Fraction | Create WebQuest

Introduction

What is a fraction?

Fractions are a way to represent parts of a whole number. Mathematical expression with a numerator and a denominator, a disconnected piece or a small part of something. Imagine you have a pizza for dinner. Each slice is a part, or fraction, of the whole pizza.
You can add fractions – if your friend had two slices of pizza and then has another. You can subtract them, too – if there are two slices left and you take one.
But adding fractions and subtracting them can be challenging. There are certain steps you have to do to make sure you get the correct answer. This lesson will walk you through those steps and show you that:

Anyone can read and write fractions
Adding fractions is easy if they have common denominators
Subtracting fractions with common denominators is a snap
Working with improper fractions and mixed numbers doesn’t have to be scary

This webquest was created to help students and teachers with the basic concepts of fractions.

Task

This webquest covers the following fractions concepts:

What is a fraction?
Parts of a fraction
Adding and Subtracting fractions
Multiplying and Dividing fractions

Process

A fraction is a number that is part of a whole.

pie chart with 8 pieces showing one shaded piece

Suppose you cut an apple pie into 8 slices. You and your friends eat 7 slices. The 1 slice that remains is a fraction of the whole pie: 1/8

card showing 1 over 8

A fraction can refer to a certain part of a group of items. For example, one of your neighbors has 3 pets: 1 dog and 2 cats.

1/3 of the pets (group) are dogs.

2/3 of the pets (group) are cats.

Numerators and Denominators

A fraction has two parts: a numerator and a denominator.

The denominator is the number of equal parts into which a whole is divided. It"s written at the bottom (below the line of the fraction).

The numerator names a certain number of those parts. It's written on top (above the line in a fraction).

Adding and Subtracting Fractions

When adding and subtracting fractions, the fractions being added or subtracted must have the same denominator. When denominators are different, you will need to convert each fraction into an equivalent fraction by finding the least common denominator (LCD) for the fractions. The two new fractions should have the same denominator, making them easy to add or subtract. (Determining the LCD of a set of fractions was reviewed in the unit Comparing Fractions.)

Rule for Addition of Fractions

When adding fractions, you must make sure that the fractions being added have the same denominator. If they do not, find the LCD for the fractions and put each in its equivalent form. Then, simply add the numerators of the fractions.

Rule for Subtraction of Fractions

When subtracting fractions, you must make sure that the fractions being subtracted have the same denominator. If they do not, find the LCD for the fractions and put each in its equivalent form. Then, simply subtract the numerators of the fractions.

This rule can be broken down into several steps:

Determine whether the fractions have the same denominator.
If the denominators are the same, move to step 4.
If the denominators are different, find the LCD for the fractions being added.
(This process is explained in detail in the previous unit.)
Find the equivalent fractions with the LCD in the denominator.
Add or subtract the numerators of the fractions.
Simplify the resulting fraction.

If we have the fractions 1/6 and 2/6, and wish to add them, we follow our steps:

Determine whether the fractions have the same denominator. If the denominators are the same, move to step 4.	The fractions 1/6 and 2/6 have the same denominator, so we can move to step 4.
Add the numerators of the fractions.
Simplify the resulting fraction. This fraction can be simplified to 1/2.

Multiplying Fractions

Multiplying two fractions is the easiest of any of the operations.

Rule for Multiplication of Fractions

When multiplying fractions, you simply multiply the numerators together and then multiply the denominators together. Simplify the result.

This works whether the denominators are the same or not.

So, if you wish to multiply the fractions 3/2 and 4/3 together you get 12/6.

As with any solution, you should report the answer in simplified form. The fraction 12/6 can be simplified to 2.

You should recall that any number divided by itself is 1, so 6/6=1. In other words, if you find the same number on both the top and the bottom of a fraction, you can cancel it out.

Example:

What do you get when you multiply 1/2 and 3/7?

The result of multiplying these two fractions is 3/14.

The fraction 3/14 cannot be simplified any further; it is in its simplest form.

Dividing Fractions

Dividing one fraction by another is almost as easy as multiplying two fractions. It even involves multiplying fractions! First, let's look at how division of two fractions may be represented. If we wish to divide 3/5 by 2/3, we could write that as:

Rule for Division of Fractions

When you divide two fractions, you take the reciprocal of the second fraction, or bottom fraction, and multiply. (Taking the reciprocal of a fraction means to flip it over.)

As with multiplication, this works whether the denominators are the same or not.

So, if you wish to divide the fraction 3/2 by 4/3, you get the result shown at the right. As with any solution, you should report the answer in its simplified form. In this case, 9/8 is in its simplest form.

Example:

What do you get when you divide 12/17 by 6/7?
The answer is 14/17.

We take the reciprocal of the second fraction and multiplying it by the first. We get 82/102, which, however, is not in its simplified form.
One easy way to simplify this fraction is go back to the step before the numerator and denominator were multiplied.
To reduce a fraction to its simplest form, we need to find the prime factors of both the numerator and denominator (This was shown in the unit on Equivalent Fraction). When we do this for the numerator and denominator we find we can cancel out a 2 and a 3 from the top and bottom. This gives us the result 14/17.