Fraction numbers
A fraction is a number in which two numbers are divided. For example, and are fractions numbers. In these examples 5 and 13 are in the numerator and 3 and 17 are in the denominator.
If a fraction is written as it is called as a mixed number. In addition to a fraction, the mixed number also has a whole number. The whole number in this example is 1 and the fraction
A mixed number can be transformed to a fraction number as follows:
In the previous example,
The software behind the exercises does not recognize mixed numbers. Therefore, if necessary, all mixed numbers must be converted to fractions as above.
Expanding
The result of fractions of equals to 0.5. The last two cases are formed by multiplying the numerator and the denominator with the same number. In the first case the multiplier is 3 and in the second case 18. This is called as expanding.
Expanding means multiplying the numerator and the denominator of a fraction with the same number.
Example 1:
Expanding is needed as in addition and subtraction of fractions numbers requires denominators to be the same.
Addision of fraction numbers
Example 2: There is a chocolate bar (see above graph). Person H1 eats one third of it and person H2 half of it. The total of chocolate bar eaten is As a calculation, it looks as follows:
Reducing
Reducing is dividing the numerator and the denominator of a fraction number with the same number.
Example 3:
The reduction is needed when the resulting calculation result is to be given in as simple a form as possible. For example, it is easier for the reader to interpret the result than
Formulas for fraction numbers
These are the formulas used for calculating with fraction numbers:
Addition and subtraction with fractions requires denominators to be the same (Formulas 1 and 2). When this is accomplished, numerators are summed and the result is divided with a common denominator.
Example 1.
If numbers are given as mixed numbers, they must be transformed to fraction numbers before performing calculations
Example 2.
If fractions numbers are multiplied with each other, numerators can be multiplied with each other and denominators with each others. Before actual multiplication, numbers could be cancelled as much as possible. In the next example, the number 3 in the numerator can be cancelled with the number 9 in the denominator.
Example 3.
When fraction numbers are divided with each other, it can be transformed into multiplication by inversing the divisor. In the next example, the divisor is and its inverse number is
Example 4.
With the applet below, you can practice adding fractions.
- In the left-hand window, you can practice expanding.
- First make the invoices on paper and then check them by ticking 'Show calculations'.
- The image associated with the expanding is reset by pressing the Clear button.
Sum of fraction numbers
With the applet below, you can practice fraction multiplication. With blue sliders, you can select numerator and denominator numbers for the blue fraction that acts as a multiplier. With red sliders, you get the corresponding figures for the red fraction multiplied.