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Multiplying Fractions - A Guide by dkmathstats

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· @dkmathstats ·
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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.

 


<center><img src="https://cdn.pixabay.com/photo/2016/11/23/15/51/book-1853677_960_720.jpg" /></center>
<center><a href="https://cdn.pixabay.com/photo/2016/11/23/15/51/book-1853677_960_720.jpg">Pixabay Image Source</a></center>


## Topics
---

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

&nbsp;

## 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.


<center>![fractions_onequarter.PNG](https://images.hive.blog/DQmXd46mazSSNyDGb2Jr5jXjJcJWDyYFQVXf5wSwzzCTQuV/fractions_onequarter.PNG)
</center>


&nbsp;



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.


<center>![fractions_twoquarters.PNG](https://images.hive.blog/DQmSrqRjtDigFiAkegJqAWZCGvQ5EUtLBqPy8aecm9c5ZN3/fractions_twoquarters.PNG)
</center>

&nbsp;


**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)



<center>![properFractions_01.PNG](https://images.hive.blog/DQmSBPNN8GfY5G9EyemR6YSLgGePvqcpqcvnaxkKBXGhevC/properFractions_01.PNG)
</center>

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).



<center>![improperFractions_01.PNG](https://images.hive.blog/DQmXjaEZxFyK9w8E6STqP6f6JwmievozDgGU4DPiKe1B7nE/improperFractions_01.PNG)
</center>


&nbsp;

## 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.



<center>![exampleOne_01.PNG](https://images.hive.blog/DQmQA3k7o8yqQi4HaQYMgbqr5rZ7EE9bxwjLQuA9xQ9PFke/exampleOne_01.PNG)
</center>


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.



<center>![exampleOne_02.PNG](https://images.hive.blog/DQmWqMgv6p4Ev9E5caERZT7hzqgNVXyuJYVraVDFe8faDe4/exampleOne_02.PNG)
</center>

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


<center>![exampleOne_03.PNG](https://images.hive.blog/DQmZbzyUdrhFCug4VxUVXKZKxfkKeUqyeFKxSvT9sVFzFwh/exampleOne_03.PNG)
</center>

&nbsp;

**Example Two**

Five ninths multiplied by one seventh.


<center>![exampleTwo.PNG](https://images.hive.blog/DQmPTndQeA7p61sdDAbeJcVMZ1vjC6SXz8Fqm5EBYRFh8uC/exampleTwo.PNG)
</center>


&nbsp;

**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.



<center>
![exampleThree_01.PNG](https://images.hive.blog/DQmW16KEHVG9fn2zkU9BhiovQaAJMCDeWGMEHDkBWf3THST/exampleThree_01.PNG)
</center>



<center>
![exampleThree_02.PNG](https://images.hive.blog/DQmUz16sHN8ukrY48TW8s7k9y5iKgsfQ5tyZPCFxMdr3wB5/exampleThree_02.PNG)
</center>


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

&nbsp;


**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. 


<center>![keywordOf_01.PNG](https://images.hive.blog/DQmXFh6Sfm6a8aMbrncmpPpxNVexgVb4pcnUkkYUGvAhZCc/keywordOf_01.PNG)
</center>

&nbsp;

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

<center>
![keywordOf_02.PNG](https://images.hive.blog/DQmceH4S8tzbR9MBTGeNi43XAf1CVQ3f6E37wCUNP9RMFmR/keywordOf_02.PNG)
</center>

&nbsp;


## 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.


<center>![generalCase.PNG](https://images.hive.blog/DQmWCaX9bLyBcbCHDXve586AGmZhSYG2S3pd7PgiZN6bb5m/generalCase.PNG)
</center>

&nbsp;

<center>Thank you for reading.</center>

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