Algebra: Finding Missing Values

Questions and Answers

What is the formula for density?

volume - mass

volume / mass

mass / volume (correct)

mass * volume

What do you get when you multiply both sides of the density equation by volume and divide both sides by density?

volume / mass

mass / volume

mass / density

volume = mass / density (correct)

What is a crucial skill for scientists to have when working with data collection and analysis?

Determining unknown values from known ones (correct)

Ignoring formulas and using intuition

Conducting experiments without a hypothesis

Only considering qualitative data

What is the unit of the volume calculated in the example?

cm^3 Signup and view all the answers

What is the first step in determining a missing value in an equation?

Memorize the formula Signup and view all the answers

What is the formula for speed in the racecar example?

distance / time Signup and view all the answers

What is the purpose of reorganizing a formula when determining a missing value?

To get all the known values on the same side of the equation Signup and view all the answers

How did the hours cancel out in the racecar example?

They were in the numerator and denominator Signup and view all the answers

If you have the equation 2 + x = 5, what should you do to get the unknown value, x, by itself?

Subtract 2 from each side Signup and view all the answers

What is the formula for force in the book example?

pressure / area Signup and view all the answers

Why might it be difficult to measure the volume of a copper chunk?

Because there are no 'clean' straight edges to measure along Signup and view all the answers

What is the unit of the force calculated in the book example?

pounds/ft^2 Signup and view all the answers

What is an alternative to calculating the volume of a copper chunk from its mass and density?

Filling a beaker with water and measuring the volume of water displaced Signup and view all the answers

What is the key to solving these types of problems?

Rearranging the equation to isolate the desired variable Signup and view all the answers

What is the density of the copper chunk given in the example?

8.96 g/cm^3 Signup and view all the answers

Study Notes

Determining a Missing Value

As a scientist, determining unknown values from known ones is a crucial skill.
This skill is frequently used in data collection and analysis.
Simple mathematic relationships can be used to calculate missing values.

Simple Algebra

To determine a missing value, you need to know the formula.
Memetrize basic formulas and look up others online or in texts.
Rearrange the formula to get all known values on the same side.

Examples

Basic example: 2 + x = 5, solve for x by subtracting 2 from each side.
Density example: given density = 8.96 g/cm^3 and mass = 25 g, calculate volume.
Formula: density = mass / volume, rearrange to get volume = mass / density.
Solution: volume = 25 g / 8.96 g/cm^3 = 2.79 cm^3.

Speed and Distance

Given speed = 125 mph and time = 15 minutes, calculate distance.
Formula: speed = distance / time, rearrange to get distance = speed * time.
Solution: distance = 125 mph * 0.25 h = 31.25 miles.

Force and Pressure

Given pressure = 2 pounds/1 ft^2, calculate force.
Formula: force = pressure / area, plug in values and calculate.
Solution: force = 2 pounds/1 ft^2 = 2 pounds/ft^2.