Simplifying Mixed Numbers: 2 3/10 x 5 1/3
In this article, we will explore how to multiply two mixed numbers, specifically 2 3/10 and 5 1/3, and simplify the result to its simplest form.
Converting Mixed Numbers to Improper Fractions
Before we can multiply the two mixed numbers, we need to convert them into improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Converting 2 3/10
To convert 2 3/10 into an improper fraction, we can multiply the whole number part (2) by the denominator (10) and then add the numerator (3):
2 × 10 = 20 20 + 3 = 23
So, 2 3/10 is equal to the improper fraction:
23/10
Converting 5 1/3
Using the same process, we can convert 5 1/3 into an improper fraction:
5 × 3 = 15 15 + 1 = 16
So, 5 1/3 is equal to the improper fraction:
16/3
Multiplying the Improper Fractions
Now that we have converted both mixed numbers into improper fractions, we can multiply them together:
23/10 × 16/3
To multiply fractions, we multiply the numerators (23 and 16) and multiply the denominators (10 and 3):
(23 × 16) / (10 × 3) = 368 / 30
Simplifying the Result
To simplify the result, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 368 and 30 is 2.
368 ÷ 2 = 184 30 ÷ 2 = 15
So, the simplified result is:
184/15
Converting Back to a Mixed Number (Optional)
If we want to convert the improper fraction back into a mixed number, we can divide the numerator by the denominator:
184 ÷ 15 = 12 with a remainder of 4
So, the mixed number equivalent of 184/15 is:
12 4/15
Therefore, the result of multiplying 2 3/10 and 5 1/3 and simplifying the result is 12 4/15.
