The document provides information on fractions, decimals, and percents including: - Definitions of fractions, decimals, and percents and how they relate to each other. - How to convert between fractions, decimals, and percents. - Examples of using mental math to calculate percentages of numbers. - Class work problems on simplifying expressions using the greatest common factor.

1.  Warm-Up
Fractions/Decimals/Percents
 Percent:Definition,Purpose&Use
MentalMathWithPercent
 ClassWork:2.8--(now3.1)Due
tomorrow
Today:January 19, 2016

3. Warm-Up:
1. Before working this problem, look at/analyze it, then
describe your plan to solve based on what you see in this
particular problem. Be specific, use complete sentences. Do
not solve yet.
______________________________________________
_____
______________________________________________
_____
_________________.
1. -3n2 + 7n
n
Because there is more than one term, I’m going to simplify
by factoring. I will cancel factors from the numerator &
denominator if I can

4. 3. Which fraction must have more than two decimal places?
Why??
A.) ¼ B.) 2/5 C.) 12/50 D.) 5/6 E.) None
________________________________________
____________________________________________
________________________________________
This is not a proportion, so I’ll have to multiply
each term by the LCD to eliminate the
denominators.
Then I’ll combine like terms and solve as usual.
2. Same directions for this problem:
2.
𝐱+ 𝟑
𝟐
+
𝐱+𝟐
𝟑
=
𝟕
𝟑
x =
𝟏
𝟓
Because six does not go evenly into 100.
Warm-Up:

5. 1. 10m – 15n
5
Simplify:
2. 20a6b5
35a2b3
3. 15x2 + 21x6
Warm-Up:

7. Vocabulary:
Fractions: From the Latin fractiō: a breaking into pieces, also
from the Latin fractus: broken
English Words from the Latin Root Fractus:
fracture, infraction, fragile, frail
Fractions are a SINGLE NUMBER and can be placed on the
number line. All positive proper fractions are a number
between 0 and 1.

8. Vocabulary:
A fraction is defined as a “part – whole” relationship of a
number.
𝟏
𝟐
means “one of two” or “one out of every two.”
The part/whole relationship is known as a ratio, and is
calculated through division.
“One out of every two” as a fraction is
𝟏
𝟐
As a decimal,
this relationship is 1 ÷ 2, 2 1 which equals 0.5

9.  October was the 8th month and December the 10th and final
month until the year 46 bc. when this Roman Dictator,
Military Genius, Conqueror of Lands, Lover of Cleopatra,
& father of Augustus changed the calendar by adding two
months to the year.
October? English: Decade, December?
 A decimal is a fraction with a denominator that is
also a place value.
Decimal: Latin decimalis, meaning tenths. Root is Latin decim,
ten.
Julius CaesarHe was.... and he added what months?

10.  Percent: From the Latin per centum. Per: for each as in
"One per student.” Centum: hundred Century, Cent,
Centimeter, Centipede
Percent: Definition
100% = 100 = 1
100
**Fractions, Decimals, & Percents are three different ways of
expressing the same amount. All three show a single number
based on the relationship (ratio) between two other
numbers.
50% = 50 =
𝟏
𝟐
= .5
100
5% = 05 = 1 = .05
100 20

12. Fractions Decimals Percent
Since the % sign cannot be +, -, x, ÷; numbers expressed as
percents must be changed to a decimal or fraction before
any calculations can be made.
 A. How to change a decimal to a percent:?
 B. How to change a percent to a decimal:?
 C. How to change a fraction to percent, or percent to
fraction?
Move the decimal 2 places to the right and add the % sign.
Move the decimal 2 places to the left and drop the % sign.
To change a fraction to percent, or percent to fraction, the
number must be changed to a decimal first.

13. Fractional Conversions:
Fraction Decimal Percent
0.5 50
0.33 33.3
0.25 25
0.20 20
0.16 16.7
0.1428571 14
0.125 12.5
0.11 11
0.09 9

14. Mental Math:
Percent of a Number
A. 10% of $1.00 is .1, or
To find 20% of any number, multiply by 2 and move the
decimal one place to the left.
𝟏
𝟏𝟎
(10 cents).
To find 20% of a number, you could multiply a number by what
fraction? B. 20% is what fraction?
.2
20% of 40 is….. 8
The easier way, though, is to multiply a number by the decimal
form of 20%, which is....
To find 10%, simply move the decimal one place to the left.
𝟏
𝟓

15. Mental Math:
Percent of a Number
Find 20% using mental math
Find 15% using mental math
1)
20
3)
42.1
1) 10
4)
120
1)
10
3)
603) 60
4) 380
Find 5% using mental math 4)
160
1)
10
3)
60
4) 125
2) 25
2) 20
2) 20
2) 3.5

16. Class Work:

17. Please note: If an expression has a single term,
48x3 y4z
56xy5z3
simplifying is accomplished by reducing ;(GCF)
If an expression has more than one term, 3c - 24
c - 8simplifying is accomplished by factoring
(GCF again) Simplify by factoring:
6x3y -12x2 + 15x -27xy
simplify by factoring
2a + 6
4a - 12

18. Reduce the fraction, if possible, by using prime factorization
to find the GCF of:
1.
𝟏𝟒𝟒
𝟏𝟓𝟎
2.
𝟏𝟒𝟎
𝟐𝟒𝟓
GCF = 7 x 5 = 35
140/35 = 4
245/35 = 7
GCF = 2 x 3 = 6
144/6 = 24
150/6 = 25
Simplify Using GCF: 48x3 y4z
56xy5z3
= 24
•3•xxx•yyyy•z
= 23
•7•x•yyyyy•zzz
= 24
•32
= 2•3• 52
6x2
7yz2

19. 2
3
= x_
18