Simplifying Fractions: 2 1/4 x 5/6 as a Fraction
In this article, we will explore how to simplify the multiplication of two mixed numbers, specifically 2 1/4 x 5/6 as a fraction.
Understanding Mixed Numbers
Before we dive into the multiplication, let's quickly review what mixed numbers are. A mixed number is a combination of a whole number and a proper fraction. In our example, 2 1/4 is a mixed number, where 2 is the whole number and 1/4 is the fraction.
Converting Mixed Numbers to Improper Fractions
To multiply mixed numbers, we need to convert them into improper fractions first. An improper fraction is a fraction where the numerator is larger than the denominator.
Let's convert our mixed numbers:
- 2 1/4 = ?
- Multiply the whole number (2) by the denominator (4): 2 × 4 = 8
- Add the numerator (1) to the product: 8 + 1 = 9
- So, 2 1/4 = 9/4
- 5/6 = no conversion needed, it's already a proper fraction!
Multiplying Fractions
Now that we have our improper fractions, we can multiply them:
- 9/4 × 5/6 = ?
- Multiply the numerators (9 × 5): 45
- Multiply the denominators (4 × 6): 24
- So, 9/4 × 5/6 = 45/24
Simplifying the Fraction
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator (45) and the denominator (24).
- GCD of 45 and 24 is 3
- Divide both the numerator and the denominator by 3: 45 ÷ 3 = 15, 24 ÷ 3 = 8
- So, 45/24 = 15/8
The Final Answer
Therefore, 2 1/4 x 5/6 as a fraction is equal to 15/8.
In conclusion, to multiply mixed numbers, we need to convert them into improper fractions, multiply the numerators and denominators, and simplify the resulting fraction. By following these steps, we can successfully simplify 2 1/4 x 5/6 as a fraction.
