Need2Know: Fractions, Decimals and Percents (6.2)

*You need to be able to Identify, Convert, Compare and Order Fractions, Decimals and Percents

*Always write as a fraction first, then convert!

*Divide in your Calculator for a Decimal *Convert a Fraction to a Percent by going through the Decimal!

*Convert all to Decimals to Order or Compare! Line up Decimals! *Start looking at columns from left to right.

Need2Know: Ratios (6.1)

*The first amount goes first and the second amount goes sec-ond! The order matters!

*You can convert a ratio into a fraction, decimal or percent.

Example: John had 12 t-shirts and 4 dress shirts

1) Write the ratio of t-shirts to dress shirts. 2) Write the ratio of dress shirts to total shirts. 3) Write the ratio of dress shirts to t-shirts

*Hint* (1) Write the ratio with words first (2) Replace the words with the numbers (3) Simplify or convert to the correct format

Write the ratio of Circles to Triangles as a percent.

12 312 4 3 1 12 : 4 3:1 3.0 300%

4 1to to

4 14 16 1 4 4 :16 1: 4 .25 25%

16 4to to

4 1 14 12 1 3 4 :12 1:3 .3 33 %

12 3 3to to

26 3.75 75%

8 42

Circles

Triangles

Fraction to decimal

Divide!! Thirteen Eighths

1st 2nd *1st number goes inside *2nd number goes outside

Decimal to a Fraction

Say the proper name!

4.006

Four and 6 thousandths

Simplify!!!

26 34 41,000 5002

Percent to decimal

Convert from a percent means that you want to get away from a %. 2 circles in the % means 2 places.

*Recall that $3=$3.00 the decimal is to the right of a whole number

160%=1.6

Decimal to Percent

Convert to a percent means that you want to move towards the %. 2 circles in the % means 2 places. *The percent sign goes on the right, that is the direction you move!

.012=1.2%

Fraction Decimal Percent Picture

4 5

.8 80%

5 8

.625 62.5%

20 100

1 5

.2 20%

25 100

1 4

.25 25%

.025

1.02

1.1

.12

Smallest

2nd Biggest

Biggest

2nd Smallest

Need2Know: Identify Integers (6.3a)

*Three types of integers: (+) positive, (-) negative and (0) neutral

It is an integer ... If you start at 0 and count forward: 0, 1, 2, 3… Or if you start at 0 and count backward: 0, -1, -2, -3…

NO FRACTIONS OR DECIMALS!! Unless it can be simplified!

Integer NOT an Integer

-7 -7.3

0 1/2

3.00 = 3 π=3.14159...

-456 .2

456,005 -6.4

-6.0 = -6 12/16 = 3/4

12/4 = 3/1 = 3 - 1/2

Point A: -4 Point B: -1 Point C: 3

Need2Know: Order and Compare Integers (6.3b)

(1) Draw a number line with 0 in the center (2) Move outwards with your positive numbers to the right. (3) Move outwards with your negative numbers.

*Left to Right: Increasing, Ascending or Least to Greatest *Right to Left: Decreasing, Descending or Greatest to Least

Order: -6, 5, 0, -8, -2, 4, 1

Ascending Order: -8, -6, -2, 0, 1, 4, 5 Decreasing Order: 5, 4, 1, 0, -2, -6, -8

*Numbers get BIGGER as you move to the right* *Plot each number on the numberline and then compare*

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

7 10 5 2 0 4 10 0

Need2Know: Absolute Value (6.3c) 1. Absolute value is the distance a number is from 0 2. Absolute value can NEVER be negative 3. Opposites have the same absolute value 4. Absolute value symbols: |4| or |-5|

The point at -4 has the greatest absolute value be-cause it is furthest away from 0

The point at 1 has the smallest absolute value because it is the closest to 0

The points -3 and 3 are opposites because they have the same absolute value

|4|=4 |0|=0 |-10|=10 |-7|=|7|

-|4|= -4 -|-3|= -3 |√25|=5 |-8|=8

Need2Know: Fraction Multiplication Pictures (6.4)

Area model of Multiplication: 1) Look at the Length. Write the fraction that you see. 2) Look at the Width. Write the fraction that you see. 3) Multiply these Fractions.

