Multiplying Fractions - A Guide

Hi there. It has been a while. In this math post, I cover multiplying fractions. It is assumed the reader knows how to multiply numbers.

For the screenshots, I use the Math Is Fun website drawing tool and witeboard.com to draw the pictures. I know have a mini Wacom pen tablet to draw stuff. Pretty much no more Latex and Quicklatex.com.

Topics

• Fractions As Part Of A Whole
• Multiply Fractions With Examples
• General Case

Fractions As Part Of A Whole

As a short review, I cover the concept of a fraction. A fraction refers to a part of a whole. One quarter would be one piece out of four equal pieces.

When one says one half, it is one piece out of two equal pieces. It can also be two pieces out of four equal pieces.

Proper Fractions vs Improper Fractions

A proper fraction is a fraction where the numerator (top number) is less than the bottom number (denominator). Examples include one half (1/2), seven tenths (7/10) and four fifths (4/5)

An improper fraction is a fraction where the numerator (top number) is greater than the bottom number (denominator). Examples include nine fifths (9/5), three halves (3/2) and ten thirds (10/3).

Multiply Fractions With Examples

It may look scary but multiplying fractions is not that bad. Practice is important. Here are some examples.

Example One

Multiply two thirds with one tenth.

Start with the two top numbers (numerators). Multiply these two top numbers to get 2. Multiply the bottom two numbers (denominators) to get the denominator for the answer.

Reduce the fraction fully. Two out of thirty can be reduced to one out of fifteen.

Example Two

Five ninths multiplied by one seventh.

Example Three - Three Fractions

You may get a rare case of more than two fractions being multiplied together. This example features one half multiplied by four tenths multiplied by two fifths.

Another variation includes cross reducing the fraction before multiplying. You should still get two out of twenty-five.

Keyword Of

In mathematics, the keyword of in many cases refers to multiplication. One basic example would be half of 8 is four. You can do eight divided by two to get four or with the multiplying fractions way.

Another example would be two sevenths of nine quarters. Replace the keyword of with the x symbol for multiply. Multiply the two fractions.

General Case

I have included a general case here for those who want a formula to memorize.

Given unknown numbers a, b, c and d where b and d are not zero, you have this formula or general case for multiplying two fractions together.

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