Multiplying Mixed Numbers: 1 1/6 x 6 3/4
This article will guide you through the process of multiplying the mixed numbers 1 1/6 and 6 3/4.
Step 1: Convert Mixed Numbers to Improper Fractions
- 1 1/6: Multiply the whole number (1) by the denominator (6) and add the numerator (1), keeping the same denominator: (1 x 6) + 1 = 7/6
- 6 3/4: Multiply the whole number (6) by the denominator (4) and add the numerator (3), keeping the same denominator: (6 x 4) + 3 = 27/4
Step 2: Multiply the Improper Fractions
Now we have the problem: 7/6 x 27/4.
- To multiply fractions, we multiply the numerators and the denominators: (7 x 27) / (6 x 4) = 189/24
Step 3: Simplify the Result
- Find the greatest common factor (GCD) of 189 and 24, which is 3.
- Divide both the numerator and denominator by 3: 189/3 = 63 and 24/3 = 8
- The simplified fraction is 63/8.
Step 4: Convert Back to a Mixed Number (Optional)
- Divide the numerator (63) by the denominator (8): 63 ÷ 8 = 7 with a remainder of 7.
- The whole number is 7, the numerator is the remainder (7), and the denominator stays the same (8).
- The final answer in mixed number form is 7 7/8.
Therefore, 1 1/6 times 6 3/4 equals 63/8 or 7 7/8.