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Basic Optical Principles
Mathematics Review and Practice Exercises

Multiplication and Division:

Like Signs: When multiplying or dividing two numbers with the same sign the answer will always result in a number with a plus sign. That is, when two numbers with plus signs are multiplied or divided the answer will be plus. When two numbers with minus signs are multiplied or divided the answer will also be plus.

–3 x – 3 = + 9

+4 x +6 = + 24

(–3) (–3) = + 9

(+4) (+6) = +24

+18 /+3 = +6

– 24/– 8 = +3

+ 18 � +3 = + 6

– 24 � – 8 = +3

Note: Multiplication may be indicated by utilizing the times sign (x) or through the use of brackets ( ) as indicated above. Division may be indicated as a fraction or by utilizing the division ( � ) sign.

Unlike Signs: When multiplying or dividing unlike signs, that is, when one number is preceded by a plus sign and the other number by a minus sign, the resulting answer will always be minus.

Examples:

– 3 x – 3 = + 9

+4 x +6 = + 24

(–3) (– 3) = + 9

(+4) (+6) = +24

+18 /+3 = +6

– 24/– 8 = +3

+ 18 � +3 = + 6

– 24 � – 8 = +3

Add The Following Numbers Algebraically:

1) +2.50 + 5.75 =

2) +1.75 + 3.00 =

3) –12.00 + 4.25 =

4) – 9.50 + 3.00 =

5) + 1.25 � 2.00 =

6) – 2.50 – 21.75 =

7) – 5.25 + 3.50 =

8) – 1.50 + 1.50 =

9) – 0.50 + 1.00 =

10) +3.375 + 5.125 =

– 4.50 + 3.00	+ 2.75 – 3.00	+ 9.00 – 3.75
+ 9.00 – 3.75	– 3.00 + 4.00	+ 3.75 – 4.50

Simplify the following by multiplying or dividing:

16) – 5 x – 6 =

17) + 24 / – 3 =

18) ( + 30)( – 3 ) =

19) + 45 / + 5 =

20) – 36 / – 6 =

21) – 12 / + 3 =

22) (+ 9)(– 4 ) / – 3 =

23) – 64 / ( – 2 )( – 4) =

24) + 12 /( – 4 )( – 3) =

(answers on last page)