Subtract $8 \frac{1}{6}-4 \frac{5}{6}$. Simplify the answer and write as a mixed number.
Answer (1)
Convert the mixed numbers to improper fractions: 8 6 1 = 6 49 and 4 6 5 = 6 29 .
Subtract the improper fractions: 6 49 − 6 29 = 6 20 .
Convert the result back to a mixed number: 6 20 = 3 6 2 .
Simplify the mixed number: 3 6 2 = 3 3 1 .
Explanation
Problem Analysis We are asked to subtract two mixed numbers, 8 6 1 and 4 6 5 , and express the result as a simplified mixed number.
Convert to Improper Fractions First, convert the mixed numbers to improper fractions.
Convert 8 1/6 8 6 1 = 6 8 × 6 + 1 = 6 48 + 1 = 6 49
Convert 4 5/6 4 6 5 = 6 4 × 6 + 5 = 6 24 + 5 = 6 29
Subtract Fractions Now, subtract the improper fractions:
Calculate Difference 6 49 − 6 29 = 6 49 − 29 = 6 20
Convert to Mixed Number Convert the resulting improper fraction back to a mixed number:
Mixed Number Form 6 20 = 3 6 2
Simplify Simplify the mixed number:
Simplified Result 3 6 2 = 3 3 1
Final Answer Therefore, 8 6 1 − 4 6 5 = 3 3 1 .
Examples
Imagine you're baking a cake and the recipe calls for 8 6 1 cups of flour. You find that you only have 4 6 5 cups of flour. To determine how much more flour you need to borrow from a neighbor, you would subtract the amount you have from the amount required. This subtraction, 8 6 1 − 4 6 5 , results in 3 3 1 cups. Therefore, you need to borrow 3 3 1 cups of flour.
