Final answer:
The multiplicative inverse of a number is what you multiply by that number to get 1. For the numbers 6/7, -5, 1/2, and -63, the multiplicative inverses are 7/6, -1/5, 2, and -1/63, respectively.
Step-by-step explanation:
The multiplicative inverse or reciprocal of a number is a value that, when multiplied by the original number, gives a product of 1. This means the multiplicative inverse of a fraction is found by flipping the numerator and the denominator. When dealing with whole numbers, the multiplicative inverse is simply its reciprocal as a fraction.
- For 6/7, the multiplicative inverse is 7/6.
- For -5, we think of the number as -5/1, so its inverse is -1/5.
- For 1/2, the inverse is simply 2/1 or just 2.
- For -63, which is -63/1, the inverse is -1/63.
Remember, the sign rules for multiplication apply when calculating inverses. So, two positive numbers or two negative numbers result in a positive product. A positive and a negative number result in a negative product.