Final Answer:
To find the amount of wire needed to cut, subtract the length needed for the job (two and five-eighths cm) from the total length of wire available (three and seven-sixteenths cm). The electrician needs to cut 13/16 cm of wire for the job.
Step-by-step explanation:
To find the amount of wire needed to cut, subtract the length needed for the job (two and five-eighths cm) from the total length of wire available (three and seven-sixteenths cm). First, convert both mixed numbers to improper fractions: 3 + 7/16 = 49/16 cm of total wire, and 2 + 5/8 = 21/8 cm needed for the job. Then, subtract the length needed from the total available: 49/16 - 21/8. To subtract fractions, ensure a common denominator (16) and perform the calculation: 49/16 - 42/16 = 7/16 cm of wire remaining. This represents the amount the electrician doesn't need for the job. Therefore, to determine how much wire to cut, subtract this remainder from the total available: 16/16 (representing the whole) - 7/16 = 9/16 cm. Hence, the electrician needs to cut 13/16 cm of wire for the job.
This calculation involves converting mixed numbers to improper fractions to facilitate subtraction. The total wire available (3 and 7/16 cm) becomes 49/16 cm, and the wire needed for the job (2 and 5/8 cm) converts to 21/8 cm. Subtracting these fractions with a common denominator of 16, the result is 7/16 cm of wire remaining. Deducting this from the whole (16/16 cm) provides the amount needed to cut, which is 9/16 cm. Hence, the electrician needs to cut 13/16 cm of wire for the job.
Understanding fractions and converting mixed numbers to improper fractions simplifies the subtraction process to find the wire length required. Converting the mixed numbers to fractions with a common denominator allows for straightforward arithmetic operations, leading to the final answer of 13/16 cm needed to be cut for the job.