Download Lesson 6-8: Cross Multiplication

Finding Proportions using
Cross Multiplication
+
Objective:
We will learn to use cross
multiplication to solve a proportion.
We will use cross multiplication to
check whether two ratios form a
proportion.
+Property of Cross Products:
If two ratios form a proportion, the cross products are
equal. When 2 ratios have equal cross products, they
form a proportion.
Example 1:

Decide whether each pair of ratios forms a proportion.
You have to multiply the numerator with the denominator of the
other fraction; and vice versa.
105=
=105



3×35 = 5 ×21
105 = 105
YES, they form a proportion.
If the two products are equal, they form a proportion.
When the cross products are not equal, the ratios do not form a proportion.
+ Cross multiplication, in a proportion,
is the product of one numerator and the
other denominator.
Example 1: 3 ? 5
9 = 15
Example 2:
2 ? 12
5 = 20
+ How to Solve a Proportion:
When solving a proportion you must cross multiply,
then find the missing variable.





: 4 = H
7
84
Steps:
7×H = 4× 84
1. Write the cross products.
7H = 336
2. Multiply
For example
7 H = 336
7
7
H = 48
3. To find the value of the variable, undo
the multiplication by dividing to both
sides.
4. Solve.
5. Write answer.
(You have to think: The opposite of multiplication is
division, so I have to divide the number that is with
the variable and do the same for both sides of the
problem. Then I cancel the opposites, and bring down
what I have left. )
+ Your Example:
Solve the proportion.
2 = 3
4
N
X = 1
6
3
+
Homework:
In 1-5, answer yes or no, but you
must show your work.
Find the value of the variable by
using cross multiplication.
1.
3 ? 5
5 = 15
6. 3 = 11
X
20
2.
5 ? 2
8 = 3
3.
7 ? 25
9 = 27
4.
6 ? 10
8 = 15
5.
7 ? 20
9 = 27
7. 4 = 10
9
M
8.
Y = 3
10 5
9. 9 = T
1
4
10. 4 = X
6
84