Solving proportions by using cross product to find unknown terms is what this lesson is about.
We will also show some principles, special techniques or shortcuts that can be used to quickly solve a proportion.
Terms to know:
Variables such as x, y, or any other letter are used to stand for an unknown number.
Unknown term: The missing or unknown number in a proportion.
We have seen in the lesson about proportions that we can use cross product to determine if the fractions or ratios are in proportions.
Cross products can also be used to find an unknown term in a proportion. Here is how!
If
a
b
=

c
d
then, a × d = b × c

If
a
b
=

c
d
then, a × d = b × c

We will illustrate this with a couple of examples.
Example #1:
Solve for x if
5
x

=
10
16

Since these two fractions or ratios are in proportions, we know that the cross product must be equal.
Using the cross product, we get:
5 × 16 = x × 10
80 = 10x
If you know your multiplication table you can quickly get the answer.
If 10 × x = 80, then x should be 8 because 10 × 8 is 80.
x = 8
The proportion becomes
5
8

=
10
16

5
x

=
10
16

Solve for n if
8
10

=
n
25

200
10

=
10n
10

If
a
b

=
c
d
then,

a + b
b

=
c + d
d

x  8
8

=
6
4

x  8 + 8
8

=
6 + 4
4

x
8

=
10
4

If
x
y

=
x
4
then, y = 4

For instance if
50
y

=
50
100
then, y = 100

If
18
y

=
x
y
then, x = 18

If
a
b

=
c
d
then,

a + c
b + d

=
a
b

a + c
b + d

=
a
b

Say you have
x + 2
8 + 4

=
x
8

It is equivalent to
x
8

=
2
4

We will illustrate this with a couple of examples.
Example #1:
Solve for x if
5
x

=
10
16

Since these two fractions or ratios are in proportions, we know that the cross product must be equal.
Using the cross product, we get:
5 × 16 = x × 10
80 = 10x
If you know your multiplication table you can quickly get the answer.
If 10 × x = 80, then x should be 8 because 10 × 8 is 80.
x = 8
The proportion becomes
5
8

=
10
16

5
x

=
10
16

Notice that to get 10, 5 was multiplied by 2. By the same token, to get 16, something or a number must be multiplied by 2. What number multiplied by 2 will give you 16? No doubt it is 8!
Solve for n if
8
10

=
n
25

200
10

=
10n
10

If
a
b

=
c
d
then,

a + b
b

=
c + d
d

x  8
8

=
6
4

x  8 + 8
8

=
6 + 4
4

x
8

=
10
4

If
x
y

=
x
4
then, y = 4

If
50
y

=
50
100
then, y = 100

If
18
y

=
x
y
then, x = 18

If
a
b

=
c
d
then,

a + c
b + d

=
a
b

a + c
b + d

=
a
b

Say you have
x + 2
8 + 4

=
x
8

It is equivalent to
x
8

=
2
4