There are 6 out of 20 boxes that are shaded in twice. *This is the answer!

Sometimes you see GROUPS of the same fraction.

1) Write the fraction that repeats 2) Multiply this fraction by the number of times

you see it.

2

5

3

4

3 2 6

4 5 20

3 3 4 12 24 2

5 5 1 5 5

5 5 6 30 10 16 3

9 9 1 9 3 3

Need2Know: Multiply and Divide Fractions (6.6a)

Multiplication 1. Get rid of “Road Blocks” (Mixed or whole numbers) with a

U-turn 2. Multiply across the highways (numerator & denominator) 3. Simplify. Divide the top and bottom by the same number

Try 2 (Only if even: end with 0, 2, 4, 6, 8)

Try 3 (Only if the sum of the digits is a multiple of 3)

Try 5 (Only if it ends in 0 or 5)

Try 7 (write multiples of 7) 4. Divide to convert into a Mixed Number

Make a U-turn 2x2+1=5 Multiply Simplify 5x1+3=8

Division

1. Get rid of “Road Blocks” (Mixed and Whole numbers) with a U-turn

2. KFC- Keep the first fraction, Flip the second fraction and Change to a multiplication problem

3. Multiply across the highways (numerator & denominator) 4. Simplify. Divide the top and bottom by the same number

Try 2 (Only if even: end with 0, 2, 4, 6, 8)

Try 3 (Only if the sum of the digits is a multiple of 3)

Try 5 (Only if it ends in 0 or 5)

Try 7 (write multiples of 7) 5. Divide to convert into a Mixed Number

Make a U-turn 4x2+1=9 KFC Multiply 7x1+2=9

Simplify Divide 7÷4=1R3

1 32 12 5

5 8

2 5

40

10

2 540 20 44

10 5 12 5

1 22 14 7

9 9

4 7

9 7

4 9

63

36

3 363 21 7

36 12 43 3

314

Need2Know: Fraction Division Pictures (6.4)

1) The original amount goes first

2) Look at how many sections each piece is being sepa-rated into.

3) Write as a division problem!

1) The whole amount or end amount goes first 2) How big each section is goes second

3) How many

times it fits in is your answer

Step 1

Step 2

Step 3 1 1 1 1 1

4 4 4 4 8

1 14 4 12 8

142

4

43

4153

3 14 54 3

Need2Know: Exponents (6.5)

NEVER MULTIPLY THE TWO DIFFERENT NUMBERS!! *To evaluate 45 you can: -Put it in the calculator. Press 4, yx, 5 and then = -Write it out 4 x 4 x 4 x 4 x 4 and multiply

Exponential form (Written with an

exponent)

Expanded form (Written as a

product of factors)

Standard form (Written as a nor-

mal number)

30 1 1

31 3 3

32 3 x 3 9

33 3 x 3 x 3 27

34 3 x 3 x 3 x 3 81

53 5 x 5 x 5 125

64 6 x 6 x 6 x 6 1,296

Need2Know: Square Roots (7.1d)

You need to know all perfect squares up to 400

*To test for a per-

fect square, take

the square root of

the number. If it

has a “perfect”

root then it is a

“perfect” square.

*You could also

write the num-

bers 1-20 and

square each num-

ber to create the

table to the right.

*You probably

won’t have a cal-

culator for these

problems

Perfect squares can be shown as squares too!

Area-Perfect squares Length x width– Roots

1 x 1 = 1

5 x 5 = 25

2 x 2 = 4

3 x 3 = 9

6 x 6 = 36

4 x 4 = 16

root Squaring Taking the

square root

Perfect

Square

1 12=1 1

2 22=4 4

3 32=9 9

4 42=16 16

5 52=25 25

6 62=36 36

7 72=49 49

8 82=64 64

9 92=81 81

10 102=100 100

11 112=121 121

12 122=144 144

13 132=169 169

14 142=196 196

15 152=225 225

16 162=256 256

17 172=289 289

18 182=324 324

19 192=361 361

20 202=400 400

1 1

4 2

9 3

16 4

25 5

36 6

49 7

64 8

81 9

100 10

121 11

144 12

169 13

196 14

225 15

256 16

289 17

324 18

361 19

400 20

Need2Know: Fraction/Decimal Word Problems (6.6b & 6.7)

ADDITION-

Are you putting two groups together?

