Final answer:
The reciprocal of 1 3/4 is found by converting it to an improper fraction (7/4) and then flipping it to get its reciprocal, which is 4/7.
Step-by-step explanation:
The reciprocal of a number is found by inverting the number, so the reciprocal of 1 3/4, which is 1.75 in decimal form, is found by dividing 1 by 1.75. First convert 1 3/4 to an improper fraction which is 7/4. Then, flip the fraction to find its reciprocal which is 4/7.
To find the reciprocal of a mixed number like 1 3/4, you need to:
- Convert the mixed number to an improper fraction: 1 3/4 = (1 × 4 + 3)/4 = 7/4.
- Flip the improper fraction to find the reciprocal: The reciprocal of 7/4 is therefore 4/7.
Using multiplication of reciprocals helps in various mathematical processes, like simplifying complex fractions and converting division into multiplication for ease of computing.