Ratio and Proportions
A or
a to b a : b _{
}.The last way
(as a fraction) is the most common way of writing a ratio in algebra. Note that
the order must be When ratios
are used in comparing units of measure, the units should be the same. For example,
the ratio of 5 hours to 3 hours would be written as To write the
ratio of 6 hours to 3 days, first convert 3 days to hours since the units must be the same
[in other words each day has 24 hours so that 3 days would have 3 The ratio
would then be Because the
units of the quantities in a ratio must be the same, ratios do not have units in their
final forms. A
_{
}.To show that
they are equal we must prove that the numerator of the first fraction times the
denominator of the second fraction must be equal to the denominator of the first fraction
times the numerator of the second fraction. In
other words, 2 This is
obviously true since both sides of the equation are equal; therefore, the ratios are
equal. This method of checking the equality
of proportions is called _{
} then _{
}.Check your
understanding by determining if the following proportions are equivalent. (a) (b) Four numbers
are given in a proportion. If any three
numbers are given then the fourth can be found. The
fourth unknown number will be represented by a variable. For example, given that Using cross
multiplication we would obtain Then
dividing both sides by 9, we would determine that Check your
understanding by solving for the variable. (a) ... using
cross multiplication, (b) ... using
cross multiplication, Using
proportions to solve application problems: A local store is offering 3 packs of toothpicks for $0.87. How much would it charge for 10 packs? Let x = the
cost of the 10 packs of toothpicks. Set up
the proportion by writing a ratio on the left hand side of the equation of 3 packs to 10
packs. This would look like Solving for
x by cross multiplication we would obtain
Check your
understanding by setting up a proportion and solving for the unknown. (a) If 5 cans of cherries cost $20.50, how many cans
of cherries can be purchased with (b) If 3 boxes of raisins cost $8.70, how much do 5 boxes cost? Answers: (a) 9 cans (b) $14.50
The views and
opinions expressed in this page are strictly those of Mary Lou Baker. This page was edited on 09-Jan-2014 |