Multiplying Mixed Numbers: 1 1/6 x 3 1/2
This article will guide you through the process of multiplying the mixed numbers 1 1/6 and 3 1/2.
Understanding Mixed Numbers
Before diving into the multiplication, let's understand what mixed numbers are. A mixed number combines a whole number with a fraction, like 1 1/6. This represents one whole plus one-sixth.
Converting to Improper Fractions
The easiest way to multiply mixed numbers is to convert them into improper fractions. To do this:
- Multiply the whole number by the denominator of the fraction: 1 x 6 = 6
- Add the numerator of the fraction: 6 + 1 = 7
- Keep the same denominator: 7/6
So, 1 1/6 is equivalent to 7/6.
Similarly, for 3 1/2:
- Multiply the whole number by the denominator: 3 x 2 = 6
- Add the numerator: 6 + 1 = 7
- Keep the same denominator: 7/2
Therefore, 3 1/2 is equivalent to 7/2.
Multiplication
Now we can multiply the improper fractions:
(7/6) x (7/2)
To multiply fractions, we multiply the numerators and the denominators:
(7 x 7) / (6 x 2) = 49/12
Converting Back to a Mixed Number
The result, 49/12, is an improper fraction. To convert it back to a mixed number:
- Divide the numerator by the denominator: 49 ÷ 12 = 4 with a remainder of 1
- The quotient becomes the whole number: 4
- The remainder becomes the numerator of the fraction: 1
- The denominator stays the same: 12
Therefore, 49/12 is equivalent to 4 1/12.
Conclusion
By converting the mixed numbers to improper fractions, we were able to multiply them easily. The final result of 1 1/6 x 3 1/2 is 4 1/12.