- Topics At a Glance
- Different Types of Numbers
- Natural Numbers
- Whole Numbers
- Integers and Negative Numbers
- Integers and Absolute Value
- Rational Numbers
- Irrational Numbers
- Real Numbers and Imaginary Numbers
**Different Ways to Represent Numbers****Fractions**- Equivalent Fractions
- Mixed Numbers
- Reducing Fractions
- Comparing Fractions
- Least Common Denominator
- Addition and Subtraction of Fractions
- Multiplication of Fractions
- Equivalent Fractions and Multiplication by 1
- Multiplication by Clever Form of 1
- Multiplicative Inverses
- Division of Fractions
- Multiplication and Division with Mixed Numbers
- Decimals
- Converting Fractions into Decimals
- Converting Decimals into Fractions
- Comparing Decimals
- Adding and Subtracting Decimals
- Multiplication and Division by Powers of 10
- Multiplying Decimals
- Dividing Decimals
- Infinite Decimals
- Percents
- Portion of the Whole
- Things to Do with Real Numbers
- Addition and Subtraction of Real Numbers
- Properties of Addition
- Subtraction
- Multiplication
- Division
- Long Division Remainder
- Exponents and Powers - Whole Numbers
- Properties of Exponents
- Prime Factorization
- Order of Operations
- Even and Odd Numbers
- Infinity
- Sequences
- is Irrational
- Counting Rational Numbers
- Counting Real Numbers?
- Counting Irrational Numbers
- In the Real World
- Decimals in Use
- How to Solve a Math Problem
- I Like Abstract Things: Summary

What is a fraction?

A **fraction** is a number written in the form where *q* is nonzero. Any rational number can be written as a fraction, and any fraction as a rational number. Fractions are usually used to think about "parts of a whole." For example, if someone steals all but 1/5 of your ball of wax, you will be 4/5 shy of having a whole ball of wax.

To understand fractions, it may be helpful to think about brownies. Unless you're on a diet. In which case, just mentally replace every occurrence of "brownies" in the following example with the words "veggie squares."

If we cut a pan of warm, double chocolate caramel brownies (man, those would be some hi-cal veggie squares) into *q* pieces of equal size and take *p* of those gooey brownies, the fraction of the pan of brownies we have is *, *because we're taking the *p *from the *q*. The size of each brownie is .

is the fraction we have if we cut the pan of brownies into 4 pieces (each piece has size ), and take 3 brownies:

Never mind the oddly-shaped pan we used to bake these brownies. We have an old, oddly shaped oven.

Getting back to this fraction of ours, we call the number on top of the line the **numerator **and the number below the line the **denominator.**

Numerator comes from the word "numerate," meaning "to number." The numerator tells you how many pieces you have. Denominator comes from the word "denominate," meaning "to give a name to." The denominator gives a name to the pieces, according to their size (for example, "fourths" or "fifths.") Just think - if you had a large litter of nameless puppies, you could numerate and denominate them at the same time.

If the fraction we're looking at is less than 1 (the numerator is less than the denominator), the fraction is called a **proper fraction**. A fraction that is greater than or equal to 1 is called an **improper fraction**. Especially if it's using its dessert fork to eat its salad.

Exercise 1

Is the following fraction proper or improper?

Exercise 2

Is the following fraction proper or improper?

Exercise 3

Is the following fraction proper or improper?