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How Do You Solve an Equation Where You're Multiplying Fractions?

Solve the equation for h: 2/3 • h = 5 • 1/2

Summary

  1. 'h' is a variable
  2. Multiply the denominator 2 times the whole number 5, and add 1 to get 11 over the same denominator, 2
  3. Multiply both sides by the reciprocal of 2/3, which is 3/2
  4. 3/2 and 2/3 cancel out on the left leaving 'h', and on the right, 11/2 times 3/2 is 33/4
  5. 33/4 converts to 8 and 1/4
  6. Check our answer by plugging it back into the original equation

Notes

    1. 5 and 1/2 is a mixed fraction
    1. 5 and 1/2 is a mixed fraction
    1. To convert 5 and 1/2 into an improper fraction:
    2. Multiply the whole number 5 by the denominator of 2, then add that product to the numerator of 1, and we get 11
    3. Put the 11 over the old denominator, 2
    1. The multiplication property of equality says that if we multiply one side of an equation by 3/2
    2. We have to multiply the other side by 3/2 also
    1. So the reciprocal of 2 over 3 is just 3 over 2
    1. So the reciprocal of 2/3 is just 3/2
    1. So the reciprocal of 2/3 is just 3/2
    1. 2/3 and its reciprocal cancel out on the left hand side
    2. The reciprocal is 3/2
    1. 11/2 times 3/2 is 33/4
    2. Multiply the numerators together, 11 • 3 = 33
    3. Multiply the denominators together, 2 • 2 = 4
    1. 11/2 times 3/2 is 33/4
    1. 33/4 is an improper fraction
    1. 8 becomes the whole number, and the remainder of 1 becomes the numerator
    2. The denominator stays the same, it's 4
    1. Plug our answer, 8 and 1/4, into the original equation to see if it is a true statement
    2. If it is true, then we know our answer is correct
    1. 'h' is a variable, which we found to be 8 and 1/4
    2. The original equation is 2/3 times 'h' is equal to 5 times 1/2
    1. We already know that 8 and 1/4 is just 33/4 and that 5 and 1/2 is just 11/2
    1. Multiply 2/3 by 33/4
    1. Multiply 2/3 by 33/4 and we get 66/12
    2. Multiply the numerators together, 2 • 33 = 66
    3. Multiply the denominators together, 3 • 4 = 12
    1. We can factor out a 6 from both the top and bottom of 66/12
    2. The 6's cancel each other out and we are left with 11/2
    1. If it is true, or both sides are equal, then we know our answer is correct