var index1=Math.round(Math.random()*(4-1))+1; var question1=new Array(5); var truevalue1=new Array(5); var closevalue1=new Array(5); question1[0]='+3 + 8 ='; truevalue1[0]='11'; closevalue1[0]='+11'; question1[1]='+3 + 8 ='; truevalue1[1]='11'; closevalue1[1]='+11'; question1[2]='+15 + 254 ='; truevalue1[2]='269'; closevalue1[2]='+269'; question1[3]='-8 + (-25) ='; truevalue1[3]='-33'; closevalue1[3]='-33'; question1[4]='+4 + (-6) ='; truevalue1[4]='-2'; closevalue1[4]='-2'; question1[5]='-8 + 5 ='; truevalue1[5]='-3'; closevalue1[5]='-3'; window.document.write('

Signed Numbers



A. The Sizes of Signed Numbers:
In chemistry we very frequently work with plain numbers like 1, 2, 3, etc. We also encounter negative numbers such as -1, -2, -3, etc., in addition to zero. A common way to show the relationship of these signed numbers is with a number line.

As we move toward the right end of the line, the numbers get bigger. One way in which this is used in chemistry is in temperature measurements. Thus, a +30 degrees is a higher temperature than a +20 degrees. Likewise, a -10 degrees is a higher temperature than a -20 degrees.

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B. Adding Signed Numbers:
Adding numbers of the same sign is quite simple. Just add the two numbers, and retain the sign. For example, if +5 is added to +3, the result is +8.

If -8 is added to -9, the result is -17.

If you added numbers with different signs, the result is the same as subtraction. Simply subtract the smaller number from the larger number, and then retain the sign of the larger number. For example, let´s add +8 and -14.

What is the result when the following numbers are added?

'+ question1[index1] + '
'); var index2=Math.round(Math.random()*(4-1))+1; var question2=new Array(5); var truevalue2=new Array(5); var closevalue2=new Array(5); question2[0]='67 - 45 ='; truevalue2[0]='22'; closevalue2[0]='+22'; question2[1]='67 - 45 ='; truevalue2[1]='22'; closevalue2[1]='+22'; question2[2]='23 - (-17) ='; truevalue2[2]='40'; closevalue2[2]='+40'; question2[3]='-28 - 19 ='; truevalue2[3]='-47'; closevalue2[3]='-47'; question2[4]='-39 - (-33) ='; truevalue2[4]='-6'; closevalue2[4]='-6'; question2[5]='49 - (91) ='; truevalue2[5]='-42'; closevalue2[5]='-42'; window.document.write('

C. Subtracting Signed Numbers:
When you subtract signed numbers, simply add the opposite of the second number to the first number. For example, subtract 15 from 12, i.e.,

12 - 15 =

Let´s first put in the signs of the numbers.

+12 - (+15) =

Now make this an addition, and change the sign of the second number.

+12 + (-15) =

We can now use the rule we looked at above when we added numbers with opposite signs, i.e., take their difference and use the sign of the larger number.

+12 + (-15) = -3

Here´s another example. Subtract -25 from -58.

-58 - (-25) = -58 + (+25) = -33

What is the result when the following numbers are subtracted?

'+ question2[index2] + '
'); var index3=Math.round(Math.random()*(6-1))+1; var question3=new Array(7); var truevalue3=new Array(7); var closevalue3=new Array(7); question3[0]='51 (6) ='; truevalue3[0]='306'; closevalue3[0]='+306'; question3[1]='51 (6) ='; truevalue3[1]='306'; closevalue3[1]='+306'; question3[2]='-16 ÷ -2 ='; truevalue3[2]='8'; closevalue3[2]='+8'; question3[3]='-45 (5) ='; truevalue3[3]='-225'; closevalue3[3]='-225'; question3[4]='-75 ÷ 5 ='; truevalue3[4]='-15'; closevalue3[4]='-15'; question3[5]='-28 (-6) ='; truevalue3[5]='168'; closevalue3[5]='+168'; question3[6]='82 (2) ='; truevalue3[6]='164'; closevalue3[6]='+164'; question3[7]='44 ÷ -4 ='; truevalue3[7]='-11'; closevalue3[7]='-11'; window.document.write('

D. Multiplying and Dividing Signed Numbers:
You may encounter different symbols to represent multiplying. Here are the most common ones.

2 x 3 = 62 3 = 62(3) = 6

Likewise, several symbols are used to designate division. The most common are:

6 / 2 = 36 ÷ 2 = 3

When multiplying signed numbers, three rules apply.

  1. A positive number times a positive number equals a positive number.
  2. A positive number times a negative number equals a negative number.
  3. A negative number times a negative number equals a positive number.

Here are a few examples

6 (8) = 48(Rule 1)
-3 (4) = -12(Rule 2)
-6 (-2) = 12(Rule 3)

The same rules for signed numbers apply when carrying out a division.

  1. A positive number divided by a positive number equals a positive number.
  2. A positive number divided by a negative number (or vice versa) equals a negative number.
  3. A negative number divided by a negative number equals a positive number.

Here are a few examples of divisions.

6 ÷ 2 = 3(Rule 1)
-6 ÷ 2 = -3(Rule 2)
6 ÷ -2 = -3(Rule 3)
-6 ÷ -2 = 3(Rule4)

Try the following problem.

'+ question3[index3] + '
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