var index=Math.round(Math.random()*(6-1))+1;
var question=new Array(7);
var truevalue=new Array(7);
var truevalue1=new Array(7);
question[0]='';
truevalue[0]='1';
truevalue1[0]='1/1';
question[1]='';
truevalue[1]='1';
truevalue1[1]='1/1';
question[2]='';
truevalue[2]='4';
truevalue1[2]='4/1';
question[3]='';
truevalue[3]='18';
truevalue1[3]='18/1';
question[4]='';
truevalue[4]='6';
truevalue1[4]='6/1';
question[5]='';
truevalue[5]='28';
truevalue1[5]='28/1';
question[6]='A loaf of bread costs 88 cents. If the bread contains 20 slices, what is the price of each slice?
';
truevalue[6]='4.4 cents';
truevalue1[6]='4.4';
question[7]='One yard contains 36 inches. The length of a house is 17 yards How long is the house in units of inches?
';
truevalue[7]='612 inches';
truevalue1[7]='612';
window.document.write('Fractions
A. Definitions and Usage in Chemistry:
A fraction is normally represented by one number over another number, with the two separated by a fraction line. The terms used for the components of a fraction are the numerator and denominator.
Here´s an example:
This means 3 of 4 equal pieces, just like three slices of a pie that was cut into four equal pieces, as shown below.
The use of a fraction is actually a way of representing a division. Thus - could also be written as 3 ÷ 4.
Any number (or unit) divided by itself is one (1). Here are some examples:
| 4 | |
| = 4 ÷ 4 = 1 |
| 4 | |
| 10 | |
| = 10 ÷ 10 = 1 |
| 10 | |
| 0 | |
| = 0 ÷ 0 = 1 |
| 0 | |
| X | |
| = X ÷ X = 1 |
| X | |
| cm | |
| = cm ÷ cm = 1 |
| cm | |
An improper fraction is one that is greater than one. For example:
When we make measurements, the result is often expressed as a fraction. For example, the gas mileage of an automobile, or its speed. The term per is used to indicate the division involved in a fraction.
| 25 miles | |
| stated as 25 miles per gallon |
| 1 gallon | |
| |
| 75 miles | |
| stated as 75 miles per hour |
| 1 hour | |
For simplicity´s sake, fractions are frequently written with the use of a slash (/).
For example:
| 25 miles / gallon | 75 miles / hour |
| 946 milliliters / quart | 2.54 centimeters / inch |
When you work with fractions in math problems, it is recommended that they be written with the horizontal fraction line, as opposed to the slanted line.
| 4 | |
| (good) | 4/5 (not as good for problem solving) |
| 5 | |
');
window.document.write('B. Multiplication and Simplification of Fractions:
When working with a math problem where you are multiplying fractions, the problem can sometimes be made simpler by first simplifying numbers, i.e., making them simpler by division (or reducing). Let´s try simplifying the following problem. First let´s work it out the long way.
| 2 | | 3 | | 2 x 3 | | 6 | | 1 |
| x |
| = |
| = |
| = |
|
| 3 | | 16 | | 3 x 16 | | 48 | | 8 |
Now let´s try the simplification process.
| 2 | | 3 | | 3 | | | 2 | | 1 |
| x |
| |
| = 1 | |
| = |
|
| 3 | | 16 | | 3 | | | 16 | | 8 |
Let´s try another example.
| 4 | | 3 | | 1 4 x 3 | | 3 |
| x |
| = |
| = |
|
| 5 | | 4 | | 5 x 4 1 | | 5 |
When you work with fractions and encounter some fraction of a number, it means multiply the fraction by the number. For example 1/4 of 8 would be:
');
window.document.write('C. Division of Fractions:
When you divide fractions, you simply multiply the numerator fraction by the reciprocal of the denominator fraction. A reciprocal is the inverse of a term, i.e., it is turned upside down. For example, the reciprocal of 2/3 is 3/2, while the reciprocal of 2/5 is 5/2.
Let´s try the following division of two fractions.
| 4 | | | | | | | | |
| | | | | | | | |
| 5 | | 4 | | 5 | | 4 | | 1 |
| = |
| x |
| = |
| = 1 |
|
| 3 | | 5 | | 3 | | 3 | | 3 |
| | | | | | | | |
| 5 | | | | | | | | |
If one of the terms in the division is a whole number, it can always be written as a fraction by placing it over a 1. Let´s see this in the following example.| | | 50 | | | | | | | | |
| | |
| | | | | | | | |
| 50 | | 1 | | 50 | | 5 | | 250 | | 1 |
| = |
| = |
| x |
| = |
| = 83 |
|
| 3 | | 3 | | 1 | | 3 | | 3 | | 3 |
| |
| | | | | | | | |
| 5 | | 5 | | | | | | | | |
');
window.document.write('D. Fractions and Units:
When working with measurements that have units, it is important to always keep the units with the numbers when doing calculations, i.e., the units must be multiplied and divided. You can be pretty sure that you have done your problem correctly if your units cancel out correctly, and leave you with the desired unit at the completion of the problem. Let´s try an example.
How many miles per gallon does a car get if it uses 20 gallons of gas when it travels 350 miles? Since we need miles per gallon, this means that the number of miles should be placed over the number of gallons.
Now we can simplify the expression by dividing numerator and denominator by 10.
Now divide the numerator by the denominator as before, and we obtain:
Here´s another example. If there are 100 centimeters per meter, how many centimeters is 0.33 meters? The relationship between the centimeter and meter gives us a fraction that equals one.
Since we are trying to find the number of centimeters, this should be the only unit left at the completion of the calculation. This means that the meter unit must divide out to equal one.
| | 100 centimeters | |
| 0.33 meter x |
| = 33 centimeters |
| | 1 meter | |
Try the following calculation.
' + question[index] + '');