Converting Mixed Numbers to Fractions: A Guide to 3 1/2 x 3 1/2
Mixed numbers can often be confusing, especially when it comes to performing arithmetic operations on them. In this article, we will explore how to convert mixed numbers to fractions, specifically focusing on the example of 3 1/2 x 3 1/2.
What is a Mixed Number?
A mixed number is a combination of a whole number and a fraction. It is often written in the form of a b/c, where a is the whole number part and b/c is the fractional part.
Converting 3 1/2 to a Fraction
To convert the mixed number 3 1/2 to a fraction, we need to follow a simple step:
- Multiply the whole number part (3) by the denominator (2):
3 x 2 = 6 - Add the numerator (1) to the product:
6 + 1 = 7 - Write the result as a fraction:
7/2
So, 3 1/2 in fraction form is 7/2.
Multiplying Fractions: 7/2 x 7/2
Now that we have converted both mixed numbers to fractions, we can multiply them together:
(7/2) x (7/2) = ?
To multiply fractions, we need to follow the rule:
(a/b) x (c/d) = (ac)/(bd)
In our case, a = 7, b = 2, c = 7, and d = 2. Plugging in these values, we get:
(7/2) x (7/2) = (7 x 7) / (2 x 2) = 49/4
Simplifying the Result
The resulting fraction, 49/4, can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1 in this case. Therefore, the final result is:
49/4
Conclusion
In this article, we have successfully converted the mixed number 3 1/2 to a fraction and multiplied it by itself. The result, 49/4, is the product of the two fractions. By following these simple steps, you can convert mixed numbers to fractions and perform various arithmetic operations on them with ease.
