Cheat Sheet
Basic Math & Pre-Algebra For Dummies
If you’re studying math and pre-algebra, you can use a little help, such as help converting English and metric units of measurements and converting fractions to decimals to percents. Then you need to know which operation to do first when solving an equation, the properties of exponents, roots, absolute values and the basic, big four math operations — addition, subtraction, multiplication and division. And, if you’re talking math or algebra, you’re talking formulas, so you need to be familiar with some of the most useful ones.
Comparing English and Metric Units
Converting measurements between the English and metric systems is a common, everyday reason to know math. The following table shows some of the more basic conversions:
| Metric to English Conversions | Metric Units in Plain English |
|---|---|
| 1 meter ≈ 3.26 feet | A meter is about 3 feet (1 yard). |
| 1 kilometer ≈ 0.62 miles | A kilometer is about 1/2 mile. |
| 1 liter ≈ 0.26 gallons | A liter is about 1 quart (1/4 gallon). |
| 1 kilogram ≈ 2.20 pounds | A kilo is about 2 pounds. |
| 0 degrees C = 32 degrees F | 0 degrees C is cold. |
| 10 degrees C = 50 degrees F | 10 degrees C is cool. |
| 20 degrees C = 68 degrees F | 20 degrees C is warm. |
| 30 degrees C = 86 degrees F | 30 degrees C is hot. |
Order of Operations, or Order of Precedence, for Math and Algebra Expressions
When mathematical or algebraic expressions get complex, use the order of operations (also called order of precedence) to simplify them. Evaluate arithmetic from left to right according to the following order of precedence:
Parentheses
Exponents
Multiplication and division
Addition and subtraction
Properties of Exponents, Roots, and Absolute Value, and the Big Four for Math and Algebra Operation
Math operations allow you to combine numbers and perform calculations. In the following list are some important properties of the Big Four operations (adding, subtracting, multiplying, and dividing), as well as three more advanced operations (exponents, square roots, and absolute value).
Converting between Fractions, Decimals, and Percents
Being able to convert fractions, decimals, and percents to their different equivalencies can be of real value when you’re working math or pre-algebra problems. For a quick reference on a range of conversions, consult the following table:
| Fraction | Decimal | Percent | Fraction | Decimal | Percent |
|---|---|---|---|---|---|
| 1⁄100 | 0.01 | 1% | 3⁄5 | 0.6 | 60% |
| 1⁄20 | 0.05 | 5% | 7⁄10 | 0.7 | 70% |
| 1⁄10 | 0.1 | 10% | 3⁄4 | 0.75 | 75% |
| 1⁄5 | 0.2 | 20% | 4⁄5 | 0.8 | 80% |
| 1⁄4 | 0.25 | 25% | 9⁄10 | 0.9 | 90% |
| 3⁄10 | 0.3 | 30% | 1 | 1.0 | 100% |
| 2⁄5 | 0.4 | 40% | 2 | 2.0 | 200% |
| 1⁄2 | 0.5 | 50% | 10 | 10.0 | 1,000% |
Common Math, Algebra, and Geometry Formulas
Math, algebra and geometry formulas are useful things to know whether you’re taking measurements for a home construction project or trying to determine whether the cake batter you intended for a round pan will fit into a square pan. Keep the following list of basic formulas on hand for when you need them:
