Evaluating Mixed Fractions: 2 3/5 x 3 1/3
In this article, we will explore how to multiply two mixed fractions: 2 3/5 and 3 1/3. Mixed fractions can be a bit tricky to work with, but with the right steps, we can simplify the calculation and get the correct answer.
Step 1: Convert Mixed Fractions to Improper Fractions
To multiply mixed fractions, we need to convert them to improper fractions first. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
2 3/5 as an Improper Fraction
To convert 2 3/5 to an improper fraction, we multiply the whole number part (2) by the denominator (5) and then add the numerator (3).
2 × 5 = 10 10 + 3 = 13
So, 2 3/5 as an improper fraction is 13/5.
3 1/3 as an Improper Fraction
To convert 3 1/3 to an improper fraction, we multiply the whole number part (3) by the denominator (3) and then add the numerator (1).
3 × 3 = 9 9 + 1 = 10
So, 3 1/3 as an improper fraction is 10/3.
Step 2: Multiply the Improper Fractions
Now that we have converted both mixed fractions to improper fractions, we can multiply them together.
13/5 × 10/3
To multiply fractions, we multiply the numerators (13 and 10) and multiply the denominators (5 and 3).
Numerator: 13 × 10 = 130 Denominator: 5 × 3 = 15
So, the result of multiplying 2 3/5 and 3 1/3 is 130/15.
Step 3: Simplify the Fraction
The final step is to simplify the resulting fraction. We can simplify 130/15 by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 130 and 15 is 5.
130 ÷ 5 = 26 15 ÷ 5 = 3
So, the simplified result is 26/3.
The Final Answer
The result of multiplying 2 3/5 and 3 1/3 is 26/3, which can also be written as a mixed fraction: 8 2/3.
In conclusion, by following these steps, we can successfully multiply mixed fractions and simplify the result to get the correct answer.
