The product of two rational numbers is 5/18. If one of the numbers is −3/20, 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 5/18. So, a × b = 5/18 Step 2: We are given one of the rational numbers as (−3)/(20). Let a = (−3)/(20). Substitute this value into the equation: (−3)/(20) × b = 5/18 Step 3: To find the second rational number b, divide the product by the given rational number. b = 5/18 ÷ ((−3)/(20)) To divide by a fraction, multiply by its reciprocal: b = 5/18 × (20)/(−3) Step 4: Multiply the numerators and the denominators. b = (5 × 20)/(18 × (−3)); b = (100)/(−54) Step 5: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. b = (100 ÷ 2)/(−54 ÷ 2); b = (50)/(−27) The negative sign can be written in the numerator or in front of the fraction. b = −50/27 The second rational number is −50/27.

The product of two rational numbers is 5/18. If one of the numbers is -3/20, 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 $\frac{-3}{20}$ .

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

Multiply the numerators and the denominators.

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

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