Converting Mixed Numbers to Fractions: 2 1/2 x 3 2/5 as a Fraction
When working with mixed numbers, it's essential to understand how to convert them to fractions. In this article, we'll explore how to convert the mixed numbers 2 1/2 and 3 2/5 to fractions and then multiply them together.
Converting Mixed Numbers to Fractions
A mixed number is a combination of a whole number and a fraction. To convert a mixed number to a fraction, we need to follow a few simple steps:
Converting 2 1/2 to a Fraction
The mixed number 2 1/2 can be converted to a fraction by multiplying the whole number part (2) by the denominator (2) and then adding the numerator (1):
$2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}$
Converting 3 2/5 to a Fraction
The mixed number 3 2/5 can be converted to a fraction by multiplying the whole number part (3) by the denominator (5) and then adding the numerator (2):
$3 \frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}$
Multiplying Fractions
Now that we have converted both mixed numbers to fractions, we can multiply them together:
$\frac{5}{2} \times \frac{17}{5} = \frac{5 \times 17}{2 \times 5} = \frac{85}{10}$
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 5:
$\frac{85}{10} = \frac{85 \div 5}{10 \div 5} = \frac{17}{2}$
Therefore, the result of multiplying 2 1/2 and 3 2/5 is 17/2.
Conclusion
In this article, we've demonstrated how to convert mixed numbers to fractions and then multiply them together. By following these simple steps, you can convert and multiply mixed numbers with ease. Remember to always simplify your fractions by dividing both the numerator and the denominator by their greatest common divisor.
