How do you solve the proportion 15/18=y/30

  Multiply by 30: 30·15/18 = y = 25

This is a "one-step" linear equation. You solve it by multiplying by the inverse of the coefficient of the variable.

The coefficient of y is 1/30, so its inverse is 30. Multiply both sides of the equation by 30 to get your answer. The fraction 15/18 can be reduced to 5/6 if you like, so that you're computing

  (5/6)·30 = 5·(30/6) = 5·5 = 25

or, you can simply do it using your calculator.

Comment on solving proportions

When you have something of the form

  a/b = c/d

you are often told to "cross-multiply." That is, you multiply both sides of the equation by b·d, so the result is

  a·d = b·c

This has the appearance of each numerator being multiplied by the opposite denominator, hence the description "cross-multiply."

If you do that to your proportion, you get

  15·30 = 18y

This still has a factor multiplying y, so you must divide by that factor to find the value of y. Doing so gets you ...

... 15·30/18 = y

This is the same thing you have if you simply multiply the original proportion by the denominator in the y-term. That is, you don't need to do a multiplication, then a division, when you can simply do one multiplication and be done.

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When the variable is in the denominator of a proportion, then the "cross-multiply" tactic can be useful. Better, if you have a choice, write the proportion with the variable in the numerator.

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