Mad Slide Ruling
Know your A, B, Cs and Ds
Teaching Multiplication and Division
2013 Ferrick Gray
http://theferrickfiles.com
Pickett
PPT
3
Recall that when multiplication or division are performed on the
slide rule, we need to determine the position of the decimal point
later.
Multiplication usingC and D Scales
Example 1:
Move C1 above D195.
Move the cursor so that the hairline is over C41.
The result is under the hairline on the D scale at D8.
Notice that only the digits are used when setting and reading
the slide.
Notice that when multiplying, we are adding two lengths.
Notice that the slide rule does not indicate the position of the
decimal point.
We can estimate the answer:
This estimation tells us that D8 must represent the answer
80.
Example 2:
Move C1 above D242.
Move the cursor so that the hairline is over C296.
The result is under the hairline on the D scale at D716.
Again, notice that only the digits are used when setting and
reading the slide.
Notice that when multiplying, we are adding two lengths.
Notice that the slide rule does not indicate the position of the
decimal point.
We can estimate the answer:
This estimation tells us that D716 must represent the answer
716.
Example 3:
Move C1 above D121.
Move the cursor so that the hairline is over C65.
The result is under the hairline on the D scale at D787.
Again, notice that only the digits are used when setting and
reading the slide.
When multiplying, we are adding two lengths.
Notice that the slide rule does not indicate the position of the
decimal point.
We can estimate the answer:
This estimation tells us that D787 must represent the answer
7870.
Division usingC and D Scales
Example 1:
Use the hairline to align C25 above D475. (Divisor on C,
dividend on D.)
Read the result under C1.
The result is on the D scale at D19.
Notice that only the digits are used when setting and reading
the slide.
When dividing, we are subtracting two lengths. This is the
reverse to multiplication.
Notice that the slide rule does not indicate the position of the
decimal point.
We can estimate the answer:
This estimation tells us that D19 must represent the answer
1.9.
Example 2:
Use the hairline to align C525 above D67. (Divisor on C,
dividend on D.)
Read the result under C1.
The result is on the D scale at D128.
Again, notice that only the digits are used when setting and
reading the slide.
When dividing, we are subtracting two lengths. This is the
reverse to multiplication.
Notice that the slide rule does not indicate the position of the
decimal point.
We can estimate the answer:
This estimation tells us that D128 must represent the answer
0.128.
Example 3:
Use the hairline to align C156 above D368. (Divisor on C,
dividend on D.)
Read the result under C1.
The result is on the D scale at D236.
Again, notice that only the digits are used when setting and
reading the slide.
When dividing, we are subtracting two lengths. This is the
reverse to multiplication.
Notice that the slide rule does not indicate the position of the
decimal point.
We can estimate the answer:
This estimation tells us that D236 must represent the answer
23.6.
Combined Operations usingC and D Scales
Example 1:
Use the hairline to align C65 above D42. (Divisor on C, dividend
on D.)
Without moving the slide, move the cursor to C37.
The result is on the D scale at D239.
Note that the operations of division (first) and multiplication
(second) alternate.
Note that there is no need to locate the C1 index as we are not
interested in the intermediate values.
In the next examples, we will find that we move the slider and
cursor alternately.
We can estimate the answer:
This estimation tells us that D239 must represent the answer
23.9.
Example 2:
Use the hairline to align C43 above D517. (Divisor on C,
dividend on D.)
Without moving the slide, move the cursor to C125.
Move the slider to align C677 with the hairline.
Without moving the slide, move the cursor to C933.
Read the result from the D scale at D207.
We can estimate the answer:
This estimation tells us that D207 must represent the answer
2.07.
Example 3:
Use the hairline to align C298 above D372. (Divisor on C,
dividend on D.)
Without moving the slide, move the cursor to C246.
Notice we have no more divisors to continue our pattern. We can
change the problem to:
In fact we can add as many 1s to the numerator or denominator as
are necessary to continue our process of alternating division and
multiplication.
Move the slider so that the left index C1 is under the hairline.
(This is the same as dividing by 1.)
Move the hairline to C295.
Read the result on the D scale at D906.
We can estimate the answer:
This estimation tells us that D906 must represent the answer
9.06.
Credits
Slide Rule Images
Dereks Virtual Slide Rule Gallery (Pickett N600-ES Log Log Speed
Rule)
Slide Borders of Scales
Scientific American Slide Rule Template
