3 1/3 x 3/4: A Guide to Multiplying Mixed Numbers
In mathematics, multiplying mixed numbers can seem intimidating, but it's a crucial skill to master. In this article, we'll explore the step-by-step process of multiplying 3 1/3 x 3/4.
Understanding Mixed Numbers
Before we dive into the multiplication process, let's quickly review what mixed numbers are. A mixed number is a combination of a whole number and a fraction. For example, 3 1/3 is a mixed number, where 3 is the whole number and 1/3 is the fraction.
Converting Mixed Numbers to Improper Fractions
To multiply mixed numbers, it's essential to convert them to improper fractions first. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Converting 3 1/3 to an Improper Fraction
To convert 3 1/3 to an improper fraction, we'll multiply the whole number (3) by the denominator (3) and then add the numerator (1). This gives us:
3 × 3 = 9 9 + 1 = 10
So, 3 1/3 is equal to the improper fraction 10/3.
Converting 3/4 to an Improper Fraction
Since 3/4 is already a fraction, we don't need to convert it.
Multiplying Improper Fractions
Now that we have our improper fractions, we can multiply them together. To do this, we'll multiply the numerators (10 and 3) and the denominators (3 and 4).
** Multiplication Process **
10 × 3 = 30 (numerators) 3 × 4 = 12 (denominators)
So, the result of multiplying 10/3 and 3/4 is 30/12.
Simplifying the Result
We can simplify the fraction 30/12 by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 30 and 12 is 6.
30 ÷ 6 = 5 12 ÷ 6 = 2
So, the simplified result is 5/2.
Final Answer
Therefore, 3 1/3 x 3/4 is equal to 5/2 or 2 1/2.
