Dividing a fraction by an integer is straightforward: you simply multiply the denominator of the fraction by the whole number.
Understanding the Process
The key to dividing fractions by integers lies in understanding that dividing by a number is the same as multiplying by its reciprocal. However, when dealing with fractions and integers, the simplest approach is to directly modify the fraction's denominator.
As the provided reference explains: "multiplying the denominator of your fraction by the whole number. There's nothing more to it!"
Step-by-Step Guide
Here's a breakdown of how to divide a fraction by an integer:
- Identify the fraction and the integer. For example, let's say we want to divide 1/4 by 2.
- Multiply the denominator of the fraction by the integer. In our example, we multiply 4 (the denominator) by 2 (the integer), which equals 8.
- Keep the numerator the same. The numerator in our example is 1, so it remains 1.
- Write the new fraction. The resulting fraction is 1/8. Therefore, 1/4 divided by 2 is 1/8.
Examples
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Example 1: Divide 2/5 by 3.
- Multiply the denominator (5) by the integer (3): 5 * 3 = 15
- Keep the numerator (2) the same.
- The answer is 2/15.
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Example 2: Divide 3/8 by 4.
- Multiply the denominator (8) by the integer (4): 8 * 4 = 32
- Keep the numerator (3) the same.
- The answer is 3/32.
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Example 3: What if you need to simplify after multiplying? Divide 4/6 by 2.
- Multiply the denominator (6) by the integer (2): 6 * 2 = 12
- Keep the numerator (4) the same.
- The answer is 4/12, which can then be simplified to 1/3.
Why This Works
Dividing by a whole number n is the same as multiplying by the fraction 1/n. So, when you divide a fraction a/b by an integer n, you are essentially doing this:
(a/b) / n = (a/b) * (1/n) = a / (b*n)
This confirms that multiplying the denominator by the integer is the correct and most efficient method.
