Fractional numbers, or fractions, represent a part of a whole. They are written as one number over another, separated by a line. Understanding fractions involves knowing what they represent and how to perform mathematical operations with them.
Understanding Fractions
A fraction consists of two parts:
- Numerator: The top number, which represents the number of parts you have.
- Denominator: The bottom number, which represents the total number of equal parts the whole is divided into.
For example, in the fraction 3/4:
- 3 is the numerator.
- 4 is the denominator.
This means you have 3 out of 4 equal parts of something.
Types of Fractions
- Proper Fraction: The numerator is smaller than the denominator (e.g., 1/2, 3/4, 7/8).
- Improper Fraction: The numerator is greater than or equal to the denominator (e.g., 5/4, 8/3, 2/2). Improper fractions can be converted to mixed numbers.
- Mixed Number: A whole number combined with a proper fraction (e.g., 1 1/4, 2 1/2, 3 2/5).
Operations with Fractions
Performing operations with fractions involves following specific rules:
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Adding and Subtracting: Fractions must have the same denominator (a common denominator) before you can add or subtract their numerators. If the denominators are different, you need to find the least common multiple (LCM) of the denominators and convert the fractions accordingly.
- Example: 1/4 + 2/4 = 3/4
- Example (different denominators): 1/2 + 1/3 = 3/6 + 2/6 = 5/6
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Multiplying: Multiply the numerators together and the denominators together.
- Example: 1/2 2/3 = (1 2) / (2 * 3) = 2/6 (which can be simplified to 1/3)
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Dividing: Invert the second fraction (flip the numerator and denominator) and then multiply.
- Example: 1/2 ÷ 2/3 = 1/2 3/2 = (1 3) / (2 * 2) = 3/4
Simplifying Fractions
Simplifying fractions means reducing them to their lowest terms. This is done by finding the greatest common factor (GCF) of the numerator and denominator and dividing both by it.
- Example: 4/8. The GCF of 4 and 8 is 4. Dividing both by 4 gives 1/2.
Converting Fractions, Decimals, and Percentages
Fractions, decimals, and percentages are different ways of representing the same value:
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Fraction to Decimal: Divide the numerator by the denominator.
- Example: 1/4 = 1 ÷ 4 = 0.25
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Decimal to Fraction: Write the decimal as a fraction over a power of 10 (10, 100, 1000, etc.) and simplify.
- Example: 0.75 = 75/100 = 3/4
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Fraction to Percentage: Multiply the fraction by 100%.
- Example: 1/2 = (1/2) * 100% = 50%
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Percentage to Fraction: Write the percentage as a fraction over 100 and simplify.
- Example: 25% = 25/100 = 1/4
In summary, working with fractional numbers involves understanding their components, learning the rules for mathematical operations, and knowing how to convert them to other forms like decimals and percentages.
