Math
Solving
Proportions
1
Vocabulary
► Proportion—an
equation that shows that
two ratios are equivalent.
► Cross
Product—the product of the
numerator of one ratio and the denominator
of the other ratio.
2
Notes
►1
=
2
3
6
1 x 6 is a cross product.
2 x 3 is a cross product.
► The
cross products of a proportion are
equal.
► Two
ratios form a proportion if their cross
products are equal.
3
Determine whether each pair of
ratios form a proportion.
a.
8/10 and 4/5
b.
9/4 and 11/6
c.
6/14 and 9/21
d.
15/12 and 9/6
e.
$2.48/4oz and
$3.72/6 oz
f.
125 mi/5.7 gal and
120 mi/5.6 gal
4
Example
► Before
dinner, Mohammed solved 8 math
problems in 12 minutes. After dinner, he
solved 2 problems in 3 minutes. Is the
number of problems he solve proportional
to the time?
5
Example
► Determine
if the quantities $30 for 12
gallons of gasoline and $10 for 4 gallons are
proportional.
6
Notes
►
Solving the proportion—Process of
using cross products to find a missing term
in a proportion.
► Solving
a proportion is similar to solving an
equation.
7
Example
x = 4
9
6
x • 6 = 9 • 4 (Cross multiply)
6x = 36 (Solve for the variable)
6x = 36 (Divide to undo multiplication
6
6
x=6
8
Examples
a.
5/8 = 18/x
b.
9/15 = k/18
c.
3.5/14 = 6/n
d.
4.6/w = 4/5
9
Solve each proportion.
a.
5/15 = 15/w
e.
52/8 = m/9
b.
24/13 = a/26
f.
3/u = 5/15
c.
y/7 = 16/28
g.
20/b = 70/28
d.
18/x = 3/36
h.
650/6.5 = z/5
10