www.VirtualNerd.com

How Do You Use a Proportion to Find a Part of a Whole?

What is 40% of 220?

Summary

  1. 'x' is a variable that represents the part of 220 that is 40% of the whole
  2. A percent proportion is the percent of something over 100 equal to the part of something over the whole
  3. Our percent is 40
  4. Our part is x, our unknown
  5. Our whole is 220
  6. Cross-multiply to solve for x
  7. Multiply 40•220 to get the left hand side
  8. Multiply 100•x to get the right hand side
  9. 88 is 40% of 220

Notes

    1. 'x' is a variable that represents the part of 220 that is 40% of the whole
    1. A percent proportion is a special kind of proportion
    2. It is the percent of something over 100 equal to the part of something over the whole
    1. A percent proportion is a special kind of proportion
    2. It is the percent of something over 100 equal to the part of something over the whole
    1. 40 goes on the top of the first ratio
    1. 100 goes on the bottom of the first ratio
    1. 'x' is a variable that represents the part of 220 that is 40% of the whole
    2. It goes on the top of the second ratio
    1. 220 goes on the bottom of the second ratio
    1. 'x' is a variable that represents the part of 220 that is 40% of the whole
    2. We can solve our proportion for x by cross-multiplying
    1. 'x' is a variable that represents the part of 220 that is 40% of the whole
    2. The means-extremes property of proportions says we can cross-multiply to solve for x
    1. First multiply the extremes, 40•220
    2. This is the left hand side of our equation
    1. Then multiply the means, 100•x
    2. 'x' is a variable that represents the part of 220 that is 40% of the whole
    3. 100x is the right hand side of our equation
    1. Now we have 8800 on the left hand side
    2. This is equal to 100x
    1. 'x' is a variable that represents the part of 220 that is 40% of the whole
    2. Division is the opposite of multiplication
    3. So to undo the multiplication, we need to divide by 100
    1. Dividing 8800 by 100 leaves us with 88 on the left hand side
    2. The 100's cancel out on the right to leave us with x
    3. So our variable, x, is equal to 88
    4. That means 88 is the part of 220 that is 40% of the whole