Question

multiplying and dividing angles
multiply or divide each of these exercises as indicated.

1. ( 6 \times ( 18 ^ { circ } 7 ^ { prime } ) )
2. ( 9 \times ( 12 ^ { circ } 5 ^ { prime } 23 ^ { prime prime } ) )
3. ( ( 53 ^ { circ } 28 ^ { prime } ) div 5 )
4. ( ( 91 ^ { circ } 42 ^ { prime } 36 ^ { prime prime } ) div 3 )

Explanation:

Step1: Multiply degrees and minutes separately

$$6\times18^{\circ}=108^{\circ}$$
$$6\times7' = 42'$$

Step2: Combine the results

Since \(108^{\circ}+42'=108^{\circ}42'\)

Step1: Multiply degrees, minutes and seconds separately

$$9\times12^{\circ}=108^{\circ}$$
$$9\times5'=45'$$
$$9\times23'' = 207''$$

Step2: Convert seconds to minutes

Since \(207''=3'27''\) (because \(207\div60 = 3\) remainder \(27\))

Step3: Add minutes

\(45'+3'=48'\)

Step4: Combine the results

\(108^{\circ}+48'+27''=108^{\circ}48'27''\)

Step1: Divide degrees first

\(53^{\circ}\div5 = 10^{\circ}\) (remainder \(3^{\circ}\))

Step2: Convert the remainder of degrees to minutes

\(3^{\circ}=180'\)

Step3: Add the original minutes

\(180'+28'=208'\)

Step4: Divide the total minutes

\(208'\div5 = 41.6'\)
\(0.6'=36''\) (because \(0.6\times60 = 36\))

Step5: Combine the results

\(10^{\circ}+41'+36''=10^{\circ}41'36''\)

Step1: Divide degrees first

\(91^{\circ}\div3=30^{\circ}\) (remainder \(1^{\circ}\))

Step2: Convert the remainder of degrees to minutes

\(1^{\circ}=60'\)

Step3: Add the original minutes

\(60'+42'=102'\)

Step4: Divide the total minutes

\(102'\div3 = 34'\)

Step5: Divide seconds

\(36''\div3=12''\)

Step6: Combine the results

\(30^{\circ}+34'+12''=30^{\circ}34'12''\)

Answer:

1. \(108^{\circ}42'\)
2. \(108^{\circ}48'27''\)
3. \(10^{\circ}41'36''\)
4. \(30^{\circ}34'12''\)