This document discusses converting fractions to decimals. It begins by asking students to explain fractions and decimals. Then it provides two methods for converting fractions to decimals: using proportions or dividing. Examples are shown for converting 1/4, 3/4, and 4/5 to decimals. The document suggests an activity of sorting Skittles by color into fractions and decimals. It concludes by directing students to an online game to practice converting fractions and decimals.

1. Converting Fractions to
Decimals
Lesson 5.2
AMSTI 2006

2. Discussion
• Who can explain what
a fraction is?
• Who can explain what
a decimal is?
• Can you find a
decimal that is
equivalent to ¼?
• What method did you
use to find this?

3. Problem of the Day
Complete the following within 1 minute.
Compare 5/13 to 4/9
Compare 0.384 to 0.4

4. Egyptian Fractions
 The Egyptians of 3000 BC had an interesting way to
represent fractions.
Although they had a notation for 1/2 and 1/3 and 1/4
and so on (these are called reciprocals or unit
fractions since they are 1/n for some number n), their
notation did not allow them to write 2/5 or 3/4 or 4/7 as
we would today. Instead, they were able to write any
fraction as a sum of unit fractions where all the unit
fractions were different.
 A fraction written as a sum of distinct unit fractions is
called an Egyptian Fraction.

5. Why use Egyptian Fractions
Today?
 For two very good reasons:
 The first reason is a practical one.
Suppose you have 5 sacks of grain to share between 8 people, so each
would receive 5/8 of a sack of grain in terms of present-day fractions. How
are you going to do it simply, without using a calculator? You could try
pouring the 5 sacks of grain into 8 heaps and, by carefully comparing them,
perhaps by weighing them against each other, balance them so they are all
the same! But is there a better way? We will see that using unit fractions
makes this easier.
 The second reason is that it is much easier to compare fractions using
Egyptian fractions than it is by using our present-day notation for fractions!
For instance: Which is bigger: 5/8 or 4/7?
 but remember - you are not allowed to use your calculator to answer this!
Again unit fractions can make this much simpler.
 On this page we see how both of these work in Egyptian fractions.

6. Video
Lets watch a video to preview how to
convert fractions to decimals, the
Egyptian way!

8. Converting Fractions to
Decimals
 To convert a Fraction to a Decimal manually,
follow these steps:
 Step 1: Find a number you can multiply by the bottom
of the fraction to make it 10, or 100, or 1000, or any 1
followed by 0s.
 Step 2: Multiply both top and bottom by that number.
 Step 3. Then write down just the top number, putting
the decimal place in the correct spot (one space from
the right for every zero in the bottom number)

9. Method #1: Converting with
Proportions
 Example # 1: Express 3/4 as a
Decimal
 Step 1: We can multiply 4 by 25 to
become 100
 Step 2: Multiply top and bottom by 25
3 = 75
4 100

10. Example # 1 continued….
 Step 3: Write down 75 with the decimal
place 2 spaces from the right (because
100 has 2 zeros);
 Answer = 0.75
 Can you explain what we just did?
 Try to express ¼ as a decimal using
method # 1.

11. Method #2: Convert by
Dividing
 Example #1: to write 5/8 as a decimal,
we need to calculate 5 ÷ 8:
0.625
8 √ 5.000
So = 0.625 as a decimal.
 Try this example: write 4/5 as a decimal
using division (method #2).

12. Skittles Activity
• Sort your skittles into groups by color.
• Find the fraction of each color.
• Convert your fractions into a decimals.
• Record your data on chart paper.
• Compare and discuss with the class.

13. Lets Practice!!
 We are going to use this website to
fish out some fractions and decimals.
 Lets see how well you understand this
lesson.
 Go to www.iknowthat.com
 Select “Math” in the left margin
 Select “Fishy Fractions”
 Select “Fractions and Decimal Match”

14. If you still don’t understand…