Multiplying Mixed Numbers: 2 3/4 times 1 2/3
When multiplying mixed numbers, we need to follow a specific procedure to ensure accurate results. In this article, we will explore the step-by-step process for multiplying 2 3/4 and 1 2/3 in fraction form.
Converting Mixed Numbers to Improper Fractions
Before we can multiply the mixed numbers, we need to convert them to improper fractions.
2 3/4
To convert 2 3/4 to an improper fraction, we multiply the whole number part (2) by the denominator (4) and then add the numerator (3).
2 × 4 = 8 8 + 3 = 11
So, 2 3/4 is equal to 11/4.
1 2/3
Following the same process, we convert 1 2/3 to an improper fraction.
1 × 3 = 3 3 + 2 = 5
So, 1 2/3 is equal to 5/3.
Multiplying Improper Fractions
Now that we have converted both mixed numbers to improper fractions, we can multiply them.
11/4 × 5/3
To multiply fractions, we multiply the numerators (11 and 5) and the denominators (4 and 3).
Numerators: 11 × 5 = 55 Denominators: 4 × 3 = 12
The result of the multiplication is 55/12.
Simplifying the Result
The final answer is 55/12. This is an improper fraction, and we can simplify it further by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 55 and 12 is 1, so the fraction 55/12 is already in its simplest form.
Conclusion
In conclusion, the result of multiplying 2 3/4 and 1 2/3 is 55/12. By converting the mixed numbers to improper fractions and then multiplying them, we arrived at the final answer in fraction form.
