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With arithmetic a little understanding can go a long way toward helping master math. Some math concepts may seem complicated at first, but after you work with them for a little bit, you may wonder what all the fuss is about. You’ll find easy-to-understand explanations and clear examples in these articles that cover basic math concepts — like order of operations; the commutative, associative, and distributive properties; radicals, exponents, and absolute values — that you may remember (or not) from your early math and pre-algebra classes. You’ll also find two handy and easy-to-understand conversion guides for converting between metric and English units and between fractions, percents, and decimals.
Converting Metric Units to English Units
The English system of measurements is most commonly used in the United States. In contrast, the metric system is used throughout most of the rest of the world. Converting measurements between the English and metric systems is a common everyday reason to know math. This article gives you some precise metric-to-English conversions, as well as some easy-to-remember conversions that are good enough for most situations.
Metric-to-English Conversions | Metric Units in Plain English |
---|---|
1 meter ≈ 3.28 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°C = 32°F | 0°C is cold. |
10°C = 50°F | 10°C is cool. |
20°C = 68°F | 20°C is warm. |
30°C = 86° | 30°C is hot. |
Pre Algebra is the first math course in high school and will guide you through among other things integers, one-step equations, inequalities and equations, graphs and functions, percent, probabilities. We also present an introduction to geometry and right triangles. In Pre Algebra you will for example study.: Review of natural number arithmetic.
Here’s an easy temperature conversion to remember: 16°C = 61°F.
![Algebra Algebra](/uploads/1/2/4/8/124802196/113998592.jpg)
Following the Order of Operations
When arithmetic expressions get complex, use the order of operations (also called the order of precedence) to simplify them. Complex math problems require you to perform a combination of operations — addition, subtraction, multiplication, and division — to find the solution. The order of operations simply tells you what operations to do first, second, third, and so on.
Evaluate arithmetic expressions from left to right, according to the following order of precedence:
- Parentheses
- Exponents
- Multiplication and division
- Addition and subtraction
Following the order of operation is important; otherwise, you’ll end up with the wrong answer. Suppose you have the problem 9 + 5 × 7. If you follow the order of operations, you see that the answer is 44. If you ignore the order of operations and just work left to right, you get a completely different — and wrong — answer:
9 + 5 × 7 = 9 + 35 = 44 RIGHT
9 + 5 × 7 = 14 × 7 = 98 WRONG!
Inverse Operations and Commutative, Associative, and Distributive Properties
The Big Four math operations — addition, subtraction, multiplication, and division — let you combine numbers and perform calculations. Certain operations possess properties that enable you to manipulate the numbers in the problem, which comes in handy, especially when you get into higher math like algebra. The important properties you need to know are the commutative property, the associative property, and the distributive property. Understanding what an inverse operation is is also helpful.
Inverse operations
Inverse operations are pairs of operations that you can work “backward” to cancel each other out. Two pairs of the Big Four operations — addition, subtraction, multiplication, and division —are inverses of each other:
- Addition and subtraction are inverse operations of each other. When you start with any value, then add a number to it and subtract the same number from the result, the value you started with remains unchanged. For example:2 + 3 = 5 so 5 – 3 = 27 – 1 = 6 so 6 + 1 = 7
- Multiplication and division are inverse operations of each other. When you start with any value, then multiply it by a number and divide the result by the same number (except zero), the value you started with remains unchanged. For example:3 × 4 = 12 so 12 ÷ 4 = 310 ÷ 2 = 5 so 5 × 2 = 10
The commutative property
An operation is commutative when you apply it to a pair of numbers either forwards or backwards and expect the same result. The two Big Four that are commutative are addition and subtraction.
Addition is commutative because, for example, 3 + 5 is the same as 5 + 3. In other words
3 + 5 = 5 + 3
Multiplication is commutative because 2 × 7 is the same as 7 × 2. In other words
2 × 7 = 7 × 2
The associative property
An operation is associative when you can apply it, using parentheses, in different groupings of numbers and still expect the same result. The two Big Four operations that are associative are addition and multiplication.
Addition is associative because, for example, the problem (2 + 4) + 7 produces the same result as does the problem 2 + (4 + 7). In other words,
(2 + 4) + 7 = 2 + (4 + 7)
No matter which pair of numbers you add together first, the answer is the same: 13.
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Multiplication is associative because, for example, the problem 3 × (4 × 5) produces the same result as the problem (3 × 4) × 5. In other words,
3 × (4 × 5) = (3 × 4) × 5
Again, no matter which pair of numbers you multiply first, both problems yield the same answer: 60.
The distributive property
The distributive property connects the operations of multiplication and addition. When multiplication is described as “distributive over addition,” you can split a multiplication problem into two smaller problems and then add the results.
For example, suppose you want to multiply 27 × 6. You know that 27 equals 20 + 7, so you can do this multiplication in two steps:
- First multiply 20 × 6; then multiply 7 × 6.20 × 6 = 1207 × 6 = 42
- Then add the results.120 + 42 = 162
Therefore, 27 × 6 = 162.
A Guide to Working with Exponents, Radicals, and Absolute Value
Exponents, radicals, and absolute value are mathematical operations that go beyond addition, subtraction, multiplication, and division. They are useful in more advanced math, such as algebra, but they also have real-world applications, especially in geometry and measurement.
