Mastering Quantitative Reasoning: Integers, Fractions, Decimals, and Percentages for GRE
Welcome to this module on foundational quantitative reasoning concepts crucial for the GRE. We'll delve into integers, fractions, decimals, and percentages, understanding their properties, conversions, and applications. Mastering these building blocks is essential for tackling more complex GRE math problems.
Integers: The Building Blocks
Integers are whole numbers, including positive numbers, negative numbers, and zero. They form the basis of many mathematical operations. Understanding their properties, such as even/odd, positive/negative, and their behavior in addition, subtraction, multiplication, and division, is key.
The set of integers includes all whole numbers (positive, negative, and zero). Example: Positive integer = 5, Negative integer = -3, Zero = 0.
Fractions: Parts of a Whole
Fractions represent a part of a whole. They consist of a numerator (the top number, indicating how many parts we have) and a denominator (the bottom number, indicating how many equal parts the whole is divided into). Understanding equivalent fractions, simplifying fractions, and performing operations with fractions is vital.
Decimals: Another Way to Represent Parts
Decimals are another way to represent numbers that are not whole numbers. They use a decimal point to separate the whole number part from the fractional part. Each digit to the right of the decimal point represents a power of 10 (tenths, hundredths, thousandths, etc.).
The relationship between fractions and decimals is fundamental. For example, the fraction 1/2 is equivalent to the decimal 0.5. The fraction 3/4 is equivalent to 0.75. To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a fraction, place the decimal digits over the appropriate power of 10 (e.g., 0.75 becomes 75/100, which simplifies to 3/4). Operations with decimals follow standard arithmetic rules, paying close attention to the placement of the decimal point.
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Percentages: Parts Per Hundred
Percentages represent a fraction out of 100. The symbol '%' means 'per hundred'. For instance, 50% is equivalent to 50/100, which simplifies to 1/2 or 0.5. Understanding how to convert between percentages, fractions, and decimals is a core skill.
| Concept | Fraction | Decimal | Percentage |
|---|---|---|---|
| One Half | 1/2 | 0.5 | 50% |
| One Quarter | 1/4 | 0.25 | 25% |
| Three Quarters | 3/4 | 0.75 | 75% |
| One Tenth | 1/10 | 0.1 | 10% |
Conversions and Applications
The GRE often tests your ability to convert between these number forms and apply them in word problems. Key applications include calculating discounts, interest, profit/loss, and proportions. Practice is crucial for fluency.
Remember the conversion shortcuts: To convert a percentage to a decimal, divide by 100 (move the decimal point two places left). To convert a decimal to a percentage, multiply by 100 (move the decimal point two places right). To convert a fraction to a percentage, convert it to a decimal first, then multiply by 100.
To find 20% of 150, convert 20% to a decimal (0.20) and multiply: 0.20 * 150 = 30.
Putting It All Together: GRE Practice
The GRE Quantitative Reasoning section will present problems that require you to seamlessly switch between integers, fractions, decimals, and percentages. Focus on understanding the underlying concepts and practicing a wide variety of problem types. Consistent review and problem-solving are your best allies.
Learning Resources
Official GRE Math Review from ETS covering the properties and operations of integers.
Official GRE Math Review from ETS detailing conversions and operations for fractions, decimals, and percentages.
Comprehensive video lessons and practice exercises on fractions, decimals, and their conversions.
A detailed blog post explaining GRE percentage concepts, including common pitfalls and strategies.
An overview of the GRE Quantitative Reasoning section, touching upon fundamental math concepts like number types.
In-depth articles on number properties, including integers, fractions, and decimals, with GRE-specific examples.
A free video tutorial from GregMat+ that breaks down percentage concepts and problem-solving techniques for the GRE.
A tutorial covering integer properties, operations, and common GRE question types involving integers.
An accessible explanation of percentages, including their definition, conversion methods, and practical uses.
A forum with a vast collection of GRE math practice questions, filterable by topic, including integers, fractions, decimals, and percentages.