of the equation in…

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Math Review of One-Step Equations

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Overview Some algebra equations can be solved with one step, using operations such as addition, subtraction, multiplication, and division. In order to solve them, use inverse operations so that the variable is on one side and real numbers are on the other side. Then, solve the problem with arithmetic. Balanced Equations An equation is solved…

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Math Review of Simplifying Expressions

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Overview Students can use the commutative, associative, and distributive properties of addition and multiplication to simplify algebraic expressions. Problems are more easily solved if compatible terms can be combined first. Some problems can then be solved mentally. Compatible Terms Real numbers, whether whole or mixed, are constants that can be added, subtracted, multiplied or divided.…

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Math Review of Order of Operations

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Overview Order of operations within math problems gives students a set of rules to follow in order to get the same answer. In the standard order of operations, expressions within parentheses are worked first, then exponents, then multiplication, division, addition, and subtraction. Conventional Order Suppose the problem is as simple as 85 +9 X 2.…

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Math Review of Operations with Real Numbers

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Overview Operations with real numbers are the most familiar types in mathematics. Those numerical expressions with constants and operations include such actions as addition, subtraction, multiplication, and division.   Many algebraic expressions are usually operations with real numbers. Real Numbers The set of real numbers include the entire set of rational numbers, such as positive and…

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