Solving the Math Problem: 1 1/2 Divided by 1/6 - 7/8
This problem involves a combination of fractions, mixed numbers, division, and subtraction. Let's break it down step by step.
1. Convert Mixed Number to a Fraction
First, convert the mixed number 1 1/2 to an improper fraction:
- Multiply the whole number by the denominator: 1 * 2 = 2
- Add the numerator: 2 + 1 = 3
- Keep the same denominator: 3/2
Now the problem is: (3/2) / (1/6) - (7/8)
2. Divide Fractions
To divide fractions, we flip the second fraction and multiply:
- Flip the second fraction: (1/6) becomes (6/1)
- Multiply: (3/2) * (6/1) = 18/2
Now the problem is: 18/2 - (7/8)
3. Find a Common Denominator
Before we can subtract, the fractions need a common denominator. The least common multiple of 2 and 8 is 8.
- Convert 18/2 to an equivalent fraction with a denominator of 8: (18/2) * (4/4) = 72/8
Now the problem is: 72/8 - (7/8)
4. Subtract the Fractions
With the same denominator, we can simply subtract the numerators:
- 72/8 - 7/8 = 65/8
5. Simplify to a Mixed Number (Optional)
If desired, we can convert the improper fraction back to a mixed number:
- Divide the numerator by the denominator: 65 ÷ 8 = 8 with a remainder of 1
- The whole number is 8, the remainder is the new numerator, and the denominator stays the same: 8 1/8
Final Answer
Therefore, 1 1/2 divided by 1/6, minus 7/8, equals 65/8 or 8 1/8.