1. Learning to Juggle with:
Fractions,
Decimals,
and Percents
© Mike’s Math Mall

2. Introduction

3. Fractions, Decimals, and Percents
Fractions, decimals, and percents are different ways of
representing the same number.
𝟏 𝟐 = = 50%
Fraction Decimal Percent
These numbers look different, but they all have the exact same value.

4. Fractions, Decimals, and Percents
Because we use fractions, decimals, and percents in everyday life, it’s helpful if we can juggle or change between each form…
…making these numbers
easier to
understand.

5. Fractions, Decimals, and Percents
When do we use
Fractions?
Telling time
𝟏 𝟒 after four
(a quarter after four)
Cooking/Recipes
𝟐 𝟑 cups flour
Reading Music
𝟏 𝟐 note
Measuring Length
𝟓 𝟏 𝟖 inches
Can you think of other ways we use fractions?

6. Fractions, Decimals, and Percents
When do we use
Decimals?
Sports
0.375 – baseball
batting averages
Prices
$299.99 Pi … 𝜋
Gas Amounts
gallons
Where else do we see decimals?

7. Fractions, Decimals, and Percents
When do we use
Percents?
Grades
25%
Retail Sales
60% off!
Thanks
for reminding me!
Statistics
100% of students choose
shorter school days!
Tipping Rates
15% to 20%
Where else do we find percentages?

8. Changing Fractions to Decimals
Part 1:
1 1 2
𝐧𝐮𝐦𝐞𝐫𝐚𝐭𝐨𝐫 𝐝𝐞𝐧𝐨𝐦𝐢𝐧𝐚𝐭𝐨𝐫
Changing Fractions to Decimals
𝟎.𝟕𝟓
𝟑 𝟒
𝒑𝒂𝒓𝒕 𝒘𝒉𝒐𝒍𝒆
𝟏.𝟓

9. Proper fractions, like this one, represent numbers less than 1.
Focusing on Fractions
A fraction is formed by two numbers; a top number, the numerator, over a bottom number, the denominator.
3 4
𝐧𝐮𝐦𝐞𝐫𝐚𝐭𝐨𝐫 𝐝𝐞𝐧𝐨𝐦𝐢𝐧𝐚𝐭𝐨𝐫 →
𝒑𝒂𝒓𝒕 𝒘𝒉𝒐𝒍𝒆 or
Proper fractions, like this one, represent numbers less than 1.

10. Does anyone know how to turn a fraction into a decimal?
Fractions to Decimals
Decimals are related to fractions because they also represent numbers less than 1.
Does anyone know how to turn a
fraction into a decimal?
Divide the numerator
by the denominator!
But how
does that give you a decimal?

11. Fractions to Decimals Let’s use 𝟑 𝟒 as an example. . 7 5 4 3.0 -2 8 2
To turn 𝟑 𝟒 into a decimal, we divide the
numerator, 3, by the denominator, 4. . 7 5 4
3.0
So 𝟑 𝟒 = 0.75
-2 8 2
-20
Hint: you can think of a fraction bar like a division (÷) symbol.

12. Fractions to Decimals Let’s try 𝟏 𝟒 . 2 5 4 1.0 - 8 2 -20. 2 5 4
1.0
So 𝟏 𝟒 = 0.25
- 8 2
-20

13. Fractions to Decimals . 6 6 3 2.0 -1 8 2 -18 2 Let’s try 𝟐 𝟑
At this point, you can see the division problem will never end, and the 6 will keep repeating. . 6 6 3
2.0
-1 8 2
So 𝟐 𝟑 = 0.6
-18 2

14. Can someone guess what the decimal form of 3 𝟑 𝟒 would be?
Fractions to Decimals
Can someone guess what the decimal form of 3 𝟑 𝟒 would be?
If you said 3.75, you’re right! Notice how the whole
number stays the
same in both forms.
I think
I get it, but can
we do more
to be sure?
Absolutely!

15. Time to Show Your Stuff! = 0.25 = 0.4 = 0.83 = 0.7 = 0.3 = 1.5 = 2.6
Change the following fractions into decimals.
1) 𝟏 𝟒
2) 𝟐 𝟓
= 0.25
= 0.4
3) 𝟓 𝟔
4) 𝟕 𝟏𝟎
= 0.83
= 0.7
5) 𝟏 𝟑
6) 1 𝟏 𝟐
= 0.3
= 1.5
7) 2 𝟑 𝟓
8) 9 𝟓 𝟖
= 2.6 =

16. Changing Decimals back to Fractions

17. Decimals to Fractions
Before we start changing decimals into fractions, we need a good understanding of how to properly say decimals.
Believe it or not, when you
properly say a decimal,
you are automatically
creating the fraction.

18. 0. 3927 Decimals to Fractions ten thousandths thousandths hundredths
Can you name the following decimal place values?
ten thousandths
thousandths
hundredths
tenths
Now let’s look at how to properly “say” decimals.
(Sample number)

19. Decimals to Fractions 1) 0.7 “seven tenths” 2) 0.23
Practice saying the following decimals:
1) 0.7
“seven tenths”
2) 0.23
“twenty-three hundredths” 3)
“thirty-four thousandths”
4) 9.8
“nine and eight tenths”

20. Decimals to Fractions = 𝟖 𝟏𝟎 = 𝟏𝟔 𝟏𝟎𝟎 = 𝟓𝟐 𝟏,𝟎𝟎𝟎 = 4 𝟒 𝟏𝟎 1) 0.8
As you say each decimal, picture the fraction you’re saying to yourself:
= 𝟖 𝟏𝟎
= 𝟏𝟔 𝟏𝟎𝟎
1) 0.8
2) 0.16
= 𝟓𝟐 𝟏,𝟎𝟎𝟎
= 4 𝟒 𝟏𝟎 3)
4) 4.4
What work still needs to be done with all of these fractions?
If you said “simplify,” you’re right!

21. Decimals to Fractions = 𝟖 𝟏𝟎 = 𝟒 𝟓 = 𝟒 𝟐𝟓 = 𝟏𝟔 𝟏𝟎𝟎 = 𝟏𝟑 𝟐𝟓𝟎 = 𝟓𝟐 𝟏,𝟎𝟎𝟎
Simplify.
1) 0.8
= 𝟖 𝟏𝟎
= 𝟒 𝟓
I get it!
But I better
do some more practice.
= 𝟒 𝟐𝟓
2) 0.16
= 𝟏𝟔 𝟏𝟎𝟎
= 𝟏𝟑 𝟐𝟓𝟎 3)
= 𝟓𝟐 𝟏,𝟎𝟎𝟎
4) 4.4
= 4 𝟒 𝟏𝟎
= 4 𝟐 𝟓

22. Time to Show Your Stuff! = 𝟐 𝟏𝟎 = 1 𝟑𝟐 𝟏𝟎𝟎 = 𝟏 𝟓 = 1 𝟖 𝟐𝟓 = 𝟏𝟐𝟒 𝟏,𝟎𝟎𝟎
Change the following decimals into fractions.
Don’t forget to simplify!
= 𝟐 𝟏𝟎
= 1 𝟑𝟐 𝟏𝟎𝟎
1) 0.2
2) 1.32
= 𝟏 𝟓
= 1 𝟖 𝟐𝟓
= 𝟏𝟐𝟒 𝟏,𝟎𝟎𝟎
= 𝟒𝟖𝟖 𝟏𝟎,𝟎𝟎𝟎 3) 4)
= 𝟔𝟏 𝟏,𝟐𝟓𝟎
= 𝟑𝟏 𝟐𝟓𝟎