Chapter 4.1: Comparing Two Quantities
Goal: Write ratios to compare two quantities.
A RATIO is a way to compare two (or more) numbers or quantities.
The numbers that make up the ratio are called ____________
Key Idea: In a ratio,
Both terms must have the _____________ ____________
numbers MATTER!
the ORDER of the
This way, we can write a comparison statement and don’t need to
include the units because we know they are the same.
Suppose there are 7 bags of orange cubes and 4 bags of green cubes. All the
bags contain an equal number of cubes. So, we can write a ratio comparing
the number of bags of orange cubes to the number of bags of green cubes
7:4
The ratio does not give the actual number of
cubes. The Ratio just shows the comparison and
relationship between the two quantities.
Example 1: Comparing Quantities with the SAME units
The length of Rod A is 5 cm long. The length of Rod B is 9 cm long.
What is the ratio of Rod A to Rod B?
What is the ratio of Rod B to Rod A?
Example 2: Comparing quantities with DIFFERENT units
Ribbon A is 3 cm long. Ribbon B is 4 meters long.
Write a ratio of Ribbon A to Ribbon B?
Ribbon A and Ribbon B are being compared using DIFFERENT UNITS, so we must CONVERT the
units so they are the same.
CAUTION! If you cannot convert the units to the be same, you cannot write them as a ratio.
(Centimeters and Kilograms measure different quantities and cannot be converted into the same units.
Therefore, you cannot compare them using a ratio).
Example 3: Using part-part of part whole models to show ratios
There were 55 adults at a party and 32 children.
Find the ratio of the number of adults to the number of children at the party.
Find the ratio of the number of children to the total number of people at the party.
Goal: Interpret ratios given in fraction form
Example 4: Write and Interpret Ratios in Fraction form
Two out of three animals in a pet store are birds.
Ratio:
Fraction:
Interpreting the fraction: __________________________________________________
__________________________________________________________________
__________________________________________________________________
The birds in a pet store are parakeets and canaries. There are 4 parakeets and 7 canaries
Write a ratio for the number of parakeets to the number of canaries
Ratio:
Fraction:
CAUTION: The ratio/fraction does not tell you what fraction of the birds are parakeets or canaries.
Instead it tells you there are 4 parakeets forever 7 canaries.
What fraction of the birds are parakeets? What fraction of the birds are canaries?
Goal: Use a ratio to find what fraction one quantity is of another or how many times as great one is
as another.
Example 5: Using ratios to find how many times one number or quantity is as great as another
The height of the horse and the height of the giraffe are represented by the model
How many times the height of the horse is the height of the giraffe?
Translation:
How many times the height of the giraffe is the height of the horse?
Translation: