To divide a fraction by an integer, you can rewrite the integer as a fraction and then multiply by the reciprocal, effectively "flipping" the second fraction (the integer).
Here’s a breakdown of the process, incorporating insights from the provided YouTube reference:
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Understand the Problem: You're starting with a fraction (e.g., 1/2) and dividing it by an integer (e.g., 3).
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Rewrite the Integer as a Fraction: Any integer can be expressed as a fraction by placing it over 1. For example, 3 becomes 3/1. The reference mentions that "the denominator needs to be one, and the numerator is three".
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Change Division to Multiplication: Division is the same as multiplying by the reciprocal. Change the division sign (÷) to a multiplication sign (×).
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Invert (Flip) the Second Fraction: This means swapping the numerator and denominator of the second fraction (the one you're dividing by). So, 3/1 becomes 1/3. The reference uses the term "invert or flip the second fraction".
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Multiply the Fractions: Multiply the numerators together and the denominators together.
- Numerator × Numerator
- Denominator × Denominator
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Simplify: If possible, simplify the resulting fraction.
Example:
Let's divide 1/2 by 3.
- Problem: 1/2 ÷ 3
- Integer as a Fraction: 3 = 3/1
- Change to Multiplication: 1/2 × ?
- Invert the Second Fraction: 3/1 becomes 1/3
- Multiply: 1/2 × 1/3 = (1 × 1) / (2 × 3) = 1/6
- Simplify: 1/6 (already in simplest form)
Therefore, 1/2 divided by 3 is 1/6.
Summary in Table Format:
| Step | Action | Example (1/2 ÷ 3) |
|---|---|---|
| 1. Prepare | Write the problem | 1/2 ÷ 3 |
| 2. Integer to Fraction | Represent the integer as a fraction over 1 | 3 = 3/1 |
| 3. Change to Multiply | Replace division with multiplication | 1/2 × ? |
| 4. Invert | Flip the second fraction | 3/1 becomes 1/3 |
| 5. Multiply | Multiply numerators and denominators | 1/2 × 1/3 = 1/6 |
| 6. Simplify (if needed) | Reduce the fraction to its simplest form | 1/6 (already simple) |
