What is the multiplicative inverse of – 7? (a). 7 (b). \[\dfrac{1}{7}\] (c). – 7 (d). \[ - \dfrac{1}{7}\]
ANSWER
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Hint: Multiplicative inverse is when one of the pairs of the numbers when multiplied with another, gives 1. Use this definition to find the multiplicative inverse of – 7.
Complete step-by-step answer: The multiplicative inverse is an inverse of a number. Inverse means something opposite in effect. It is one of a pair of numbers which when multiplied with another number equals 1, which is the multiplicative identity. For example, the multiplicative inverse of 2 is \[\dfrac{1}{2}\].
In this problem, we need to find the multiplicative inverse of – 7. In other words, we need to find a number, which when multiplied with – 7, we get the result as 1. Let the other number be x. Hence, we have the following equation: \[ - 7 \times x = 1\] We divide both the left-hand side and the right-hand side of the above equation by 7. Then, we get as follows: \[\dfrac{{ - 7 \times x}}{7} = \dfrac{1}{7}\] Canceling the common terms in the numerator and denominator in the left-hand side of the above equation, we have: \[ - 1 \times x = \dfrac{1}{7}\] Next, we multiply both the left-hand side and the right-hand side of the equation with – 1 to get as follows: \[ - 1 \times - 1 \times x = - 1 \times \dfrac{1}{7}\] When two negative numbers are multiplied we get a positive number and when one negative and one positive number is multiplied we get a negative number, so we get: \[1 \times x = - \dfrac{1}{7}\] The number 1 is the multiplicative identity, hence, 1 multiplied with any number is the number itself. \[x = - \dfrac{1}{7}\] Hence, the multiplicative inverse of – 7 is \[ - \dfrac{1}{7}\]. Hence, the correct answer is option (d).
Note: You might confuse with additive inverse and choose the number 7 as the correct answer but it is wrong. The multiplicative inverse is when one of the pair of the numbers when multiplied with another, gives 1.