Hi there. This math education post is on multiplying fractions. Multiplying fractions can be taught to middle school students of around Grade 6 and 7. Harder cases of multiplying fractions are seen in high school mathematics (Grade 9, 10) which involve more algebra.
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The main idea with multiplying fractions is actually simple. Two fractions can be multiplied together by multiplying the numerators together and the denominators together to obtain a single fraction.
Example
Multiplying one half with three tenths gives 3 over 20.
It seems that people forget from time to time that whole numbers have a denominator of one when expressed as a fraction. The number 8 can be written as
As an example, multiplying 9 with one eighth gives nine eighths or 1 and one eighth.
Some fractions contain large numbers which are annoying to multiply without a calculator. There are cases where you can reduce fractions before multiplying. Reducing fractions makes things easier as you avoid multiplying large numbers.
Example One
Example Two (Cross Reduce)
Note that the second three is obtained from 15 divided by 5.
The next extension of multiplying fractions is working with variables. When possible, you can reduce/eliminate variables if they divide out each other. Do be careful with dealing with exponents and simplifying.
Example One
Example Two (Cross Reduce)
Example Three (Negative Exponents)
Multiplying fractions can get more advanced with the addition of the distributive law. The distribuive law allows for multiplying a monomial with a binomial/trinomial/polynomial. An example of the distributive law is:
Example One
Example Two
The distributive law consists of a monomial multiplied by a binomial. Expanding binomials involves a binomial multiplied by another binomial. With this case the FOIL method is a nice way of "unpacking" two binomials.
The FOIL method consists of First, Outer, Inner and Last. First is for the ax term, outer is for the a and y to obtain ay, inner is for bx and last is for by.
Example One
Example Two
Thank you for reading.
