What is a ratio?
• The ratio of male students to female
students at a school is 2:3.
• The ratio of juice concentrate to water is
1:3.
• Josie rode her skateboard 5 miles per
hour.
What is the difference between a
ratio and a fraction?
• Can a ratio always be interpreted as a
fraction?
Some ratios or rates can’t be
written as fractions
• Josie rode her skateboard 5 miles per
hour.
• There is no “whole”, and so a fraction does
not really make sense.
What is a proportion?
Proportions
• A comparison of equal fractions
• A comparison of equal rates
• A comparison of equal ratios
Ratios and Rates
• If a : b = c : d, then a/b = c/d.
• If a/b = c/d, then a : b = c : d.
• Example:
• 35 boys : 50 girls = 7 boys : 10 girls
• 5 miles per gallon = 15 miles using 3
gallons
Exploration 6.3
#1 Do a and b on your own. Then,
discuss with a partner.
Additive vs Multiplicative
relationships
• This year Briana is making $30,000. Next
year she will be making $32,000.
• How much more will she be making next
year?
• What is her increase in salary?
• How does her salary next year compare
with her salary this year?
We can add fractions, but not
ratios
• On the first test, I scored 85 out of 100
points.
• On the second test, I scored 90 out of 100
points.
• Do I add 85/100 + 90/100 as
• 175/100?
What is the meaning of?
“proportional to”
To determine proportional
situations…
•
•
•
•
•
I can buy 3 candy bars for $2.00.
So, at this rate, 6 candy bars should cost…
9 candy bars should cost…
30 candy bars should cost…
1 candy bar should cost… this is called a unit
rate.
To determine proportional
situations
• Cooking: If a recipe makes a certain
amount, how would you adjust the
ingredients to get twice the amount?
• Maps (or anything with scaled lengths) If 1
inch represents 20 miles, how many
inches represent 30 miles?
• Similar triangles.
To solve a proportion…
• If a/b = c/d, then ad = bc. This can be
shown by using equivalent fractions.
• Let a/b = c/d. Then the LCD is bd.
• Write equivalent fractions:
a/b = ad/bd and c/d = cb/db = bc/bd
• So, if a/b = c/d, then ad/bd = bc/bd.
To set up a proportion…
• I was driving behind a slow truck at 25
mph for 90 minutes. How far did I travel?
• Set up equal rates:
units?
Reciprocal Unit Ratios
• Suppose I tell you that 4 doodads can be
exchanged for 3 thingies.
• How much is one thingie worth?
• 4 doodads/3 thingies means
1 1/3 doodads per thingie.
• How much is one doodad worth?
• 3 thingies/4 doodads means
3/4 thingie per doodad.
Exploration 6.4
Part 1:
Determine whether each situation is a
proportional relationship or not. Can it be
solved using a proportion?
Can you write an equation that relates the
quantities in the situation?
Ratio problems
• Suppose the ratio of men to women in a
room is 2:3
• If there are 10 more women than men,
how many men are in the room?
• If there are 24 men, how many women are
in the room?
• If 12 more men enter the room, how many
women must enter the room to keep the
ration of men to women the same?
Proportional Reasoning
• I see that 1/4 of the balloons are blue, and there
are 6 more red balloons than blue.
• Let x = number of blue balloons, and so x + 6 =
number of red balloons.
• Also, the ratio of blue to red balloons is 1 : 3
• Proportion: x/(x + 6) = 1/3
• Alternate way to think about it. 2x + 6 = 4x
x
x+6