The product of two rational numbers is −1. If one of the numbers is −17/8, find the other number.

Question

ScanSolve AI Tutor · Accepted Answer

Step 1: Let the two rational numbers be a and b. We are given that the product of two rational numbers is −1. So, a × b = −1 Step 2: We are given one of the rational numbers as (−17)/(8). Let a = (−17)/(8). Substitute this value into the equation: (−17)/(8) × b = −1 Step 3: To find the second rational number b, divide the product by the given rational number. b = −1 ÷ ((−17)/(8)) To divide by a fraction, multiply by its reciprocal: b = −1 × (8)/(−17) Step 4: Multiply the numbers. b = (−1 × 8)/(−17); b = (−8)/(−17) When both the numerator and the denominator are negative, the fraction is positive. b = 8/17 The second rational number is 8/17.

The product of two rational numbers is -1. If one of the numbers is -17/8, find the other number.

Answer

Step-by-step solution

Let the two rational numbers be $a$ and $b$ .

We are given one of the rational numbers as $\frac{-17}{8}$ .

To find the second rational number $b$ , divide the product by the given rational number.

Multiply the numbers.

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