SUBTRACTION- Are you taking something away from a group?

Are you finding the difference between two groups? *The total always comes first in the problem!

MULTIPLICATION- Do you have multiple groups of a fraction?

Do you have a fractional portion OF something? Are you adding the same amount multiple times?

DIVISION- Are you taking away the same amount each time?

Are you SEPERATING into a number of groups? Are you SEPERATING something into a certain sized group? *The total always comes first in the problem!

READ TABLES CAREFULLY!!

Need2Know: Order of Operations (6.8)

P E M D A S Always move from left to right in the problem. With a fraction, use PEMDAS on the numerator, then use PEMDAS on the de-nominator. Once there is only a number on the bottom and on the top, then you should simplify your answer.

3

3

3

2 (24 4 3)

2 (6 3)

2 (18)

8 (18)

26

2 2 2 2 2

17 12 15 5 15 20 20 20 20

(8 4 5) (8 4 5) 100( 8 4 5) ( 2 5 ) 10

2 2 520 10 5 1

100 50 25 52 2 5

0

0

0

0

( 8 4 3 2)

(2 3 2 )

( 2 6 )

(8)

1

6 3 2 5( 4 3 )

6 3 2 5(7)

2 2 5 (7)

2 10(7)

2 70

72

Need2Know: Measurement (6.9)

–1 inch is about 2.5 centimeters. –1 foot is about 30 centimeters. –1 meter is a little longer than a yard, or about 40 inches. –1 mile is slightly farther than 1.5 kilometers. –1 kilometer is slightly farther than half a mile. –1 ounce is about 28 grams. –1 nickel has the mass of about 5 grams. –1 kilogram is a little more than 2 pounds. –1 quart is a little less than 1 liter. –1 liter is a little more than 1 quart. –Water freezes at 0°C and 32°F. –Water boils at 100°C and 212°F. –Normal body temperature is about 37°C and 98°F. –Room temperature is about 20°C and 70°F

Need2Know: pi (6.10a)

Pi is the ratio:

of a Circle’s CIRCUMFERENCE to its DIAMETER

*It is NOT the other way around! Remember that the order matters in math! Especially ratios!

If the Circumference is about 25.12 in. And the Diameter is about 8 in.

Then Circumference ÷ Diameter=pi 25.12 ÷ 8 = 3.14 = π

Circumference

Diameter

Need2Know: Circles (6.10) *USE THE FORMULA SHEET!!* *Use order of operations* *Use a calculator*

If I want to find the distance AROUND a circular object I would use CIRCUMFERENCE —C=2πr— Use only when given the radius or the distance HALFWAY across the circle —C=πd— Use only when given the diameter or the distance ACROSS the circle If I want to COVER a circular object, then I want to use AREA —A=πr2— ONLY use the radius here. If given the diameter, take half to find the radius

Replace π with 3.14 Replace r with the radius Replace d with the diameter

Need2Know: Volume, Surface Area (6.10d) Draw the figure, label the figure, Measurement (Cover-Surface Area; Fill-Volume), Formula, Substitute, Solve. *Use order of Operations once you plug in all values Replace l with the length Replace w with the width Replace h with the height L=4 ft w=3 ft h=5 ft

Volume of a

Rectangular Prism

Surface Area of a

Rectangular Prism

V=Lwh S.A.=2Lw+2Lh+2wh

V=4•3•5 S.A.=2•4•3+2•4•5+2•3•5

V=12•5 S.A.=24+40+30

V=60 ft3 S.A.=94 ft2

Need2Know: Circumference, Area and Perimeter (6.10bc)

What type of shape is it? You will look at the formulas under this shape

Are you going to be COVERING or going AROUND the shape?

COVERING—Use the A= formula under the correct shape

AROUND—Use C= for Circles and P= for other shapes P=add all sides for EVERY shape!

Plug in the correct values

b is the base of a Triangle h is the height of a triangle s is the side of a square l is the length of a rectangle w is the width of a rectangle r is the radius of a circle d is the diameter of the circle π is 3.14

Sides-15cm, 15cm, 12 cm Height-13cm Base-12cm *Don’t forget 1/2 in the Area formula!!

Length-14 in. Width-8 in. *A SQUARE is a type of rectangle, so this formula also works for a square!

Radius-6 m. Diameter– 12 m.

π-ALWAYS 3.14

*Pi doesn’t change with the size of the circle!

Area of the Triangle

Perimeter Of the Triangle

A= 1/2 bh P=add all sides

A=1/2•12•13 P=15+15+12

A=1/2•156 P=30+12

A=78 cm2 P=42 cm

Area of the Rectangle

Perimeter Of the Rectangle

A= lw P= 2l+2w

A=14•8 P=2•14+2•8

A=112 in2 P=28+16

P=44 in

Area of the Circle

Circumference

Of the Circle Circumference

Of the Circle

A=πr2 C=πd C=2πr

A=3.14•62 C=3.14•12 C=2•3.14•6

A=3.14•36 C=37.68 C=6.28•6

A=113.04 m2 C=37.68 m. C=37.68 m.

Need2Know: Coordinate Plane (6.11)

*You need to be able to Identify the coordinates of a point *Plot a point on the Coordinate Plane from an ordered pair

*Helpful Hints* **The first coordinate (number) is the x-coordinate and refers to the x-axis (horizontal numberline)

**The second coordinate (number) is the y-coordinate and re-fers to the y-axis (vertical numberline)

** Draw a line from the point to the x-axis and the y-axis to see what the coordinates are. USE THE LINE TOOL!!

**On the SOL, you need to answer every question with the curser/pointer tool. DO NOT plot a point with the “point” tool

**The Quadrants go around in a “C” shape Quadrant I-top right Quadrant II-top left

Quadrant III-bottom left Quadrant IV-bottom right

Point A (-3, 4)

Point B (6, 5)

Point C (-5, -4)

Point D (5 , -2)

Point E (0, -6) x=0,

so plot y=-6 on the y-axis

Point F (3, 0)

y=0, so plot x=3

on the x-axis

Need2Know: Congruence (6.12)

**Congruent angles have the same measurement in degrees **Congruent line segments have the same length **Congruent shapes are the same shape and size. All corresponding angles and lines are the same measurement.

These two shapes are CONGRUENT. I can flip one to land on the other and match up perfectly!

These two shapes are NOT congruent. All of the angles match up, but the

sides are not the same in both shapes.

These angles are CONGRUENT. They both measure to 60°. Even though the lines are longer, the angles are the same! Turn them around and you can place them on top of each other.

Trapezoid ABCD is congruent to Trapezoid EFGH. This means that all COORESPONDING (matching) parts are congruent.

Congruent angles Congruent Segments A E

B F

C G

D H

AB EF

BC FG

CD GH

DA HE

Need2Know: Quadrilaterals (6.13)

Quadrilateral-Must be a 4-sided Polygon

Parallelogram- 2 pairs of parallel sides

Trapezoid- 1 pair of

Parallel sides

Rectangle- 4 congruent right angles

Rhombus-

4 congruent sides

Square-

4 right angles

AND 4 congruent sides

Kite-

0 pairs of parallel sides AND

2 pairs of congruent adjacent sides

Isosceles Trapezoid-

Congruent Legs

Need2Know: Probability (6.16a)

Independent Events: —Independent events-When the first event DOESN’T effect the probability of the second event occurring

If I spin a spinner, that doesn’t effect what I can roll on a die

If I choose a card at random and put it back, then the total possible cards that I can choose from next didn’t change.

If I draw from bag A and then I draw from bag B, then the two bags are separate and don’t effect each other

If I choose a card at random and put it back, then the total possible cards that I can choose from next didn’t change.

Dependent Events: —Dependent events-When the first event DOES effect the probability of the second event occurring.

If I choose a card at random without putting it back, then the total possible cards that I can choose from next changed.

If I select 2 items from bag A, that implies that I did not put back the first item. This means that you can-not choose that item for your second selection.

