Multiplying fractions by large whole numbers can seem daunting, but it's much simpler than it looks! This guide breaks down the process into easy-to-follow steps, using a winning formula that guarantees success. We'll cover the fundamental concepts and offer practical examples to build your confidence and mastery. By the end, you'll be confidently tackling even the most challenging fraction multiplication problems.
Understanding the Fundamentals
Before diving into the formula, let's solidify our understanding of the key components: fractions and whole numbers.
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Fractions: A fraction represents a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). The denominator tells you how many equal parts the whole is divided into, while the numerator tells you how many of those parts you have. For example, ¾ represents three parts out of a total of four equal parts.
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Whole Numbers: These are the counting numbers (1, 2, 3, and so on) and zero (0). They represent complete units.
The Winning Formula: Turning Whole Numbers into Fractions
The secret to effortlessly multiplying fractions with large whole numbers lies in converting the whole number into a fraction. Here's how:
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Write the whole number as the numerator: Place the whole number on top of the fraction.
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Give it a denominator of 1: Every whole number can be expressed as a fraction with a denominator of 1. For example, the whole number 5 can be written as 5/1.
Now you're ready to multiply two fractions!
Step-by-Step Multiplication Process
Let's illustrate the process with an example: Multiply ¾ by 12.
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Convert the whole number to a fraction: 12 becomes 12/1.
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Multiply the numerators: Multiply the top numbers together: 3 x 12 = 36
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Multiply the denominators: Multiply the bottom numbers together: 4 x 1 = 4
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Simplify the result (if necessary): You now have the fraction 36/4. To simplify, divide both the numerator and denominator by their greatest common factor (GCF), which in this case is 4. 36 ÷ 4 = 9 and 4 ÷ 4 = 1. Therefore, the simplified answer is 9/1, or simply 9.
More Examples to Practice
Let's try a few more examples to solidify your understanding:
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Example 1: 2/5 x 25 = (2/5) x (25/1) = 50/5 = 10
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Example 2: 7/8 x 16 = (7/8) x (16/1) = 112/8 = 14
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Example 3: 3/7 x 49 = (3/7) x (49/1) = 147/7 = 21
Mastering Fraction Multiplication
With consistent practice and a solid grasp of this winning formula, multiplying fractions by large whole numbers becomes a breeze. Remember the key steps: convert the whole number to a fraction, multiply the numerators, multiply the denominators, and simplify the result. This method guarantees accuracy and efficiency, ensuring success every time!
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