Rearranging Formulas
Rearranging Formulas
Slide: 1
Formulas and their Applications In formulas, the relationship among many variables is written as a rule for performing calculations.
Example
The distance travelled by an object in uniform motion can be calculated using the following formula:
Rate Distance
D= R t
This means that if we know any two quantities, we can calculate the third using this formula. Slide: 2
Time
Formulas and their Applications In formulas, the relationship among many variables is written as a rule for performing calculations.
Example
The distance travelled by an object in uniform motion can be calculated using the following formula:
If R = 90km/h and t = 4 hours:
D= R t = 90 × 4 = 360 km Slide: 3
Formulas and their Applications In formulas, the relationship among many variables is written as a rule for performing calculations.
Example
Rate (R) can be calculated using the following formula:
If D = 480 m and t = 16 seconds, and R is unknown, rearrange the formula.
R = D= 480 = 30 m/s t 16 Slide: 4
Formulas and their Applications In formulas, the relationship among many variables is written as a rule for performing calculations.
Example
Time (t) can be calculated using the following formula:
If D = 325 km and R = 130 km/h, and t is unknown, rearrange the formula.
t = D= 325 = 2.5 hours R 130 Slide: 5
Rearrange the following formula for the volume of a cylinder for radius (r).
V = πr2h a. r =
b. r = c. r = d. r = Slide: 6
𝑽 𝝅𝒉 𝑽 𝝅𝒉 𝑽 𝟐 ( ) 𝝅𝒉 𝑽𝟐 𝝅𝒉
Rearrange the following formula for the volume of a cylinder for radius (r).
V = πr2h
Slide: 7
Rearranging Formulas When rearranging formulas that have more than one term on at least one side of the equal sign, we first isolate the desired term using properties of addition and subtraction, and then isolate the desired variable using properties of multiplication and division.
Example
The velocity at time t of a uniformly accelerating object can be calculated using the following formula:
Acceleration Velocity
v = v0 + at Time
Initial Velocity Slide: 8
Rearranging Formulas When rearranging formulas that have more than one term on at least one side of the equal sign, we first isolate the desired term using properties of addition and subtraction, and then isolate the desired variable using properties of multiplication and division.
Example
The velocity at time t of a uniformly accelerating object can be calculated using the following formula:
v – v0 = at Rearrange for t. Slide: 9
Isolate the term containing t.
Rearranging Formulas When rearranging formulas that have more than one term on at least one side of the equal sign, we first isolate the desired term using properties of addition and subtraction, and then isolate the desired variable using properties of multiplication and division.
Example
The velocity at time t of a uniformly accelerating object can be calculated using the following formula:
v – v0 = t a Rearrange for t. Slide: 10
Isolate the variable t.
Rearrange the following formula for z .
𝟓𝒙 y= 𝒘−𝒛 a. z = – b. z =
Slide: 11
𝟓𝒙 𝒚
+w
−𝟓𝒙+𝒚𝒘 𝒚
Rearrange the following formula for z .
Slide: 12
𝟓𝒙 y= 𝒘−𝒛
Rearranging Formulas by Factoring When the variable you are trying to isolate appears more than once in the formula, it is necessary to factor out that variable.
Recall
We remove grouping symbols by distributing through the brackets.
P (1 + r t )
P + P rt
When factoring, we are doing the opposite process.
P + P rt Slide: 13
P (1 + r t )
Rearrange the following formula for c .
Slide: 14
𝟏 − 𝒃𝒄 a= 𝒄
Rearrange the following formula for p .
Slide: 15
𝒑 m–n= 𝟏 + 𝟓𝒑
Slide: 1
Formulas and their Applications In formulas, the relationship among many variables is written as a rule for performing calculations.
Example
The distance travelled by an object in uniform motion can be calculated using the following formula:
Rate Distance
D= R t
This means that if we know any two quantities, we can calculate the third using this formula. Slide: 2
Time
Formulas and their Applications In formulas, the relationship among many variables is written as a rule for performing calculations.
Example
The distance travelled by an object in uniform motion can be calculated using the following formula:
If R = 90km/h and t = 4 hours:
D= R t = 90 × 4 = 360 km Slide: 3
Formulas and their Applications In formulas, the relationship among many variables is written as a rule for performing calculations.
Example
Rate (R) can be calculated using the following formula:
If D = 480 m and t = 16 seconds, and R is unknown, rearrange the formula.
R = D= 480 = 30 m/s t 16 Slide: 4
Formulas and their Applications In formulas, the relationship among many variables is written as a rule for performing calculations.
Example
Time (t) can be calculated using the following formula:
If D = 325 km and R = 130 km/h, and t is unknown, rearrange the formula.
t = D= 325 = 2.5 hours R 130 Slide: 5
Rearrange the following formula for the volume of a cylinder for radius (r).
V = πr2h a. r =
b. r = c. r = d. r = Slide: 6
𝑽 𝝅𝒉 𝑽 𝝅𝒉 𝑽 𝟐 ( ) 𝝅𝒉 𝑽𝟐 𝝅𝒉
Rearrange the following formula for the volume of a cylinder for radius (r).
V = πr2h
Slide: 7
Rearranging Formulas When rearranging formulas that have more than one term on at least one side of the equal sign, we first isolate the desired term using properties of addition and subtraction, and then isolate the desired variable using properties of multiplication and division.
Example
The velocity at time t of a uniformly accelerating object can be calculated using the following formula:
Acceleration Velocity
v = v0 + at Time
Initial Velocity Slide: 8
Rearranging Formulas When rearranging formulas that have more than one term on at least one side of the equal sign, we first isolate the desired term using properties of addition and subtraction, and then isolate the desired variable using properties of multiplication and division.
Example
The velocity at time t of a uniformly accelerating object can be calculated using the following formula:
v – v0 = at Rearrange for t. Slide: 9
Isolate the term containing t.
Rearranging Formulas When rearranging formulas that have more than one term on at least one side of the equal sign, we first isolate the desired term using properties of addition and subtraction, and then isolate the desired variable using properties of multiplication and division.
Example
The velocity at time t of a uniformly accelerating object can be calculated using the following formula:
v – v0 = t a Rearrange for t. Slide: 10
Isolate the variable t.
Rearrange the following formula for z .
𝟓𝒙 y= 𝒘−𝒛 a. z = – b. z =
Slide: 11
𝟓𝒙 𝒚
+w
−𝟓𝒙+𝒚𝒘 𝒚
Rearrange the following formula for z .
Slide: 12
𝟓𝒙 y= 𝒘−𝒛
Rearranging Formulas by Factoring When the variable you are trying to isolate appears more than once in the formula, it is necessary to factor out that variable.
Recall
We remove grouping symbols by distributing through the brackets.
P (1 + r t )
P + P rt
When factoring, we are doing the opposite process.
P + P rt Slide: 13
P (1 + r t )
Rearrange the following formula for c .
Slide: 14
𝟏 − 𝒃𝒄 a= 𝒄
Rearrange the following formula for p .
Slide: 15
𝒑 m–n= 𝟏 + 𝟓𝒑
