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How Do You Use a Proportion to Find a Whole?

Use a percent proportion to solve the following problem: 12 is 40% of what number?

Summary

  1. The percent, 'p', is the number with the percent symbol after it, 40
  2. 12 is a part of some unknown whole, so it is 'a', the part
  3. 'b', the whole, is what we're trying to find
  4. Cross-multiply to get an equation we can solve for 'b'
  5. Divide by 40 on both sides to get 'b' by itself

Notes

    1. The percent proportion says that the value of the percent over 100 is equal to the part over the whole
    1. The percent, 'p', is the number with the percent symbol after it
    2. So p=40
    3. We know that 12 is 40% of something, so it is a part of something
    4. So 12 is 'a', the part
    5. 'b', the whole, is what we're trying to find
    1. When we plug 40 in for 'p' and 12 in for 'a', we get 40/100 = 12/b
    1. Multiply the numerator of the first fraction, 40, by the denominator of the second fraction, 'b'
    2. Then multiply the denominator of the first fraction, 100, by the numerator of the second fraction, 12
    3. The Means-Extremes Property of Proportions tells us these two values are equal, so we have 40b = 100•12
    1. Divide by 40 on both sides to get 'b' by itself
    2. The 40's cancel out on the left hand side
    3. On the right hand side, 1200/40 is 30
    4. So we find that 'b', the whole, is equal to 30, which means that 12 is 40% of 30