Multiplying Mixed Numbers: A Step-by-Step Guide
Let's break down how to multiply the mixed numbers 1 2/3 and 1 1/4 to arrive at a single fraction.
Converting Mixed Numbers to Improper Fractions
The first step is to convert our mixed numbers into improper fractions. To do this, we follow these simple steps:
- Multiply the whole number by the denominator:
- For 1 2/3: 1 x 3 = 3
- For 1 1/4: 1 x 4 = 4
- Add the numerator to the result:
- For 1 2/3: 3 + 2 = 5
- For 1 1/4: 4 + 1 = 5
- Keep the original denominator:
- 1 2/3 becomes 5/3
- 1 1/4 becomes 5/4
Now we have our original problem as: (5/3) x (5/4)
Multiplying Fractions
To multiply fractions, we simply multiply the numerators and the denominators:
- Numerator: 5 x 5 = 25
- Denominator: 3 x 4 = 12
This gives us the result: 25/12
Simplifying the Fraction
The fraction 25/12 is an improper fraction because the numerator is larger than the denominator. We can simplify this into a mixed number:
- Divide the numerator by the denominator: 25 ÷ 12 = 2 with a remainder of 1.
- The quotient (2) becomes the whole number part of the mixed number.
- The remainder (1) becomes the numerator of the fraction.
- The denominator remains the same (12).
Therefore, 25/12 simplifies to 2 1/12.
Conclusion
By following these steps, we have successfully multiplied the mixed numbers 1 2/3 and 1 1/4, arriving at the answer 2 1/12.