How to Solve Equations With Rational Numbers


Rational numbers are numbers that can be expressed as the quotient x/y of two integers, with the denominator y not being equal to zero. Rational numbers can be whole numbers such as 9, which can be expressed as 9/1; fractions, such as 4/5; a mixed number, such as 1 3/4; or a decimal, such as 1.50, which can be expressed as 1 1/2. Rational numbers also include the negative image of all positive rational numbers (e.g., -9, -4/5, -1 3/4 and -1.50).

  • Isolate the variable. Multiply both sides of the equation by the inverse of the fraction that precedes the variable. For example, in the equation 3/4y = 5/2, multiply both sides by 4/3:

    (3/4y)(4/3) = (5/2)(4/3).

  • Simplify the resulting equation:

    (3/4y)(4/3) = y;

    (5/2)(4/3) = 20/6.

    Therefore, y = 20/6.

  • Simplify the resulting fraction:

    20/6 = 3 2/6.

  • Simplify the resulting fraction a final time:

    3 2/6 = 3 1/3.

  • Equate the variable and the fraction. The answer is y = 3 1/3.

Tips & Warnings

  • Remember to begin by inverting the operations as necessary. If an equation involves subtraction, add the necessary integer to both sides of the equation. Similarly, if an equation involves multiplication, divide by the necessary integer on both sides of the equation.


  • Photo Credit Hemera Technologies/ Images
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