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Mixed Number A mixed number has a part that is a whole
number and a part that is a fraction.
= 1 34
#1
An improper fraction is when the numerator is greater than the denominator.
Improper Fraction
1/4 1/4
1/4 1/4
1/4 1/4
1/4 1/484=
numeratordenominator
How To Change An Improper Fraction To A Mixed Number
=52
2 ) 5 numeratordenominator 2
1
Divide the numerator by the denominator.Put your remainder over the denominator.
2
#2
How To Change A Mixed Number To An Improper
Fraction1) Multiply the whole number
times the denominator.
2) Add your answer to the numerator.
3) Put your new number
over the denominator.
4 12x
+=
92
#3
DecimalsTerminating Decimal Is a decimal that stops. The decimal terminates if you reach a remainder of zero when you divide.
Repeating DecimalIs a decimal that shows a pattern of repeating digits.
#4
10.5
2
40.36
11
Decimal Place Value
___ , ___ ___ ___ ___ ___ ___ ___
Th
ou
san
ds
Hu
nd
red
s Ten
s On
es
Ten
ths
Hu
nd
red
ths
Th
ou
san
dth
sTen
Th
ou
san
dth
s
2 4 3 1 6
Read as 243 and 16 hundredths
#5
Decimals are read as “and”
To A Fraction: Read the decimal using the correct place value. How you say it determines the fraction.
0.2 2
10
#6
Two tenths
To a Decimal: Divide the numerator by the denominator.
#7
34
34 0.7
2 82
0
0
5
200
30.75
4
means 3 4
#8 Writing Repeating Decimals as Fractions
one tenth0.1
19
0.1
110
less than one trepea
enthting
22 hundredths0.22 22100
2299
0.22 less than 22 hundrepe
redthsating
three tenths0.3
39
0.3
310
less than 3 terepea
nthsting
123 thousandths0.123 123
1000
123999
0.123 less than 123 thourep
sanea
dthsting3
3 13
Equivalent Fractions
Equivalent fractions name the same amount or the same part of a whole. You use the giant one to show equivalent fractions.
Example:
#9
1
2 2
4
A fraction shows:
35
610
35
915
22 3
3
Parts ShadedTotal Parts
NumeratorDenominator
Least Common Denominator
TO FIND THE LCM OF 4 and 12:
2) Find the least multiple that both numbers have in common.
1) List the multiples of both numbers
4 = 4, 8, 12, 16, 20…12 = 12, 24, 36…
LCM is 12
#10
Least Common Multiple is also known as LCD.
< Less than> Greater than
Less than or equal to Greater than or equal to
Read these symbols from left to right.
****************************************************************
Comparing Fractions #11
To compare fractions you must show your work!
810
91260
60
48 45> 66 5
5
Steps for RoundingFind the number. Circle it.
Look next door.4 or less just ignore.5 or more add one more.
Example: Round 5.328 to nearest hundredth. Circle the 2 in the hundredths place.
Look next door at the 8. It is 5 or more so add 1 more to the hundredths place.
5.328 rounds to 5.33
# 12
Add DecimalsAdd 3.41 + 2.5
1
Step 1: Line up the decimals 3.41+ 2.5 Step 2: If needed, put zeros in
as place holders
Step 3: Add decimals
Step 4: Bring decimal down
. 0
#13
9 5
Subtract DecimalsSubtract 3.58 – 1.6
8
Step 1: Line up the decimals 3.58- 1.6
Step 2: If needed, put zeros in as place holders
Step 3: Subtract decimals
Step 4: Bring decimal down
.
0
#14
2 1
91
2 3ADD
6 6
-2
6
3
6
1
+You ADD numerators
The denominator STAYS THE SAME!
Add Fractions With The Same Denominator#15
6
2 3
Giant One/ Simplest Form
The Giant One is used to reduce or simplify fractions.
#16
4 2 2
10 2 5
16 4 4
20 4 5
To find the simplest form divide the numerator and denominator by the greatest common factor.
12 6 2
18 6 3
Draw one-third (horizontal)
Draw negative one-half (vertical)
1
3-1 2
What is of ? Draw a picture (overlay them).
#17
1 1
3 2
One-Third of a Negative One-Half Piece
1
3
1
2
1
6
1 3
1
2
1
6
+ • – = –
Multiply
43
72 = 28
6
6)284
244
= 234
You do NOT need common denominators Multiply the numerators and denominators straight across.
#18
Change the improper fraction to a mixed number4
6÷
÷22
Reduce!
4 46
7 4
2 3
Multiplying Decimals
Steps for Multiplying Decimals
Step 1: Write the problem vertically.
Step 2: Ignore the decimal point(s) and multiply.
Step 3: Determine where the decimal point goes in the product.
Place the decimal point in the answer by counting how many places the decimal point has moved.
#19
Divide 3 1) Draw a picture to show 3 wholes.
2) How many ’s fit into 3 wholes?
There are 12 one-fourths that fit into 3.
1 2 3 4 5 6 7 8 9 10 11 12
1
4
1
4
#20
To find the reciprocal just flip the fraction over.
#21Two numbers are reciprocals if their product is one.
Change your mixed number to an improper fraction to find the reciprocal.
5 23x
+=
173
317
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
#22
NO decimal point in the divisor.
Divide 0.27 3
3 0. 27. 0
0 02 7
9
27 0
#23 Divisor Dividend
Step 2: Move the decimal point in the dividend straight up into the quotient
Step 3: Divide as usual
Step 1: Write the problem in the long division format
TRICK: Dead Monkeys Smell Bad!
Divide Decimals
Step 2: Move the decimal point in the divisor to the far right of the divisor
Step 5: Divide as usual
Step 1: Write the problem in the traditional long division
Divide 0.42 0.6
0 6 0 4 2. 0
0 042
7
42 0
Step 3: Move the decimal point the SAME NUMBER of places in the dividendStep 4: Move the decimal point in the dividend straight up into the quotient
. .. .
#24Dividend Divisor
Yes, decimal point in the divisor.
EQUIVALENT FRACTIONS OF #25
2
3
4
6
6
9
8
12
2
3
23
22
2
333
2
344
One-Third Plus Two-Fourths#26
horizontal
vertical
1
3
2
4
• 4
• 4
Giant One
• 3
• 3
4
12
6
12
10
12
+
5
6
=
=
Add Fractions
45-23+
15
15x 5 =
x 3 =x 5 =
x 3 =
-10
12
215
1) Find a common denominator.
2) Add the numerators.
3) Keep the common denominator the same.
#27
4) Simplify or reduce. Change improper fractions to mixed #s.
Subtract Fractions5618-
24
24x 3 =
x 4 =x 3 =
x 4 =
3
20
1724
Always SHOWYOUR WORK! This includes theGiant One.
#28
Giant O
ne
Add Mixed Numbers
5658+
24
24x 3 =
x 4 =x 3 =
x 4 =
15
20
3524
24
3 24)351
11
1124
24
1
28 1124
#29
IMPROPER
Subtract Mixed Numbers
2767-
7
7 13
30
177
41
= 1st: Change your mixed numbers to improper fractions.
= 2nd: Subtract numerators.
3rd : The denominator stays the same.
4th : Change your answer to a mixed number.
7)172
14
37
3
#30
Multiply Mixed Numbers
14
=47x
35
35+4
5+ 39
73928
28)391
1128
#31
IMPROPER
FRACTION REVIEWAdd Fractions: Find a common denominator. Add the numerators, and keep the denominator the same.Subtract Fractions: Find a common denominator. Subtract the numerators, and keep the denominator the same.Multiply Fractions: Multiply the numerators and denominators straight across.Divide Fractions: Multiply the first fraction by the reciprocal of the second fraction.Mixed Numbers: Change it to an improper fraction first.
#32