To work with ratios involving mixed fractions, the key is to first convert all mixed numbers into improper fractions. Here's how:
Steps for Ratios with Mixed Fractions
- Convert Mixed Numbers to Improper Fractions:
- A mixed number consists of a whole number and a fraction (e.g., 3 2/3).
- To convert it to an improper fraction:
- Multiply the whole number by the denominator of the fraction.
- Add the result to the numerator of the fraction.
- Keep the same denominator.
- Example: 3 2/3 becomes (3 * 3 + 2)/3 = 11/3
- Write Ratios as Fractions:
- A ratio can be written as a fraction. For instance, a ratio of 4 to 3 2/3 would be written as 4 / (3 2/3).
- Rewrite Whole Numbers as Fractions:
- Any whole number can be written as a fraction by putting it over 1.
- Example: 4 becomes 4/1. So, 4 / (3 2/3) becomes (4/1) / (11/3) after converting the mixed number.
- Divide Fractions (Invert and Multiply):
- When dividing fractions, invert the second fraction and multiply.
- Example: (4/1) / (11/3) becomes (4/1) * (3/11) = 12/11.
- Simplify (If Possible):
- After multiplying, simplify the fraction if needed.
Example
Let's use the example from the reference provided. The ratio is 4 to 3 2/3.
| Step | Description | Calculation |
|---|---|---|
| 1. Convert Mixed Number | Convert the mixed fraction to improper fraction | 3 2/3 = (3*3 + 2)/3 = 11/3 |
| 2. Express Ratio | Write the ratio as a fraction | 4 / (11/3) |
| 3. Convert Whole Number | Write the whole number as fraction | 4 = 4/1 |
| 4. Invert and Multiply | Invert the second fraction and multiply | (4/1) * (3/11) |
| 5. Result | Multiply the numerators, and multiply the denominators for the final result. | 12/11 |
Therefore the ratio of 4 to 3 2/3 is 12/11.
The reference video states "... So four we write as 4 over 1 3 and 2/3. Well 3 * 3 is 9 + 2 is 11. So that becomes 11/3 the next step is to then get a common denominator...". It highlights the importance of converting the mixed fraction to an improper fraction which is a crucial step to solving the problem.
