Rational Equations Using Proportions
Key Questions

Answer:
Solving proportions is like solving fractions:
#a:b > c:d# can be rewritten as#a/b = c/d# and now you can solve for any of the variables.See an example below:
Explanation:
3 to 4 is like what to 16?
This can be rewritten as a proportion:
#3:4 > c:16# Which can be rewritten as:
#3/4 = c/16# Which can be solved as:
#color(red)(16) xx 3/4 = color(red)(16) xx c/16# #cancel(color(red)(16))color(red)(4) xx 3/color(red)(cancel(color(black)(4))) = cancel(color(red)(16)) xx c/color(red)(cancel(color(black)(16)))# #12 = c# #c = 12# 3 to 4 is like 12 to 16?

We multiply the numerator of each (or one) side by the denominator of the other side.
For example, if I have want to solve for
#x# for the following equation:#x/5=3/4# I can use crossmultiplication, and the equation becomes:
#x*4=3*5# #4x=15# #x=15/4=3.75#

A proportion is a statement that two ratios are equal to each other.
For example#3/6=5/10# (We sometimes read this "3 is to 6 as 5 is to 10".)There are
#4# 'numbers' (really number places) involved. If one or more of those 'numbers' is a polynomial, then the proportion becomes a rational equation.For example:
#(x2)/2=7/(x+3)# ("x2 is to 2 as 7 is to x+3").Typically, once they show up, we want to solve them. (Find the values of
#x# that make them true.)In the example we would "cross multiply" or multiply both sides by the common denominator (either description applies) to get:
#(x2)(x+3)=2*7# . Which is true exactly when
#x^2+x6=14# Which in turn, is equivalent to
#x^2+x20=0# (Subtract 14 on both sides of the equation.)
Solve by factoring#(x+5)(x4)=0#
so we need#x+5=0# or#x4=0# the first requires
#x=5# and the second#x=4# .Notice that we can check our answer:
#(52)/2=7/2# and#7/(5+3)=7/2=7/2# . So the ratios on both sides are equal and the statement is true.
Questions
Rational Equations and Functions

Inverse Variation Models

Graphs of Rational Functions

Division of Polynomials

Excluded Values for Rational Expressions

Multiplication of Rational Expressions

Division of Rational Expressions

Addition and Subtraction of Rational Expressions

Rational Equations Using Proportions

Clearing Denominators in Rational Equations

Surveys and Samples