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:

*Remember*:

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.

**Example:**

- 54° 14` 29.27” x 2 =

**Further examples:**

- If 28.253` gets multiplied by 2, will carrying over be needed?

### Worksheet: Level 1 Answer Key

**Answer:**

**No carrying is needed.**

### Download Worksheet: Level 1

### Worksheet: Level 2

### Worksheet: Level 2 Sample Questions

**Example**:

Multiply in DMS:

**Question:**

- 26° 37` 29.92” x 5 =

**Further examples:**

Multiply 54° 33` 43.23” x 3 ½ =

### Worksheet: Level 2 Sample Answer Key

**Answer:**

### Download Worksheet: Level 2

### Worksheet: Level 3

### Worksheet: Level 3 Sample Questions

**Example:**

Multiply in DMS:

**Question:**

- 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` ?

**Further example:**

- 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

Answer:

### 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)

Enter 3

Press =

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