Dividing Mixed Numbers: 2 2/3 ÷ 3 1/4 as a Fraction
When dividing mixed numbers, it's essential to follow a specific process to ensure accurate results. In this article, we'll explore how to divide 2 2/3 by 3 1/4 as a fraction.
Converting Mixed Numbers to Improper Fractions
Before we can divide the mixed numbers, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Converting 2 2/3 to an Improper Fraction
To convert 2 2/3 to an improper fraction, we'll multiply the whole number part (2) by the denominator (3) and then add the numerator (2):
2 × 3 = 6 6 + 2 = 8
So, 2 2/3 is equal to 8/3.
Converting 3 1/4 to an Improper Fraction
Using the same process, we'll convert 3 1/4 to an improper fraction:
3 × 4 = 12 12 + 1 = 13
So, 3 1/4 is equal to 13/4.
Dividing Improper Fractions
Now that we have our improper fractions, we can divide them:
8/3 ÷ 13/4
To divide fractions, we'll invert the second fraction (i.e., flip the numerator and denominator) and then multiply:
8/3 × 4/13
Multiplying Fractions
To multiply fractions, we'll multiply the numerators and denominators separately:
8 × 4 = 32 3 × 13 = 39
So, the result of the division is:
32/39
Simplifying the Fraction (Optional)
If we want to simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 32 and 39 is 1, so the fraction is already in its simplest form.
Final Answer
The result of dividing 2 2/3 by 3 1/4 as a fraction is:
32/39
