Sometimes in your work you will need to multiply angles in degrees and minutes. Multiplication works the same way as it does with whole numbers. There is only one difference: Carrying over is done in multiples of 60 between the degrees, minutes or seconds columns, but it is done in multiples of 10 within a column. Watch the video and see.
A Short Review
To multiply 5° 20` 30” by 3, carrying is necessary from the seconds to minutes and minutes to degrees. Carrying within the minutes and seconds column is 10-based, carrying between columns is 60-based.
30” x 3 = 90”, but 60” of this is carried to the minutes column, where it shows up as a 1`
20` x 3 = 60`, but this carries over to the degrees column where it shows up as 1°.
5° 20` 30” = 5° 60` 90” = 16° 1` 30”
Worksheet: Level 1
Worksheet: Level 1 Sample Questions
- Decide whether carrying-over is needed in the following multiplications in DMS and;
- Specify where exactly carrying is needed, if any:
Multiply mentally or estimate the subtotals of the seconds and minutes units and decide if a subtotal is more or less than 59 or 59.99 If more, carrying over will be needed to the next column to the left.
25° 10` 25.11” × 2 > No carrying is needed.
25° 10` 25.11” × 3 > Carrying is needed from seconds to muinutes.
- 54° 14` 29.27” x 2 =
- If 28.253` gets multiplied by 2, will carrying over be needed?
Worksheet: Level 1 Answer Key
No carrying is needed.
Download Worksheet: Level 1
Worksheet: Level 2
Worksheet: Level 2 Sample Questions
Multiply in DMS:
- 26° 37` 29.92” x 5 =
Multiply 54° 33` 43.23” x 3 ½ =
Worksheet: Level 2 Sample Answer Key
Download Worksheet: Level 2
Worksheet: Level 3
Worksheet: Level 3 Sample Questions
Multiply in DMS:
- A cabinetmaker is trying to make a full inlaid circle of 68 pieces of alternating tapered slices of black walnut and spruce veneer. What is the total angle of turn if each slice has an angle of
5° 21` ?
- What is the total turn of a segmented elbow of a pipe if 4 sections are joined, each with a turn of 4° 27` 45.67”?
Worksheet: Level 3 Sample Answer Key
Download Worksheet: Level 3
Infosheet: Advanced Additional Information
Additional Information: Another Way To Get The Answer
Another Way to Get the Answer
What is the total angle of turn of 3 tapered pieces, each with an angle of 26° 21` 28.44”?
Layout your calculations neatly, so you can review, track changes, correct or learn from them. One way a layout can look is like this:
Additional Information: Another Way To Get The Answer Using A Scientific Calculator
Another way to get the answer, using a scientific calculator:
Enter 26 DMS 21 DMS 28.44 DMS
Press x (multiply)
The number on the display changes to 79° 4` 25.32”
Get a $20-or-so dual-display scientific calculator, even if you can`t take it with you into the exam hall. A calculator is also a learning tool, Technology Use is one of the 9 Essential Skills you can`t do without.
Download Infosheet: Advanced Additional Information