Fractions in Action: Simplifying 2 1/2 × 2/3
In this article, we'll delve into the world of fractions and explore how to simplify the multiplication of two mixed numbers: 2 1/2 and 2/3.
Understanding Mixed Numbers
Before we dive into the problem, let's quickly review what mixed numbers are. A mixed number is a combination of a whole number and a fraction. In our case, we have two mixed numbers:
- 2 1/2, which consists of a whole number 2 and a fraction 1/2
- 2/3, which is a fraction
Multiplying Mixed Numbers
To multiply mixed numbers, we need to follow these steps:
- Convert mixed numbers to improper fractions: We'll convert both mixed numbers to improper fractions.
- Multiply the numerators and denominators: We'll multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom).
- Simplify the fraction: We'll simplify the resulting fraction to its lowest terms.
Converting to Improper Fractions
Let's convert our mixed numbers to improper fractions:
- 2 1/2 = (2 × 2) + 1 = 5/2
- 2/3 = 2/3 (no change needed)
Multiplying the Fractions
Now, let's multiply the numerators and denominators:
- Numerators: 5 × 2 = 10
- Denominators: 2 × 3 = 6
So, our resulting fraction is:
- 10/6
Simplifying the Fraction
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD is 2.
- 10 ÷ 2 = 5
- 6 ÷ 2 = 3
So, our final answer is:
- 5/3
Conclusion
In conclusion, the multiplication of 2 1/2 and 2/3 is equal to 5/3. Remember to follow the steps of converting mixed numbers to improper fractions, multiplying the numerators and denominators, and simplifying the fraction to get the correct answer.
