The product of two rational numbers is −13/33. If one of the numbers is −7/11, what is the other number?

Question

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Step 1: Let the two rational numbers be a and b. We are given that the product of two rational numbers is (−13)/(33). So, a × b = (−13)/(33) Step 2: We are given one of the rational numbers as (−7)/(11). Let a = (−7)/(11). Substitute this value into the equation: (−7)/(11) × b = (−13)/(33) Step 3: To find the second rational number b, divide the product by the given rational number. b = (−13)/(33) ÷ ((−7)/(11)) To divide by a fraction, multiply by its reciprocal: b = (−13)/(33) × (11)/(−7) Step 4: Multiply the numerators and the denominators. b = (−13 × 11)/(33 × (−7)); Simplify by canceling out common factors. Here, 11 is a common factor for 11 in the numerator and 33 in the denominator (33 = 3 × 11). b = −13 × 11(3 × 11) × (−7); b = (−13)/(3 × (−7)); b = (−13)/(−21) Step 5: Simplify the fraction. When both the numerator and the denominator are negative, the fraction is positive. b = 13/21 The second rational number is 13/21.

The product of two rational numbers is -13/33. If one of the numbers is -7/11, what is 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 $\frac{-7}{11}$ .

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

Multiply the numerators and the denominators.

Simplify the fraction.

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