Let us recall that rational numbers are numbers that can be written into fractions (or as a ratio 
where 
and 
are integers and 
. As previously shown, rational numbers include integers, decimals and fractions since these numbers can be written into ratio forms. Thus, the rule(s) for multiplication of rational numbers is a collection of the rules for multiplication of decimals, integers and fractions. Before multiplying two or more rational numbers, first we identify what kind of rational numbers is involved then follow the rules of multiplication exclusive for that number sets. Listed below are some helpful tips.
A. If the rational numbers are in decimal form, follow the rules for multiplying decimals. Multiply the numbers as if they were just whole numbers. Count the number of decimal places to the right in both decimals. The total number of decimal places in the factors is the same in the final product.
Examples
Solution:
Since 0.25 is a decimal number so we follow the rules for multiplying decimals. Thus,
Solution:
Applying the same principle in example 1, we get
B. If the given numbers are already in rational forms, we follow the rules for multiplying fractions. We multiply the numerators and the denominators then simplify the resulting fractional product.
Examples
C. If one of the given or both are mixed fractions such as 
, it is better to express them into improper fractions first (fraction whose numerator is greater than its denominator). This can be done by adding the product of the denominator and the whole number part to the numerator and then affixing the same denominator. For instance the mixed fraction can be converted into 
.
Examples
D. If the given set involves a fraction, a decimal or an integer, then we must convert them into the same set of numbers. The best way is to express each into rational form then follow the rules for multiplication of fractions.
Examples
Find the product.
Solution:
Solution:
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