Need2Know: Circle Graphs (6.14ab)

**A Circle Graph shows the fraction or the part of the whole for each category. **Find the total of all categories this is your denominator **The category total is your numerator.

You should be able to answer different questions about circle graphs

**The KEY is important**

(1) What type of shirt does Joey have the most of?

Striped Shirts

(2) What type of shirt does Joey have the least of?

White Shirts

(3) If Joey had the same fractions of shirts, but had 80 total shirts how many Striped, White, Checkered and Grey shirts would he have?

Striped-40 White-8 Checkered-16 Grey-16

(4) What two categories could be combined to make up 30% of Joey’s shirts?

Grey and White or Checkered and White

(5) Half of Joey’s Striped shirts have collars. What fraction out of all of Joey’s shirts is this?

1/4

20 5 1

40 10 2

4 1

40 10

8 2 1

40 10 5

Pattern Number

of shirts Fraction Decimal Percent

Striped 20 .5 50%

White 4 .1 10%

Grey 8 .2 20%

Checkered 8 .2 20%

Total=40

8 2 1

40 10 5

Need2Know: Arithmetic and Geometric Sequences

Be able to identify the common difference/ratio, extend the

pattern.

Geometric-Common ratio (x) Arithmetic-Common Difference(+)

Sequence Ratio/difference Type Next term

80, 20, 5, 1.25... Ratio x 1/4 (÷4) Geometric .3125

1, 5, 25, 125, 625... Ratio x 5 Geometric 3,125

3, 6, 9, 12, 15… Diff. +3 Arithmetic 18

54, 53.5, 53, 52.5... Diff. +(-.5) Arithmetic 52

Need2Know: Scientific Notation

Format: _ . _ _ _ _ x 10#

Exponent: # of spaces moved NOT the # of zeros!!

*Hint* use order of operations to figure it out in your calculator!

Evaluate the exponent and then multiply

Standard Form Spaces Scientific Notation

24,500,000 7 spaces

2.45 x 107

6,502,000,000 9 spaces 6.502 x 109

Need2Know: Properties

The Additive and Multiplicative Identity Properties *What could you do to a number where the IDENTITY of that number does not change? With addition, you can add 0 if you don’t want to change a number. With multiplica-tion, you can multiply by 1 if you don’t want to change a number.

*0 is the Additive Identity element *1 is the Multiplicative Identity element

5+0=5 or 0+5=5 5•1=5 or 1•5=5

The Multiplicative Inverse Properties *What could you add or multiply together to get the Identity elements?

(2/3)•(3/2)=1 (1 is the Multiplicative Identity Element)

Multiplicative Property of Zero *When you multiply by zero, you get zero

6•0=0 0•5=0 1039457•0=0

Need2Know: All Graphs (6.16c) LOOK AT THE KEY!!!!

The key is used to figure out how many of each type, then we transfer this to the bar graph.

3x4=12 12 Golden Retrievers 1x4=4 4 Beagles 4x4=16 16 Mutts 1.5x4=6 6 Labradors 2x4=8 8 Great Danes

Need2Know: Equations **Always do the OPPOSITE operation for the first step!!

Look at a key to determine what equation is being represented:

4 groups of x = 12 groups of 2 4(x)= 12(2) 4x=24

1 group of t and 3 groups of 1 on the left

t+3

15 groups of 1 on the right

15

Answer B: t+3=15

2x=8 3+x=9 x/5 =10 x-8=12

x is being multiplied by 2

3 is being add-ed to x

X is being divided by 5

8 is being sub-tracted from x

First step: Divide BOTH

sides by 2

First step: Subtract 3 from BOTH

sides

First step: Multiply

BOTH sides by 5

First step: Add 8 to

BOTH sides

x=4 x=6 x=50 X=20

Need2Know: Balance Point **Write numbers on the number line and find the mean

To find the mean, add up all the numbers and divide by the total amount of numbers.

**OR you can move each of the pieces in towards the middle. ONLY move one right for every left move.

1+1+1+5+7=15 (sum of all numbers)

5 (total numbers) 15/5=3 (mean of the numbers)

OR we can show our moves