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The product of two rational numbers is 3/2. If one of the numbers is -3/10, what is the other number?

Mathematics

ScanSolve AI Answer

Answer

-5

Step-by-step solution

5 steps

  1. Let the two rational numbers be aa and bb.

    We are given that the product of two rational numbers is 32\frac{3}{2}.
    So, a×b=32a \times b = \frac{3}{2}

  2. We are given one of the rational numbers as −310\frac{-3}{10}.

    Let a=−310a = \frac{-3}{10}.
    Substitute this value into the equation:

    −310×b=32\frac{-3}{10} \times b = \frac{3}{2}

  3. To find the second rational number bb, divide the product by the given rational number.

    b=32÷(−310)b = \frac{3}{2} \div \left(\frac{-3}{10}\right)

    To divide by a fraction, multiply by its reciprocal:

    b=32×10−3b = \frac{3}{2} \times \frac{10}{-3}

  4. Multiply the numerators and the denominators.

    b=3×102×(−3)b = \frac{3 \times 10}{2 \times (-3)} b=30−6b = \frac{30}{-6}

  5. Simplify the fraction.

    b=−5b = -5

    The second rational number is −5-5.

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