Exponents (powers) are repeated multiplication: When you raise a number to the power of an exponent, you multiply that number by itself the number of times indicated by the exponent. For example:
72= 7 × 7 = 49
25= 2 × 2 × 2 × 2 × 2 = 32
Square roots (radicals) are the inverse of exponent 2 — that is, the number that, when multiplied by itself, gives you the indicated value.
Absolute value is the positive value of a number — that is, the value of a negative number when you drop the minus sign. For example:
Absolute value is used to describe numbers that are always positive, such as the distance between two points or the area inside a polygon.
A Quick Conversion Guide for Fractions, Decimals, and Percents
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Fractions, decimals, and percents are the three most common ways to give a mathematical description of parts of a whole object. Fractions are common in baking and carpentry when you’re using English measurement units (such as cups, gallons, feet, and inches). Decimals are used with dollars and cents, the metric system, and in scientific notation. Percents are used in business when figuring profit and interest rates, as well as in statistics.
Use the following table as a handy guide when you need to make basic conversions among the three.
Fraction | Decimal | Percent |
---|---|---|
1/100 | 0.01 | 1% |
1/20 | 0.05 | 5% |
1/10 | 0.1 | 10% |
1/5 | 0.2 | 20% |
1/4 | 0.25 | 25% |
3/10 | 0.3 | 30% |
2/5 | 0.4 | 40% |
1/2 | 0.5 | 50% |
3/5 | 0.6 | 60% |
7/10 | 0.7 | 70% |
3/4 | 0.75 | 75% |
4/5 | 0.8 | 80% |
9/10 | 0.9 | 90% |
1 | 1.0 | 100% |
2 | 2.0 | 200% |
10 | 10.0 | 1,000% |
Learning Basic Algebra For Dummies
To successfully master basic math, you need to practice addition, subtraction, multiplication, and division problems. You also need to understand order of operations, fractions, decimals, percents, ratios, weights and measures, and even a little geometry. After you’ve become proficient in these and other basic math concepts, you can begin to tackle pre-algebra, which involves variables, expressions, and equations.
Basic Math Tips: Fractions
Fractions are a common way of describing parts of a whole. They’re commonly used for English weights and measures, especially for small measurements in cooking and carpentry. If you want to be proficient in basic math, and if you want to prepare for pre-algebra, you need to know the ins and outs of fractions.
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- Remember that the numerator of a fraction is the top number and the denominator is the bottom number.
- The reciprocal of a fraction is that fraction turned upside-down.
- To increase the terms of a fraction, multiply the numerator and denominator by the same number.
- To reduce the terms of a fraction to lowest terms, divide both the numerator and denominator by the greatest possible number.
- To simplify complex fractions, first simplify the numerator and denominator to two separate fractions; then change the problem to division.
Basic Math Tips: Decimals
Decimals are commonly used for money, as well as for weights and measures, especially when using the metric system. As you practice basic math and pre-algebra problems, you’ll find that decimals are easier to work with than fractions.
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- To change a decimal to a fraction, put the decimal in the numerator of a fraction with a denominator of 1. Then, continue to multiply both the numerator and denominator by 10 until the numerator is a whole number. If necessary, reduce the fraction.
- To change a fraction to a decimal, divide the numerator by the denominator until the division either terminates or repeats.
- To change a repeating decimal to a fraction, put the repeating portion of the decimal (without the decimal point) into the numerator of a fraction. Use as a denominator a number composed only of 9s with the same number of digits as the numerator. If necessary, reduce the fraction.
- To add or subtract decimals, line up the decimal points.
- To multiply decimals, begin by multiplying without worrying about the decimal points. When you’re done, count the number of digits to the right of the decimal point in each factor and add the result. Place the decimal point in your answer so that your answer has the same number of digits after the decimal point.
- To divide decimals, turn the divisor (the number you’re dividing by) into a whole number by moving the decimal point all the way to the right. At the same time, move the decimal point in the dividend (the number you’re dividing) the same number of places to the right. Then place a decimal point in the quotient (the answer) directly above where the decimal point now appears in the dividend.
- When dividing decimals, continue until the answer either terminates or repeats.
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Basic Math Tips: Percents
Percents are commonly used in business to represent partial amounts of money. They’re also used in statistics to indicate a portion of a data set. As you practice basic math problems, you’ll discover that percents are closely related to decimals, which means that they’re easier to work with than fractions.
- To change a percent to a decimal, move the decimal point two places to the left and drop the percent sign.
- To change a decimal to a percent, move the decimal point two places to the right and attach a percent sign.
- To change a percent to a fraction, drop the percent sign and put the number of the percent in the numerator of a fraction with a denominator of 100. If necessary, reduce the fraction.
- To change a fraction to a percent, first change the fraction to a decimal by dividing. Then change the decimal to a percent by moving the decimal point two places to the right and attaching a percent sign.
- Calculate simple percents by dividing. For example, to find 50% of a number, divide by 2; to find 25%, divide by 4; to find 20%, divide by 5; and so forth.
- You can calculate some percents by reversing the numbers. For example 14% of 50 is the same as 50% of 14, which equals 7.