Solving a Proportion by
“Cross” Multiplying
A Ratio and a Proportion
Ratio: The relationship in quantity, amount, or size
between two or more things. Typically expressed
as a quotient of two mathematical expressions (i.e.
A FRACTION). For example:
a
b
Proportion: An equation that equates two ratios (i.e. TWO
EQUAL FRACTIONS). For example:
a
b

c
d
Solving a Proportion
Solve:
3
2
5
15
Cancel 2
the
divide
by 2
2

x3
5
5
Solve:
Cancel
the
divide
by 5
 x3
2
15  2  x  3
15  2 x  6
9  2x
4.5  x
7
3

4
x
x x
Cancel
the
divide
by 3
7x
3
4
3 3
7 x  12
12
x 7
Cancel
the
divide
by X
Solving a Proportion
Multiply opposite
numerators and
denominators.
Solve:
3
2
5
15
2
2

x3
5
5
 x3
Solve:
Notice the
pattern will
eliminate a lot
of work.
2
7
3

4
x
x x
7x
3
4
3 3
15  2  x  3
7 x  12
12
15  2 x  6
x 7
9  2x
“Cross” Multiplication can be
4.5  x
used to solve a proportion.
The products
are EQUAL.
Solving a Proportion
Solve:
x 4
12

7
3
3  x  4   84
3x 12  84
12 12
3x  96
3
3
x  32
Solve:
100
30

4
3x
300x  120
300
300
x  0.4
Multiply each numerator by
the opposite denominator
and set the products equal
to each other.