Workbook Chapter 1 Area, Volume & Ratios
Ratio and Proportions are about division, so:

1-1 Division: Is basically a chopping into pieces.

When you think of it, that is why division by zero is not defined. An object cannot be chopped into no pieces at all. Division of two numbers tells how many numbers the size of the denominator can be removed, or subtracted form the numerator.

 

1-2. Area: Is obtaining the number of designated units of area into which an object can be divided. Can you estimate the number of designated unit squares that make up the pencil?

The Area is:

Conclusion: Area is obtained by dividing an object into "unit areas". 1-3. Volume : Volume is dividing an object into "unit volumes".

1-4 Ratios

A. Ratios of like quantities: Gives the size of the top quantity relative to the bottom quantity.

Explain what each of the following ratios tell you. First, what is it's value, and second, what is the meaning of that value?

a. 30 story building/60 story building

b. 8 cm/4 cm

c. 50 g/2 g

B. Unlike quantities: A ratio of unlike quantities tells how much of the top for each one of the bottom. Practice on these first. First, what is the value, and second, what is it's meaning?

a. 1 Hershey bar/3 people Hint: Try it!

b. 50 chickens/100 people

c. 500 g/20 cm3 (that's 20 cubic centimeters)

d. If a lab cart travels 180 cm in 2.3 seconds, what is the meaning of:

l. 180/2.3 ?

2. 2.3/180 ?

e. If an automobile increases speed from 20 m/s to 60 m/s over a time period of 10 seconds, what is the meaning of :

1. 40/10

2. 10/40

Test your understanding problems.

Problem 1-1. If a 3 kg box of material costs $5, what is the value and what is the meaning of:

l. 5/3 ? 2. 3/5 ?

Problem 1-2. Suppose you discovered that when carbon burns, 16 g of oxygen combines with 12 g of carbon.

1. What is the value and what is the meaning of 16/12 ?

2. What is the value and what is the meaning of 12/16 ?

Problem 1-3. Now suppose we have 500 g of a material in which there are 3 g in each cubic centimeter.

l. What is the value and what is the meaning of 500/3 ?

2. What is the value and what is the meaning of 3/500 ?

Thought experiment: Suppose you had a 5000 g block of material whose density is known to be 2.5 g/cm3. If we added 800 g of this material to the block, by how much would its volume increase? Explain your reasoning carefully.