RATIO AND PROPORTION

Properties of Circles
Wheels in Motion
Graphing Ratios
Scale Drawings
Putting it Together
Proportions as Ratio
Inverse Proportion
Ohm's Law
Credits
Student CopyTeacher CopyReference Copy

Proportion as Ratio
(Reference Copy)


Activity  11:  Proportion as Ratio

In Activity 8, Part B (estimating the distance across a river), you were working with proportion.  In that problem, the ratio of the scale of the drawing was about 2 inches : 4 inches (the actual scale was 2 : 4.125).  To find the distance across the river, a proportion could be written as follows:  2/4 = 150/300.

Then the ratio of the distance between the marked spots to the distance across the river is 1/2.  Rather than thinking of a table or using guess and check to find the answer, we can go directly to the fraction form of a proportion, using a variable to represent the row in the table that is missing.  For example, we could write the ratio for the distance between marked spots as:

We could write the ratio for the distance across the river as:

To find X in the first proportion we think, "The denominator of the first fraction (2) is two times the numerator so the denominator of the second fraction must also be two times as big (300)."  To find X in the second proportion we think, "What number, when multiplied by two, gives 300?  It must be 150."  When numbers get too large to do in your head, use a calculator.

Remember also that the proportion,

can be written as,

For practice, use a calculator to find 221/17.  Now use your result to find X:

Suppose the proportion was written:

Solve for X in the above proportion.  Your answer for X should be the same for both proportions, X = 312.

To find the missing term in a proportion (X), one technique that is commonly used is to "cross multiply and divide."  To use the technique, you must multiply the denominator (bottom number) of one fraction by the numerator (top number) of the other and set it equal to the second denominator multiplied by the first numerator.  The arrows show which numbers to multiply.

In other words:

    17X = 221(24)
Solving for X:

    17X = 5304 (multiply 221 x 24)

    X = 312 (divide both sides of the equation by 17)

In brief, proportions involving a variable are always set up like the numbers in a table.  They can be solved by (a) finding out what the numerator of the first fraction must be multiplied by to get the denominator of that fraction and then using the same multiplier on the second fraction, or (b) cross multiplying the numerators and denominators and then dividing by the number that is multiplying X.




© Copyright
Area 10 Mathematics and Technology Professional Development Center
Permission is granted to duplicate these materials for classroom use.

Last updated on 1/30/1999
Comments: egalindo@indiana.edu
http://www.indiana.edu/~atmat/units/ratio/ratio_r6.htm