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Transpositions
SLIDE 1
Consolidation
?
Find I when
?
Find P when
?
Find v when
SLIDE 2
?
Find I when
Solution
?
Find P when
Solution
?
Find v when
Solution
SLIDE 1B
Consolidation
?
Find I when
?
Find P when
The answer is in horsepower (hp)
?
Find v when
SLIDE 2B
?
Find I when
Solution
?
Find P when
Solution
?
Find v when
Solution
SLIDE 3
In the subject of the equation is F.
Consolidation
In each case, state the subject of the formula
?
?
?
SLIDE 4
?
The subject of the equation is P
?
The subject of the equation of K
?
The subject of the equation is v
SLIDE 5
Transposition
To transpose is to make another symbol the subject of the equation. It is the same as rearranging the equation to bring another symbol to the left.
Example
Make F the subject of the formula
It is not necessary to include all these steps. It is customary to go from the first to the last line in one step, though when you are learning the process, it can be helpful to include as many lines as you need.
SLIDE 6
What is the fundamental rule for equations and how is this rule used in this process of transposing the equation for F?
SLIDE 7
The fundamental rule for equations is what you do to (all of) one side of the equation, you also do to (all of) the other side of the equation.
At line (2) we divide both sides by d. This is an example of the fundamental rule. We divide one side by d in order to �cancel it out�, so we divide the other side by d, at the same time.
SLIDE 8
The fundamental rule for equations is what you do to one side of the equation, you also do to the other side of the equation.
Annotate each of the following to show how the fundamental rule for equations has been used when changing the subject of the formula.
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?
?
SLIDE 9
The fundamental rule for equations is what you do to one side of the equation, you also do to the other side of the equation.
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SLIDE 10
Transpose each of the following formulae
? ?
? ?
? ?
SLIDE 11
? ?
? ?
? ?
SLIDE 12
Rearranging the equation of the straight line
Make y the subject of the equation
Solution
Putting the equation in the form
We have
SLIDE 13
Put each of the following equations in the form . Find in each case the gradient and intercept on the y-axis.
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SLIDE 14
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SLIDE 15
Sketch the graph of
SLIDE 16
Sketch the graph of
Solution
We first put in the form .
SLIDE 17
Example
Make x the subject of
Solution
SLIDE 18
? Make t the subject of
? Rearrange to make y the subject
SLIDE 19
? Make t the subject of
Solution
? Rearrange to make y the subject
Solution
SLIDE 20
Transpose for C
SLIDE 21
Transpose for C
Solution
SLIDE 22
Error in manipulation of algebraic fractions
What is the error in the following?
SLIDE 23
This is a blunder. It arises because the student has not mastered the addition of fractions at an earlier stage.
The correct manipulation is
SLIDE 24
? Complete the following algebraic description of the rule for the addition of fractions.
? Cancel the bottom factor into the top, being careful to avoid a blunder.
SLIDE 25
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?
SLIDE 26
If p is a positive number and q is a negative number, which of the following is true?
A
B
C
D
SLIDE 27
If p is a positive number and q is a negative number, which of the following is true?
A B
C D
Solution
Solving this problem depends on the correct manipulation of fractions.
Since p is positive and q is negative, is a negative number, possibly a fraction. Then
This gives option C, . To show that B, , is incorrect, observe that to add any number to 1 (positive or negative) is to make it not equal to 1.
SLIDE 28
Factor and solve
Rearrange for k
Solution
Step 1 Bring everything with k to the left, and everything else to the right.
Step 2 Factor for k
Step 3 Solve for k
SLIDE 29
? Make k the subject of
? Make x the subject of
SLIDE 30
? Make k the subject of
Solution
? Make x the subject of
Solution
SLIDE 31
Fractions appearing
A small fraction appearing in front of a formula can cause difficulties.
Example
Make m the subject of .
Solution
SLIDE 32
? Make x the subject of
? Make P the subject of
SLIDE 33
? Make x the subject of
Solution
? Make P the subject of
Solution
SLIDE 34
Move �as one�
Make m the subject of
Here the may move as one expression.
Solution
SLIDE 35
? Make S the subject of
? Make x the subject of
SLIDE 36
? Make S the subject of
Solution
? Make x the subject of
Solution
SLIDE 37
Square roots, roots in general
Make v the subject of
Here we must take the square root to obtain v
Solution
SLIDE 38
? Make x the subject of
? Make T the subject of
SLIDE 39
? Make x the subject of
Solution
? Make P the subject of
Solution
SLIDE 40
Transpose
?
?
SLIDE 41
?
Solution
?
Solution
SLIDE 42
Transpose
?
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SLIDE 43
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Solution
?
Solution
SLIDE 44
Transpose
?
?
SLIDE 45
?
Solution
?
Solution
SLIDE 46
Example
Make x the subject of
Solution
SLIDE 47
Make x the subject of
Annotate the following solution to this problem, explaining each step of the process.
SLIDE 48
SLIDE 49
Rearrange
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?
SLIDE 50
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SLIDE 51
Clearing a square root
Make k the subject of
Solution
SLIDE 52
? Make T the subject of
? Make x the subject of
SLIDE 53
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SLIDE 54
? Make r the subject of
? Make x the subject of
SLIDE 55
?
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SLIDE 56
? Transpose
? Make v the subject of
SLIDE 57
?
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SLIDE 58
The ratios and are the same. Find a in terms of b and k.
SLIDE 59
The ratios and are the same. Find a in terms of b and k.
Solution
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