Scenario: Carpentry Work - Calculate precise measurements with mixed numbers!
A carpenter has a piece of wood that is 5½ meters long. They cut off 1¾ meters, then cut off another 2 meters. How much wood is left?
Problem: 5½ - 1¾ - 2 = ?
Step 1: Convert mixed numbers to improper fractions
5½: 5 + ½ = 10/2 + 1/2 = 11/2
1¾: 1 + ¾ = 4/4 + 3/4 = 7/4
2: 2/1 = 8/4 (to match denominators)
Step 2: Find common denominator
LCD of 2 and 4 is 4
11/2 = 22/4
So: 22/4 - 7/4 - 8/4
Step 3: Perform subtraction
22/4 - 7/4 - 8/4 = (22 - 7 - 8)/4 = 7/4
Step 4: Convert back to mixed number
7/4 = 1¾ meters
Answer: 1¾ meters of wood is left.
Remember: Parentheses first, then multiplication/division, then addition/subtraction.
Example: (¾ + ½) × ⅔ = ?
Step 1: Parentheses first: ¾ + ½
¾ + ½ = ¾ + 2/4 = 5/4
Step 2: Multiply: 5/4 × ⅔
5/4 × ⅔ = (5×2)/(4×3) = 10/12 = 5/6
A carpenter needs 3⅔ meters of wood. They already have 1¼ meters. How much more do they need?
Your solution:
Calculate: (2⅓ + 1½) × ⅔
Your solution: