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# NUMERATOR - PowerPoint PPT Presentation

TOP #. NUMERATOR. HOW MANY PIECES OUT OF THE WHOLE. BOTTOM #. DENOMINATOR. HOW MANY TOTAL PARTS MAKE 1 WHOLE. 1. 3. 2. 4. 6. 8. 9. 5. 7. IMPROPER. 14. MORE THAN 1 WHOLE. 9. PROPER. 5. LESS THAN 1 WHOLE. 9. WHOLE # AND A FRACTION. MIXED. 1. 5. MORE THAN 1 WHOLE. 9.

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### NUMERATOR

HOW MANY PIECES OUT OF THE WHOLE

### DENOMINATOR

HOW MANY TOTAL PARTS MAKE 1 WHOLE

1

3

2

4

6

8

9

5

7

### IMPROPER

14

MORE THAN 1 WHOLE

9

### PROPER

5

LESS THAN 1 WHOLE

9

### MIXED

1

5

MORE THAN 1 WHOLE

9

9

9

27

9

### EQUIVALENT

18

3

EQUAL PART OF 1 WHOLE

24

4

FRACTIONS

COMMON DENOMINATOR

X9

X5

X5

X9

20

27

45

45

MULTIPLY

9

3

X3

RAISE

4

12

X3

### EQUIVALENT

SIMPLIFY

1

3

÷3

DIVIDE

12

÷3

4

0.625

.000

DIVIDE!!

TOP DOG IN THE HOUSE

IMPROPERFRACTIONS

TOP DOG IN THE HOUSE

PROPERFRACTIONS

TOP DOG IN THE HOUSE

THE NAME OF A DIGIT’S LOCATION AND VALUE

DECIMALS / FRACTIONS

LESS THAN 1 WHOLE

102,102,102.102102

WHOLE NUMBERS

TENS

TENTHS

MILLIONS

HUNDREDS

THOUSANDS

MILLIONTHS

TEN MILLIONS

HUNDREDTHS

THOUSANDTHS

UNITS OR ONES

TEN THOUSANDS

TEN THOUSANDTHS

HUNDRED MILLIONS

HUNDRED THOUSANDS

HUNDRED THOUSANDTHS

DECIMAL BACK TO A FRACTION

USE TO CHANGE A

DECIMAL INTO A FRACTION

.125

125 THOUSANDTHS

.08

8 HUNDREDTHS

5.6

5 AND 6 TENTHS

.05is NOT.5

7060

TO THE RIGHT

7060.0

### + OR –DECIMALSLINE THEM UP!!

67.0

- 4.8

÷ DECIMALS

MOVE DECIMAL TO MAKE THE DIVISOR A WHOLE NUMBER

÷ DECIMALS

MOVE DECIMAL TO MAKE THE DIVISOR A WHOLE NUMBER

÷ DECIMALS

MOVE DECIMAL TO MAKE THE DIVISOR A WHOLE NUMBER

X DECIMALS

DON’T LINE THEM UP!!

COUNT ….

TOTAL DECIMAL PLACES!!

6.04

X2.5

15.100

3020

+1208

15100

MULTIPLY A NUMBER BY10, 100, 1000, 10000

COUNT ZEROS

MOVE DECIMAL TO THERIGHT

DIVIDE A NUMBER BY10, 100, 1000, 10000

COUNT ZEROS

MOVE DECIMAL TO THELEFT!

MULTIPLY

BIGTO SMALL

GALLONS TO CUPS

X BY 16

M TO CM

X BY 100

YARDS TO INCHES

X BY 36

### CONVERSION

DIVIDE

CUPS TO QUARTS

SMALL TOBIG

÷BY 16

CM TO M

÷BY 100

SECONDS TO MINUTES

÷BY 60

PERCENT

PER HUNDRED

15%

.15

HUNDREDTHS

15

100

PERCENT

OF A NUMBER

MULTIPLY!!

43%OF 25

.43 X 25

USE FOR TIPS, TAX, AND SALES!

1.85

DECIMAL TO

MULTIPLY BY 100

DECIMAL 2 TO THE RIGHT

185%

28.5%

TODECIMAL

DIVIDE BY 100

DECIMAL 2 TO THE LEFT.

.285

0.85

FRACTIONTO

• TOP DOG IN THE HOUSE

%

• DECIMAL TO

85%

28.5%

TOFRACTION

1. %TO DECIMAL

.285

2. PLACE VALUE AS FRACTION & SIMPLIFY

MULTIPLY

• BY ABOUT 8 CENTS OR \$0.08 FOR DENTON TEXAS.

• BACK ONTO THE TOTAL COST.

TOTAL WITH TAX

45.37 + 3.63 =

\$49.00

X.08 =

\$3.6296 OR

\$3.63

TOTAL COST=

\$45.37

HALF

X BY.5

BY 2

.5

NUMBERS THAT EQUAL HALF

00.5000

.50

0.500

0.5

0.50

.500

HALF

OR .25

HALF OF HALF

4 OUT OF 28

FREE THROWS

1 OUT OF 7

FREE THROWS

WHAT YOU CAN DIVIDE A NUMBER BY (DIVISIBILITY) WITHOUT A REMAINDER

FACTORS OF 72:

1, 72, 2, 36, 3, 24, 4, 18, 6, 12, 8, 9

GREATEST COMMON FACTOR

GCF OF

36 AND 90

1 36

2 18

3 12

4 9

6 6

90

2 45

3 30

5 18

6 15

10 9

GCF =18

BY “9”

2+7=9

4+5=9

SUM OF THE DIGITS is 9

BY “9”

3+9+4+2=18

1+8= 9

SUM OF THE DIGITS is 9

BY “3”

2+7=9

5+7=12

SUM OF THE DIGITS is 3, 6, 9,12

BY “3”

7+3+4+1=15

1+5= 6

SUM OF THE DIGITS is 3, 6, 9,12

BY “4”

EVEN AND LAST TWO DIGITSARE 04, 08, 12, 16, 20, 24, 28, 32, …..

BY “4”

EVEN AND LAST TWO DIGITSARE 04, 08, 12, 16, 20, 24, 28, 32, …..

BY “6”

1+8=9

4+8=12

EVEN AND SUM OF DIGITS IS3,6,9…

BY “6”

9+7+8=24

2+4=6

EVEN AND SUM OF DIGITS is 3, 6, 9

BY “5”

LAST DIGIT IS A “5” OR “0”

BY “5”

LAST DIGIT IS A “5” OR “0”

BY “10”

LAST DIGIT IS A “0”

Move decimal once to the left.

BY “10”

LAST DIGIT IS A “0”

Move decimal once to the left.

BY “2”

EVEN! LAST DIGIT IS A

“0, 2, 4, 6, or 8”

MIXED TO IMPROPER

THINGY

X OR ÷

FRACTIONS

MIXED NUMBERS

MUST DO

CHECKIE THINGY!

X FRACTIONS

AINT NO PROBLEM TOP X TOP AND BOTTOM X BOTTOM

FRACTION OFA #

MULTIPLY

⅔ OF 84

÷FRACTIONS

DON’T CRY!!

FLIP THE Right& MULTIPLY!

÷FRACTIONS

FLIP THE right

A NUMBER’S MULTIPLICATION FACTS

MULTIPLES OF 72:

72, 144, 216, 288, 360, 432, 504, 576, 648, 720, 792, 864…

LEAST COMMON MULTIPLE

LCM OF

36 AND 90

36X2=72

36X3=108

36X4=144

36X5=180

90X2=180

90X3=270

90X4=360

LCM =180

TOTAL DISTANCE AROUND THE OUTER EDGES

FENCE, BORDER, TAPE, CUT AROUND, FRINGE, LACE, CUFF, OUTLINE, FRAME, EDGE, TRACE,

TOTAL INSIDE FLAT SPACE

MEASURED IN SQUARE UNITS

USES MULTIPLICATION!!

FLAT SPACE, INSIDE, PAINT, CARPET, COVER, SPREAD, ROOM, TILE, MOW LAWN, VACUUM, ….

MEASURES OF CENTRAL TENDENCY

MEAN

MODE

MEDIAN

CONCLUSION OF THE DATA

Average

+, ÷

MEDIAN

Middle #

MOST

RANGE

Highest

– lowest

ARE

ARE NOT

• IRRATIONAL

• PROPER

• LESS THAN ONE

• RATIONAL

• IMPROPER

• EQUAL TO OR MORE THAN 1

DECIMAL OUT OF SIGHT TO THE RIGHT!!

CAN BE MADE INTO A FRACTION

ARE NOT

4 67, …

-8 -38 -101…..

⅔ ⅓ ½

.833333333……

1.625

CAN NOT BE MADE INTO A FRACTION

DECIMAL GOES ON FOREVER WITH NO REPEATING PATTERN

><=

LESS

THAN

EQUAL

TO

GREATER THAN

=

IS EQUAL

TO

<

2

-4

IS LESS

THAN

>

2

-4

IS GREATER THAN

ONE AFTER THE OTHER

CONSECUTIVE PRIME NUMBERS

1, 3, 5, 7, 11, 13, 17, 19, 23..

ONLY TWO FACTORS

ONE AND ITSELF

3 = 1 X 3 11 = 1 X 11

5= 1 X 5 13 = 1 X 13

7= 1 X 7 17 = 1 X 17

19= 1 X 1923 = 1 X 23

NUMBERS THAT HAVE MORE THAN 2 FACTORS

UNPOPULAR

COMPOSITE NUMBERS:

THEY LOOK PRIME, BUT ARE ACTUALLY COMPOSITE!

39, 51, 57, 87, 91, 117, 119, 133, 203

5.007

FIVE AND SEVEN THOUSDANDTHS

1 ¾

ONE AND THREE FOURTHS

SKIP COUNTING

EXAMPLE: AN INTERVAL OF

.125 .25 .375 .5 .625…

SHOWS THE NUMBER OF TIMES AN EVENT OCCURS

DISPLAY, REPRESENT,

COMPARE DATA

A NUMBER LINE THAT USES “X” MARKS

TO SHOW THE FREQUENCY OF AN EVENT

X

X

X

X

X

X X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

XL

XS

M

XXL

S

L

# OF TEAM UNIFORMS

SHOW A CHANGE OF DATA OVER TIME

VERTICAL AXIS

HORIZONTAL AXIS

PARTS OF THE WHOLE 100%

REPRESENTS DATA parts AS A FRACTION, DECIMAL, OR PERCENT

.25 ¼ OR 25%

.2, 1/5, OR 20%

USES OVERLAPPING SHAPES TO SHOW HOW DATA IS RELATED

WHOLE NUMBERS FROM 1 TO 10

PRIME

NUMBERS

EVEN NUMBERS

1,3,57

4, 6, 8, 10

2

9

11, 13, 14, 15, 21, 24, 27, 27, 34, 35, 34, 36

1

1,3,4,5

1,4,7,7

2

STEMS

3

4,4,5,6

LEAF(S)

A GRAPH THAT DISPLAYS DATA FROM A STEM AND LEAF PLOT.

Groups information together!!

SHAPES, SYMBOLS OR NUMBERS THAT OCCUR IN A PREDICTABLE ORDER.

3, 9, 27, 81, 243…..

THE NUMBER THAT TELLS WHERE SOMETHING OCCURS IN A PATTERN

POSITION

1 2 3 4 5

3, 9, 27, 81, 243…..

THE ACTUAL NUMBERS IN A PATTERN OR

A PATTERN WHERE A RULESHOWS THE RELATIONSHIP BETWEEN THE POSITIONAND THE TERM

N

RULE :

3 TO THE POWER OF THE POSITION

An expression that describes the relationship between the POSITION and TERM

1 2 3 4 5

.5, 1, 1.5, 2, 2.5….

³

PEMDAS

1 2 3 LAST

WORK

LEFT TO RIGHT

WORK

LEFT TORIGHT

INSIDE PARENTHASIS

-+

÷

X

INCREASEDTIMESTRIPLEDOUBLETWICEOF

TWICE OR MULTIPLY BY 2

Divide by .5!!

TRIPLE

MULTIPLY BY 3

multiply

QUOTIENT

DECREASEDSHARED EQUALLYDIVIDEDSPLIT EVENLYCUT OFFSEPARATEDFIT INTOEACH

SUBTRACTMINUS LESSNEGATIVECUT OFFTAKE AWAYDECREASE

+

-

POSITIVE AND NEGATIVE WHOLE NUMBERS

+

1

-72

-1001

299

INTEGER EXPRESSION NUMBER LINE

1 + 3 + 3 - 8

### ABSOLUTE VALUE

-13=13

DISTANCE FROM 0

INTEGERS

MOVE ON A NUMBER LINE

1 + 3 + 3 - 8

INTEGERS

MOVE RIGHT ON A NUMBER LINE

-(-3)

+7

MOVE RIGHT 7

MOVE RIGHT 6

MOVE RIGHT 3

DOUBLE NEGATIVE!

+(6)

INTEGERS

MOVE LEFT ON A NUMBER LINE

+(-3)

-1

MOVE LEFT 9

MOVE LEFT 9

MOVE LEFT 3

-(9)

-7+(-8)

MOVE LEFT 8

### SUBTRACTING INTEGERS

7+(-8)

MOVE LEFT 8

T CHARTEVALUATING INTEGER EXPRESSIONS

14-24+2+(-12)

24

12

14

2

36

16

20 More negatives, so a negative answer

Become POSITIVE

PUNCH EM OUT!

X or ÷INTEGERS

NEGATIVES

POSITIVE

Xor÷INTEGERS

1 NEGATIVE

NEGATIVE

\$120 FOR 15 HOURS

DENOMINATOR OF 1

45 STUDENTS 18 GIRLS

GIRLS TO STUDENTS

BOYS TO GIRLS

ARE EQUAL

CONGRUENT

SAME SIZE

=

~

DIFFERENT SIZE

SAME SHAPE

SAME LOCATION

A

B

a

b

~

SAME SHAPE DIFFERENT SIZE

A

B

a

b

~

CORRESPONDING SIDES PROPORTIONAL

CORRESPONDING ANGLESCONGURENT =

~

ON A MAP, 1 CM REPRESENTS 3 KM

ACUTE ANGLESLESS THAN 90˚

89.5 ˚

50 ˚

22 ˚

OBTUSE ANGLESMORE THAN 90˚

113˚

91 ˚

RIGHT ANGLES90˚

90 ˚

90 ˚

90 ˚

STRAIGHT ANGLES180 ˚

180 ˚

31 + 59 = 90

59˚

31˚

133˚

47˚

47 + 133 = 180

ADJACENT ANGLESSHARE A VERTEX AND SIDE

VERTICAL ANGLESSHARE A VERTEXOPPOSITESARE EQUAL!

115˚

65˚

65˚

115˚

CORRESPONDING ANGLESSAME LOCATIONARE EQUAL!

75˚

75˚

CONGRUENT ANGLESARE EQUAL!

47˚

47˚

PARALLELL LINES

NEVER INTERSECT

PERPINDICULARLINES

INTERSECT TO FORM90˚ RIGHT ANLGES

A CLOSED FIGURE WITH STRAIGHT SIDES

PARALLELOGRAMS:

SQUARE, RECTANGLE, RHOMBUS

PENTAGON

HEXAGON

TRAPEZOID

TRIANGLE

DODECAGON

HEPTAGON

DECAGON

OCTAGON

4 SIDES

PARALLELOGRAM

TOP AND BOTTOM II AND

RIGHT AND LEFT II AND

OPPOSITE ANGLES

SQUARE

RHOMBUS

RECTANGLE

PARALLELOGRAM

PARALLELOGRAM

RIGHT & LEFT TOP CORNERS SUPPLEMENTARY ∠

RIGHT & LEFT BOTTOM CORNERS SUPPLEMENTARY ∠

=180°

SQUARE

RHOMBUS

RECTANGLE

PARALLELOGRAM

=180°

NOT A

PARALLELOGRAM

TRAPEZOID

TRAPEZIUM

KITE

40 ˚

140 ˚

80 ˚

100 ˚

140 ˚

40 ˚

90 ˚ + 90 ˚ + 100 ˚+80 ˚ = 360 ˚

90˚

90˚

3 SIDES

TRIANGLE

RIGHT

ISOSCELES

RIGHT

SCALENE

ACUTE

EQUILATERAL

ACUTE ACUTE

SCALENE ISOSCELES

OBTUSE

ISOSCELES

OBTUSE

SCALENE

110 ˚

40 ˚

30 ˚

110 ˚+ 40 + 30 = 180

30˚

45˚

90˚

45˚

75˚

75˚

2 = SIDES

2 = ANGLES

POLYGON ALL SIDES EQUAL

5 CM

5 CM

5 CM

REGULAR

OCTAGON

IRREGULAR

OCTAGON

5 CM

5 CM

5 CM

5 CM

5 CM

SQUARE

Parallelogram

Rectangle

Rhombus

s

s

PERIMETER = 4s

AREA = s²

s

has 4 right angles

Parallelogram

PERIMETER =2L + 2W

AREA =LWORbh

AREA =bh

2

height

base

PERIMETER

base

AREA =

(b+b)h

height

2

base

3.141592….

PI

THE CIRCUMFERENCE THE DIAMETER OF A CIRCLE

A LITTLE MORE THAN 3!

CIRCUMFERENCE

DIAMETER

CIRCUMFERENCE

DIAMETER

CIRCUMFERENCE

THE PERIMETER OF A CIRCLE

MULTIPLY PI x d

MULTIPLY PI x2r

πd

PERIMETER , DISTANCE AROUND, EDGE, RIM, FENCE, BORDER…

πr²

INSIDE SPACE, INSIDE FLAT SQUARES, COVER, OVERLAY, CARPET, FLOOR, ….

HALFWAY ACROSS A CIRCLE FROM THE CENTER

2r=d

r

Circumference ÷2π=

ALL THE WAY ACROSS A CIRCLE THROUGH THE CENTER

d

Circumference ÷π=

π

diameter

IS”

EQUALS

SIMPLIFY OR SOLVE

5(12)-4

EVALUATED IS 56

A MATH SENTENCE NO EQUAL SIGN

NUMERICAL EXPRESSIONHAS ONLY NUMBERS

EVALUATE THEM!

VARIABLE EXPRESSIONHAS NUMBERS AND VARIABLES

3X 2Y+4

VARIABLE OUT

NUMBER IN

A LETTER

REPRSENTS AN AMOUNT OR QUANTITY

MATH SENTENCE WITH = SIGN

SOLVE FOR THE VARIABLE

3X - 4 = 5

X = ????

THREE TO THE POWER OF THREE

3³=

27

THE PRODUCT OF THREE AND THREE

3(3) = 9

POWERSEXPONENTS

5

3

POWER OR

EXPONENT

= 125

BASE

3RD POWER

VOLUME of CUBE

V=SxSxS

S

S

S

2NDPOWER

AREA of SQUARE

A=SxS

S

S

AREA OF SQUARE

=

ONE SIDE LENGTH

9

3

=

3 ways

### BABY ÷REMAINDER

15

r 1

1

AS FRACTION

15

1

TEEN ÷DECIMAL

KEEP DIVIDING!

15

.

.3

3

1

.0

0

0

9

0

1

TESSELATIONS

RELFECTIONS

TRANSLATIONS

ROTATIONS

TESSELATIONS

RELFECTIONS

REFLECT

ACROSS X AXIS

X STAYS THE SAME

REFLECT

ACROSS Y AXIS

Y STAYS THE SAME

TRANSLATION

SLIDE`

ROTATION

TURN

(+X,+Y)

(-X,+Y)

POINT OF ORIGIN

START

(-X,-Y)

(+X,-Y)

(X,Y)

-LEFT OR +RIGHT FIRST

-DOWN OR +UP NEXT

LOCATION OF A COORDINATE POINT

(-4, 3)

(-X, Y)

+3

-4

X AXIS

HORIZONTAL

Y AXIS

VERTICAL

LAST DIGIT 0, 2, 4, 6, 8

LAST DIGIT 1, 3, 5, 7, 9