Fraction Calculation: 5/16 x 3-3/4
In this article, we will explore the calculation of multiplying a fraction with a mixed number. Specifically, we will look at the problem 5/16 x 3-3/4.
Understanding the Problem
Before we dive into the calculation, let's break down the problem into its components.
- 5/16: This is a fraction, where 5 is the numerator and 16 is the denominator.
- 3-3/4: This is a mixed number, which is a combination of a whole number and a fraction. We can break it down further into:
- 3: The whole number part
- 3/4: The fraction part
Converting the Mixed Number to an Improper Fraction
To make the calculation easier, we need to convert the mixed number 3-3/4 to an improper fraction. An improper fraction is a fraction where the numerator is greater than the denominator.
To convert 3-3/4 to an improper fraction, we multiply the whole number part (3) by the denominator (4), then add the numerator (3).
(3 x 4) + 3 = 15
So, the improper fraction is 15/4.
Multiplying the Fraction and the Improper Fraction
Now we can multiply the fraction 5/16 with the improper fraction 15/4.
(5/16) x (15/4)
To multiply fractions, we multiply the numerators (5 and 15) and multiply the denominators (16 and 4).
(5 x 15) / (16 x 4) = 75 / 64
Simplifying the Result
The result of the multiplication is 75/64. This is an improper fraction, and we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 75 and 64 is 1, so the simplified result is still 75/64.
Conclusion
In this article, we have calculated the result of multiplying the fraction 5/16 with the mixed number 3-3/4. By converting the mixed number to an improper fraction and then multiplying the two fractions, we arrived at the simplified result of 75/64.
