Transcript proportion - msgreenshomepage

Introduction to Proportions &
Using Cross Products
Lesson 6-3 & 6-4
CCS: 6.RP.3. Use Proportional reasoning to solve
real-world and mathematical problems
6.RP.3.d Use ratio reasoning to convert
measurement units; manipulate and transform
units appropriately when multiplying or dividing
quantities.
• Objectives:
• Students will be able to:
– Test Ratios and Proportions
– Complete and Identify Proportions
– Use cross multiplication to solve proportions
Vocabulary
• A proportion is an equation stating that two
ratios are equal.
To prove that two ratios form a proportion, you must prove that
they are equivalent. To do this, you must demonstrate that the
relationship between numerators is the same as the relationship
between denominators.
Video Explanations for Proportions
• Identifying Proportions
Examples: Do the ratios form a
proportion?
x3
7 , 21
10 30
Yes, these two ratios DO form a proportion,
because the same relationship exists in both
the numerators and denominators.
x3
No, these ratios do NOT form a
proportion, because the ratios are not
equal.
÷4
8 , 2
9 3
÷3
Completing a Proportion
• Determine the relationship between two
numerators or two denominators
(depending on what you have).
• Execute that same operation to find the
part you are missing.
Example
÷5
35
40
7
=
8
÷5
Video for Examples Using Cross
Products
• Cross Products Proportional
Relationships
• Using Mental Math to Solve Proportions
Cross Products
• When you have a proportion (two equal
ratios), then you have equivalent cross
products.
• Find the cross product by multiplying
the denominator of each ratio by the
numerator of the other ratio.
Example: Do the ratios form a
proportion? Check using cross
products.
4
12
,
3
9
12 x 3 = 36
9 x 4 = 36
These two ratios DO
form a proportion
because their cross
products are the same.
Example 2
5
8
8 x 2 = 16
3 x 5 = 15
,
2
3
No, these two ratios DO
NOT form a proportion,
because their cross products
are different.
Solving a Proportion Using Cross
Products
• Use the cross products to create an
equation.
• Solve the equation for the variable
using the inverse operation.
Example: Solve the Proportion
k
17
=
20
68
68k = 17(20)
68k = 340
68
68
k = 5
Start with the
variable.
Simplify.
Now we have an
equation. To get the
k by itself, divide
both sides by 68.
Classwork: Play Dirt Bike Proportions
to practice solving proportions. You
can play against up to 3 friends!
Try this interactive math lesson to
solve proportions.
Homework Time- 6-3 & 6-4
Handout