Multiplying Mixed Numbers: 1 2/9 x 1 4/5
This article will guide you through the steps of multiplying the mixed numbers 1 2/9 and 1 4/5.
Understanding Mixed Numbers
Before we start, let's remember what mixed numbers are. They are a combination of a whole number and a fraction. For example, 1 2/9 represents one whole plus two-ninths.
Converting to Improper Fractions
The first step in multiplying mixed numbers is to convert them into improper fractions. To do this:
- Multiply the whole number by the denominator of the fraction. In 1 2/9, 1 x 9 = 9.
- Add the numerator. 9 + 2 = 11.
- Keep the same denominator. This gives us 11/9.
We apply the same process to 1 4/5: 1 x 5 = 5, 5 + 4 = 9, so 1 4/5 becomes 9/5.
Multiplying the Improper Fractions
Now that we have improper fractions, we can multiply them like any other fraction:
- Multiply the numerators. 11 x 9 = 99.
- Multiply the denominators. 9 x 5 = 45.
This gives us 99/45.
Simplifying the Answer
The final step is to simplify the improper fraction 99/45. We can do this by finding the greatest common factor (GCF) of the numerator and denominator, which is 9. Dividing both by 9, we get 11/5.
Converting Back to Mixed Number (Optional)
Since the answer is an improper fraction, we can convert it back to a mixed number:
- Divide the numerator by the denominator. 11 ÷ 5 = 2 with a remainder of 1.
- The quotient becomes the whole number. So we have 2.
- The remainder becomes the numerator of the fraction. The denominator stays the same. This gives us 2 1/5.
Conclusion
Therefore, 1 2/9 multiplied by 1 4/5 equals 11/5 or 2 1/5. Remember to always convert mixed numbers to improper fractions before multiplying, and simplify your answer if possible.