Multiplying fractions, especially those nestled within brackets, can seem daunting at first. But with a structured approach and a solid understanding of the fundamental rules, you'll master this skill in no time. This comprehensive guide breaks down the process step-by-step, ensuring you gain confidence and accuracy in your calculations.
Understanding the Fundamentals: Fractions and Brackets
Before tackling the complexities of multiplying fractions within brackets, let's refresh our understanding of the individual components:
Fractions: A fraction represents a part of a whole. It's expressed as a numerator (the top number) over a denominator (the bottom number), like this: numerator/denominator. For example, 1/2 represents one-half.
Brackets (Parentheses): Brackets, or parentheses, in mathematical expressions dictate the order of operations. Calculations within brackets must be performed before operations outside the brackets. This is crucial when dealing with fractions. Following the order of operations (often remembered by the acronym PEMDAS/BODMAS) ensures accuracy.
Multiplying Fractions: The Basic Process
The core of multiplying fractions involves multiplying the numerators together and then multiplying the denominators together. Here's the formula:
(a/b) * (c/d) = (a * c) / (b * d)
Example:
(2/3) * (4/5) = (2 * 4) / (3 * 5) = 8/15
Multiplying Fractions in Brackets: A Step-by-Step Guide
Now, let's integrate brackets into our fraction multiplication. The key is to tackle the calculations within the brackets first, then proceed with any remaining operations.
Example 1: Simple Brackets
[(1/2) * (3/4)] * 2 = ?
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Solve the bracketed expression: (1/2) * (3/4) = (13) / (24) = 3/8
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Complete the remaining multiplication: (3/8) * 2 = (3*2) / 8 = 6/8 = 3/4 (Simplified)
Example 2: More Complex Brackets
[(2/5 + 1/5) * (1/3)] / 2 = ?
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Solve the addition within the brackets: (2/5 + 1/5) = 3/5
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Perform the multiplication within the brackets: (3/5) * (1/3) = (31) / (53) = 3/15 = 1/5
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Complete the final division: (1/5) / 2 = (1/5) * (1/2) = 1/10
Simplifying Fractions: A Crucial Step
After performing any multiplication, always simplify your answer to its lowest terms. This involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
Example:
6/8 can be simplified to 3/4 (dividing both by 2, the GCD).
Practice Makes Perfect!
The best way to master multiplying fractions in brackets is through consistent practice. Start with simpler examples and gradually work your way up to more complex problems. Online resources and textbooks offer plenty of practice exercises. Remember to break down each problem step-by-step, focusing on accuracy and understanding. Soon, you'll be confidently tackling even the most challenging fraction multiplication problems!
