Multiplying Mixed Numbers: 1 2/3 x 1 1/5
Let's solve the multiplication problem: 1 2/3 x 1 1/5.
Understanding Mixed Numbers
Before we multiply, let's understand what mixed numbers are. A mixed number combines a whole number and a fraction, like 1 2/3.
Converting Mixed Numbers to Improper Fractions
To make multiplication easier, we'll convert the mixed numbers into improper fractions. Here's how:
- 1 2/3: Multiply the whole number (1) by the denominator (3) and add the numerator (2): (1 * 3) + 2 = 5. Keep the same denominator (3). The improper fraction is 5/3.
- 1 1/5: Multiply the whole number (1) by the denominator (5) and add the numerator (1): (1 * 5) + 1 = 6. Keep the same denominator (5). The improper fraction is 6/5.
Multiplying the Improper Fractions
Now we have: 5/3 x 6/5. To multiply fractions, we multiply the numerators and the denominators:
- (5 x 6) / (3 x 5)
- 30/15
Simplifying the Fraction
The fraction 30/15 can be simplified. Both the numerator and denominator are divisible by 15:
- 30/15 = 2/1 = 2
Conclusion
Therefore, 1 2/3 x 1 1/5 = 2.