What is 1 1/6 times 3?
This problem involves multiplying a mixed number (1 1/6) by a whole number (3). Here's how to solve it:
Step 1: Convert the mixed number to a fraction.
- Multiply the whole number part (1) by the denominator of the fraction (6): 1 * 6 = 6.
- Add the numerator of the fraction (1): 6 + 1 = 7.
- Keep the same denominator: 7/6.
So, 1 1/6 is equivalent to 7/6.
Step 2: Multiply the fraction by the whole number.
- Multiply the numerator of the fraction (7) by the whole number (3): 7 * 3 = 21.
- Keep the denominator the same: 21/6.
Step 3: Simplify the fraction.
- Both 21 and 6 are divisible by 3.
- Divide both the numerator and denominator by 3: 21/3 = 7 and 6/3 = 2.
This gives us a simplified fraction of 7/2.
Step 4: Convert the improper fraction back to a mixed number.
- Divide the numerator (7) by the denominator (2): 7 / 2 = 3 with a remainder of 1.
- The quotient (3) becomes the whole number part of the mixed number.
- The remainder (1) becomes the numerator of the fraction.
- The denominator (2) stays the same.
Therefore, 7/2 is equal to 3 1/2.