Before you can make “heads” or “tails” out of fractions, it would be helpful if we first agree that the basic idea of a fraction can be ABSTRACT, unless we name the WHOLE to which we are referring. So it is important to keep this in mind while doing your assignments.[box color=”blue”]

### Definition of a Fraction

[/box]You might recall that in math a number is a point on the number line. Well, there is a special collection of numbers called fractions, which are usually denoted by **a/b**, where **“a”** and **“b”** are whole numbers and **“b” is not equal to “0”**.

It may be helpful to get your homework off to a great start by defining what fractions are, that is to say, specifying which of the points on the number line are fractions.

So, here goes…

**There are three distinct meanings of fractions** —part-whole, quotient, and ratio, which are found in most elementary math programs. To reduce confusion while using this homework helper, our lessons will only cover the part-whole relationship.

**The Part-Whol**e – The part-whole explanation of a fraction is where a number like 1/5 indicates that a whole has been separated into five equal parts and one of those parts are being considered.

This table is a great help to get a feel of how a fractional part compares to the whole…

As a homework helper, this table shows you how the “same” whole can be divided into a different number of equal parts.

The Division Symbol** (“/” or “__”)** used in a fraction tells you that **everything above** the division symbol is the **numerator** and must be treated as if it were one number, and e**verything below** the division symbol is the **denominator** and also must be treated as if it were one number.

Basically, the **numerator** tells you how many part we are talking about, and the **denominator** tells you how many parts the whole is divided into. So a fraction like **6/7** tells you that we are looking at six (**6**) parts of a whole that is divided into seven (**7**) equal parts.

Although we do not cover fractions as a quotient or as a ratio, here is a brief explanation of them.

**A Quotient** – The fraction 2/3 may be considered as a quotient, 2 ÷ 3. This explanation also arises from a dividing up situation.

For example…

Suppose you want to give some cookies to three people. Well, you could give each person one cookie, then another, and so on until you had given the same amount to each. So,…

If you have six cookies, then you could represent this process with simple math by dividing 6 by 3, and each person would get two cookies.

**But what if you only have two cookies?**

One way to solve the problem is to break-up each cookie into three equal parts and give each person 1/3 of each cookie so that in the end, each person gets 1/3 + 1/3 or 2/3 cookies. So 2 divided by 3 = 2/3.

Here’s a brief explanation of…

**A Ratio** – A comparison of things as a ratio can be expressed in one of two ways: first, the “old fashioned” method, **a:b**, pronounced “**a** is to **b**“; and second, as found in newer books, **a/b**. If the ratio of **“a to b”** is **1 to 4**“, or **1/4**, then “a” is one-quarter of “b”. Alternately, “b” is four times as great as “a”.

**For example:**

The width of a rectangle is 7ft and its length is 19ft. The ratio of its width to its length is 7ft to 19 ft, or…

**7ft/19ft = 7/19**

Since we are comparing feet to feet, we don’t need to write the units.

**The ratio of its length to its width is…19 to 7**

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