Multiplying Mixed Fractions: 1 2/9 x 1 4/5
This article will guide you through the process of multiplying the mixed fractions 1 2/9 and 1 4/5. We will break down each step to ensure understanding.
Step 1: Convert Mixed Fractions to Improper Fractions
First, we need to convert our mixed fractions into improper fractions.
- 1 2/9: Multiply the whole number (1) by the denominator (9) and add the numerator (2): (1 * 9) + 2 = 11. Keep the same denominator (9). This gives us 11/9.
- 1 4/5: Multiply the whole number (1) by the denominator (5) and add the numerator (4): (1 * 5) + 4 = 9. Keep the same denominator (5). This gives us 9/5.
Step 2: Multiply the Improper Fractions
Now, multiply the two improper fractions we just found:
(11/9) * (9/5)
To multiply fractions, we multiply the numerators and the denominators:
(11 * 9) / (9 * 5) = 99 / 45
Step 3: Simplify the Result
The fraction 99/45 can be simplified. Both the numerator and denominator are divisible by 9:
99 / 45 = (99/9) / (45/9) = 11/5
Step 4: Convert Back to a Mixed Fraction
Finally, convert the improper fraction 11/5 back to a mixed fraction. Divide the numerator (11) by the denominator (5):
11 ÷ 5 = 2 with a remainder of 1.
The quotient (2) becomes the whole number, and the remainder (1) becomes the numerator of the fraction. The denominator stays the same. Therefore, 11/5 is equal to 2 1/5.
Conclusion
Therefore, the product of 1 2/9 and 1 4/5, expressed as a mixed fraction, is 2 1/5.