Multiplying Mixed Numbers: 1 1/6 x 6 3/4
This article will guide you through the steps of multiplying the mixed numbers 1 1/6 and 6 3/4.
Converting Mixed Numbers to Fractions
Before multiplying, we need to convert the mixed numbers into improper fractions. Here's how:
- 1 1/6: Multiply the whole number (1) by the denominator (6) and add the numerator (1). This gives us 7. Keep the same denominator (6). So, 1 1/6 becomes 7/6.
- 6 3/4: Multiply the whole number (6) by the denominator (4) and add the numerator (3). This gives us 27. Keep the same denominator (4). So, 6 3/4 becomes 27/4.
Multiplication of Fractions
Now we can multiply the improper fractions:
(7/6) x (27/4)
To multiply fractions, we multiply the numerators and the denominators:
(7 x 27) / (6 x 4)
This simplifies to 189/24.
Simplifying the Result
The fraction 189/24 can be simplified. Both the numerator and denominator share a common factor of 3. Dividing both by 3, we get:
63/8
Converting Back to a Mixed Number
Finally, we can convert the improper fraction 63/8 back to a mixed number:
- Divide the numerator (63) by the denominator (8). 63 divided by 8 is 7 with a remainder of 7.
- The quotient (7) becomes the whole number part of the mixed number.
- The remainder (7) becomes the numerator of the fraction.
- Keep the same denominator (8).
Therefore, the final answer is 7 7/8.