Objective:

To perform combined multiplication and division with the C and D Scales

General:

• More complex problems require more than one multiplication or division; many times it involves a combination of both.
• As a rule, always start with division and then alternate the multiplication and division.
• No intermediate readings are necessary.

Method:

Consider the following type of problem:

• Move the cursor to a on the D scale.
• Align x on the C scale with the cursor.
• Move the cursor to b on the C scale.
• Align y on the C scale with the cursor.
• Move the cursor to c on the C scale.
• Align z on the C scale with the cursor.
• Read the result on the D scale at the C index.

 

Example 1:  Calculate the value of

• Move the cursor to D13.8
• Align C16.8 with the cursor
• Move the cursor to C25.4
• Align C31.6 with the cursor
• Move the cursor to C4.25
• Align C5.12 with the cursor
• Read the resulting digits; D55

Estimating this result:

So this means that the result must be greater than 0 and less than 1, hence the answer 0.55 is appropriate.

 

Example 2:  Calculate the value of

• Move the cursor to D41.5
• Align C152 with the cursor
• Move the cursor to C2.55
• Align C3.48 with the cursor
• Move the cursor to C15.6
• Read the resulting digits; D312

Estimating this result:

So this means that the result must be greater than 1 and less than 10, hence the answer 3.12 is appropriate.

 

Example 3:  Calculate the value of

You will notice that there are a greater number of divisors in this question, we can add more factors to the numerator by multiplying by 1 and proceed in the usual manner.

• Move the cursor to D15.8
• Align C3240 with the cursor
• Move the cursor to C1 (in this case the right index or C10)
• Align C14.5 with the cursor
• Move the cursor to C1 (in this case the left index)
• Align C16.4 with the cursor
• Read the resulting digits; D205

Estimating this result:

So this means that the result must be in the hundred-thousandths, hence the answer 0.0000205 is appropriate.

 

Practice Questions:  Determine the value for each of the following.

1.

2.

3.

 

(Answers: 0.279; 41.3; 0.0267)