1. Fractions, Decimals, and Percents Learning to Juggle with:
I juggled
Granny’s china
teacups…
once!
Fractions,
Decimals,
and Percents
A Bundled Unit
© Created by Mike Walker

2. Introduction Not that kind of introduction, big fella! Hi!
My name’s Sparky!
Introduction
Not that kind of introduction, big fella!

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.
I don’t understand how I got a 25% on my last math test.
I understand
that ¼ pound of cheesy bacon burger is good!
Hopefully, you just had an off day!

5. Fractions, Decimals, and Percents
When do we use
Decimals?
Sports
0.375 – baseball
batting average
Prices
$299.99
Gas Quantities
gal Pi …
What are some other decimal uses?

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

7. Changing Decimals to Percents
Part 1:
40%
0.25
Changing Decimals to Percents
110%
𝐨𝐮𝐭 𝐨𝐟 𝟏𝟎𝟎
𝟎.𝟒

8. Pondering the Percent A percent represents an amount out of 100.
We use the (%) symbol instead of writing fractions with a denominator of 100.
Why
does this
number haunt me?
So, for example,
instead of saying Sparky
got 25 out of 100 on his last
math test, we say Sparky got a 25%.

9. Decimals to Percents 62% = 62 100 × 0.62 200 + 600 62.00
Because a percentage represents
an amount out of 100, to turn a decimal into a percent, all we do is
multiply the decimal by 100.
Let’s change 0.62 to a percent!
100
× 0.62
200
+ 600
62.00
Don’t forget the percent sign!
= 62
62%

10. seems waaaaay easier to me!
Decimals to Percents
Someone
told me that when
you multiply by 100, it’s
just like moving the
decimal point 2 places
to the right!
Moving
the decimal
seems waaaaay easier to me!
Got it!
That someone was right!
It is! Just don’t forget to add the percent sign after you move the decimal!

11. Decimals to Percents 0.45 = 45% = 70% 0.7 → 45.0 → 70.0
So, let’s use Sparky’s method to easily change some decimals into percents.
Example 1:
0.45
→ 45.0
= 45%
Example 2:
0.7
→ 70.0
= 70%
Before we can move the decimal 2 places to the right, we have to add a zero.

12. I’m pretty sure I have this!
Decimals to Percents
Example 3:
1.25 →
= 125%
Example 4:
= 200% 2 00 → .
I’m pretty sure I have this!
An “understood” decimal comes after the 2.
Add two zeros so we can move the decimal!
We better practice just in case!

13. Decimals to Percents 1) 0.75 2) 0.11 3) 0.8 4) 0.333 5) 1.45 = 75%
Change the following decimals into percents.
1) 0.75
2) 0.11
3) 0.8 4)
5) 1.45
= 75%
= 11%
= 80%
= 33.3%
= 145%
6) 0.2 7)
8) 4
9) 0.5
10) 0.99
= 20%
= 61.5%
= 400%
= 50%
= 99%

14. Changing Percents back to Decimals
Part 2:
I’m getting dizzy!
Changing Percents back to Decimals
This won’t be bad. Trust me!

15. Check this out, Professor!
Percents to Decimals
If we move the decimal 2 places to the right to change a decimal to a percent, what do you suppose we do to change a percent back to a decimal? It
runs in the
family!
Move the
decimal 2 places
to the left?
Pure genius!
Check this out, Professor!

16. Then, move the decimal 2 places to the left.
Percents to Decimals
Example 1: 85 %
→ .85
= 0.85 .
Locate the “understood” decimal after the 5 and remove the percent sign.
Then, move the decimal 2 places to the left.
Example 2: 30 %
→ .30
= 0.3 .
Example 3:
115 %
= 1.15 .
Your turn!

17. Percents to Decimals 1) 18% 2) 100% 3) 5% 4) 12.9% 5) 88% = 0.18 = 1
Change the following percents into decimals.
1) 18%
2) 100%
3) 5%
4) 12.9%
5) 88%
= 0.18
= 1
= 0.05
= 0.129
= 0.88
6) 7.43%
7) 150%
8) 11%
9) %
10) 7.7% =
= 1.5
= 0.11
= 3.162
= 0.077

18. Changing Decimals to Fractions
Part 3:
Head…
going…to…
explode!
Changing Decimals to Fractions
Stay with me Sparticus!

19. 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
Measuring Length
𝟓 𝟏 𝟖 inches
Reading Music
𝟏 𝟐 note
Can you think of other ways we use fractions?

20. 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.

21. At least the crazy face is gone!
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.
I’ll believe
it when I see it…
or hear it!
At least the crazy face is gone!

22. 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 try to properly
“say” some decimals?
(Sample number)

23. Practice saying the following decimals to yourself:
Decimals to Fractions
Practice saying the following decimals to yourself:
say “seven tenths”
say “twenty-three hundredths”
say “thirty-four thousandths”
say “nine and eight tenths”
1) →
2) →
3) →
4) →

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

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

26. Decimals to Fractions = 𝟐 𝟏𝟎 = 𝟏 𝟓 1) 0.2 = 1 𝟑𝟐 𝟏𝟎𝟎 = 1 𝟖 𝟐𝟓 2) 1.32
Change the following decimals into fractions.
Don’t forget to simplify!
= 𝟐 𝟏𝟎
= 1 𝟑𝟐 𝟏𝟎𝟎
= 𝟏𝟐𝟒 𝟏,𝟎𝟎𝟎
= 𝟓,𝟎𝟎𝟖 𝟏𝟎,𝟎𝟎𝟎
= 𝟏 𝟓
= 1 𝟖 𝟐𝟓
= 𝟑𝟏 𝟐𝟓𝟎
= 𝟑𝟏𝟑 𝟔𝟐𝟓
1) 0.2
2) 1.32 3) 4)

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

28. Decimals are related to fractions because they also represent numbers
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?
If you said to divide
the numerator by the denominator, you’re right!
But how
does that give you a decimal?
Check this out!

29. Hint: you can think of a fraction bar like a division (÷) symbol.
Fractions to Decimals
Let’s use 𝟑 𝟒 as an example.
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.

30. 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 one more
to be sure?
Absolutely!

31. Let’s change 5 𝟐 𝟑 into a decimal!
Fractions to Decimals
Let’s change 5 𝟐 𝟑 into a decimal!
Remember! The whole number will stay the same, so we just need to divide 2 by 3.
At this point, you can see the division problem will never end, and the 6 will keep repeating. . 6 6 3
2.0
I’m
still iffy!
-1 8 2
So 5 𝟐 𝟑 = 5.6
-18
Let’s practice! 2

32. Fractions to Decimals 2) 𝟐 𝟓 3) 𝟓 𝟔 4) 𝟕 𝟏𝟎 6) 1 𝟏 𝟐 7) 2 𝟑 𝟓 8) 9 𝟓 𝟖
Change the following fractions into decimals.
1) 𝟏 𝟒
2) 𝟐 𝟓
3) 𝟓 𝟔
4) 𝟕 𝟏𝟎
5) 𝟏 𝟑
6) 1 𝟏 𝟐
7) 2 𝟑 𝟓
8) 9 𝟓 𝟖
= 0.25
= 0.4
= 0.83
= 0.7
= 0.3
= 1.5
= 2.6 =