Transcript Proportions Review

Ratios and Rates
• Key Skill: TLWBAT use ratios to make
comparisons.
How do we compare Numbers?
• A basketball player shoots 8 free
throws in a game.
• She makes 5 out of 8.
• How might we state this fact using
ratios?
Ways to Write Ratios
5:8
5
8
5 to 8
5 out of 8
Another Ratio
• What is another ratio we could write to
describe making 5 out of 8 free throws?
Another Ratio
• What is another ratio we could write to
describe making 5 out of 8 free throws?
5:3 the ratio of made shots to missed shots
Making Predictions
• Over the course of a season, the 5:8
player will shoot 72 free throws.
• Use a ratio to predict how many shots
the player will make.
Making Predictions
• Over the course of a season, the 5:8
player will shoot 72 free throws.
• Use a ratio to predict how many shots
the player will make.
FT made
FT taken
5 x

8 72
FT made
FT taken
Key Vocabulary
• Equivalent Ratios are two ratios with
the same value.
• Example: 2:3 and 4:6 are equivalent
ratios.
10.1.2 - Compare Ratios
• Mixture A has 3 bottles of red and 1 of
white:
• Mixture B has 2 bottles of red and 1 of
white:
• Which is a darker red?
Solution
• We could use either the ratio of
red:total paint, OR the ratio of
red:white.
• 3:4 is greater than 2:3, so mixture A is
darker, OR
• 3:1 is greater than 2:1, so mixture A is
darker
Remember!
• If you put the number of red bottles on
the left side in the first ratio, you
MUST put the number of red bottles on
the left side in the second ratio.
Using the Ratio
• If I want to paint a house using the
color made by mixture A, but I will
need 16 total bottles of paint.
• How many bottles of red do I need?
• How many bottles of white do I need?
Ratio Table
Red
3
6
9
12
White
1
2
3
4
Total
4
8
12
16
Proportional
Relationships
• Key Skill: TLWBAT determine if a
proportional relationship applies to
given situations.
Example
• In a small bag of 40 M&Ms, we find 9
reds.
• In a large bag of 80 M&Ms, we find 18
reds.
• What does this tell us?
Example
• In a small bag of 40 M&Ms, we find 9
reds.
• In a large bag of 80 M&Ms, we find 18
reds.
• What does this tell us?
• The ratios between red M&Ms and total
M&Ms are equivalent.
Key Vocabulary
• Proportional relationship is one in
which all pairs of corresponding values
have equivalent ratios.
• Remember, equivalent ratios are ratios
with the same value, such as 1:2 and
2:4.
Proportions
• This is what a proportion looks like:
1 3

3 9

Proportions
• A Proportion is two ratios set equal to each
other.
• This is what a proportion looks like:
1 3

3 9
• We can prove they are equal by crossmultiplying: 1 x 9 = 3 x 3
9 = 9
Cross-Multiplying
• To cross multiply means to multiply
the numerator (top) of one ratio by the
denominator (bottom) of the other and
set the results equal to each other.
• We then solve for ‘x’ in the usual way
to find the missing value.
Example
3 8

11 x

Example
3 8

11 x
3(x) = 8(11)
3x = 88
x =29.3