Final answer:
To calculate the new length, multiply the original length of the ¹⁴/³⁵ foot block by three-quarters (¾). The new length is 69/70 feet.
Step-by-step explanation:
To find the new length of a ¹⁴/³⁵ foot block of wood after it is cut to three-quarters of its original length, multiply the original length by ¾:
- Convert the mixed fraction to an improper fraction: ¹⁴/³⁵ = (3 × 14) + 4 = 42 + 4 = 46, so ¹⁴/³⁵ = 46/35
- Multiply the original length by ¾: (46/35) × (¾) = (46/35) × (3/4)
- Perform the multiplication: (46 × 3) / (35 × 4) = 138/140
- Simplify this fraction: 138/140 = 69/70
The new length of the block of wood is 69/70 feet.