Divide the numerator by the

denominator . When there is

nothing left to bring down, add a

decimal and zero.

Multiply by 100 and add a percent

sign

or

“SWOOPIE” move the decimal

two places to the right

Convert to

Convert to

Convert to

DECIMAL PERCENTAGE

PERCENTAGE

DECIMAL

FRACTION

FRACTION

Fraction

Decimal

Percentage

1. Divide numerator

by denominator

2. Multiply answer by 100 and

add a percent sign

1. Remove decimal point and

write the number as the nu-

merator.

.125

2. The denominator is a multiple

of 10, depending on the place val-

ue of the last digit

1000

3. Write the fraction and reduce to

the lowest terms

125 = 25 = 1

1000 200 8

0 .125

8 1.000

0.125

8 1.000

-8

20

-16

40

-40

0.175 x 100 = 12.5% Or “SHWOOPIE” move the dec-

imal two places to the right

1. Divide the percentage by 100

and drop the percent sign.

12.5% = .125

Or

SHWOOPIE two steps to the left

2. Write the decimal as a fraction

and reduce it to lowest terms

125 = 1

1000 8

1. Divide the percentage by 100

and drop the percent sign.

12.5% = .125

Or “Swoopie” two decimal places

to the left

14

To turn a FRACTION into

a DECIMAL, DIVIDE.

Which number goes in the

house? NUMERATOR

No REMAINDERS.

When you have nothing to

bring down, add a

DECIMAL and a ZERO!

FRACTION TO DECIMAL EXAMPLES:

1 3 1

5 8 9

To write a FRACTION as a PERCENT, first turn it into a

decimal, then move the decimal 2 times to the right.

To turn a DECIMAL into a PERCENT,

move the DECIMAL two times to the

RIGHT.

EXAMPLES:

O.72 = 72 %

0.124 = 12.4 %

1.34 = 134 %

To write a DECIMAL as a FRACTION

write the number over its place value.

EXAMPLES:

0.23 = 23 0.7 = 7

100 10

To turn a PERCENT into a DECIMAL,

move the DECIMAL two times to the

LEFT.

EXAMPLES:

50% = 0.50

6% = 0.06

200% = 2.00

To write a PERCENT as a FRACTION

write it over 100, because percent

means “out of 100.”

EXAMPLES:

26% = 26 13 5% = 5 1

100 50 100 20

0.2

5 1.0

0

1 0

1 0

0

0.375

8 3.000

0

3 0

2 4

60

56

40

40

0

0.11111

9 1.00000

-0

1 0

- 9

10

- 9

10

- 9

1

= =

15

PROPORTION STRATEGY:

Part = Percent

Whole 100

EXAMPLE 46% of 120

X = 46

120 100

100x = 5520

÷100 ÷100

X = 55.20

Write a

PROPORTION.

Cross Multiply

and Divide

DECIMAL METHOD:

Change the PERCENT into a DECIMAL and

then MULTIPLY!

EXAMPLE: 46% of 120

46% = 0.46

120

x 0.46

720

+4800

5520

Change the

PERCENT into

a DECIMAL

Multiply (“of”

means multiply

in some cases)

Don’t forget

to

SHWOOP-

10% STRATEGY: To find 71% of $80, first start by

finding what 10% would be.

10% of $80 is $8

Move the decimal one place to the left to find 10% or divide by 10.

1% of $80 would be 0.8

Move the decimal two places to the left to find 1% or divide by 100.

If 10% is $8, then 70% would be $56

(THINK: 7 times 8 = 56) 71% would be $56 + $0.80 or $56.80

(70% + 1% = 71%) EXAMPLE:

To find 25% of $48…

10% of 48 is 4.8

20% of 48 is 9.6 (THINK: 2 times 4.8)

5% of 48 is 2.4 (THINK: half of 4.8)

25% of 48 is 12 (THINK: 9.6 + 2.4)

20% + 5%

TO FIND 10%, DIVIDE BY 10 (OR MOVE THE DECIMAL ONE PLACE TO THE LEFT!)

FRACTION STRATEGY:

STEP 1: Write the percent as a

fraction.

20% of 48 20

100

STEP 2: Multiply and simplify! 20

100

20 48 960 60 3

100 1 100 100 5

EXAMPLE:

x 48

x = =9 = 9

16

FINDING DISCOUNT (using decimal method):

A shirt which regularly cost $45.00 is

on sale for 20% off. What is the

discount?

20% of $45

20% of 45

45

X0.20

000

+900

900 $9.00

Change the

PERCENT into

a DECIMAL

Multiply (“of”

means multiply

in some cases) Discount

= $9.00

FINDING SALES PRICE (using decimal

method):

A shirt which regularly cost

$45.00 is on sale for 20% off.

What is the sales price?

20% of 45

45

X0.20

000

+900

900

$45

- 9

$36

Find the

DISCOUNT

first

Then subtract

the discount

from the

original price

In Georgia, we have a 6% sales tax. You

want to buy a shirt that costs $12.00.

How much does the shirt cost after tax-

es?

STEP 1: Find TAX

6% = 0.06 12.00

x 0.06

.7200

STEP 2: Add TAX

12.00 Original price

+ 0.72 + Tax $12.72 TOTAL

Turn the percent into a decimal

There are four decimal plac-

es in your problem, so the tax is 72

cents!

COMMISSION:

Cinthia earns 20% commission on her sales.

In February, she sold $380 in merchandise.

How much did Cinthia make in commission in

February?

$380 x 0.20 = $76.00

She earned $76 in commission.

INTEREST:

Alberto’s savings account earns 3% interest

ever month. If Alberto puts $45.00 in his

bank account at the beginning of the month,

how much does he make in interest by the

end of the month?

$45.00 x 0.03 = $1.35

Alberto earns $1.35 in interest.

17

KILO Kangaroos

HECTO HOP

DEKA DOWN

BASE BANKS DECI

DRINKING

CENTI CHOCOLATE

MILLI MILK

CUSTOMARY SYSTEM:

LENGTH:

1 foot = 12 inches 1 yard = 3 feet 1 mile = 5,280 feet

WEIGHT:

1 ton = 2,000 lbs. 1 lb. = 16 oz.

CAPACITY (VOLUME):

1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts

METRIC SYSTEM:

LENGTH:

1,000 mm = 1 m 100 cm = 1 m 1,000 m = 1 km

WEIGHT:

1,000 mg = 1 g 1,000 g = 1 kg

CAPACITY (VOLUME):

1,000 mL = 1 L

To convert move the decimal in the direction of the step you are moving to. For example: To change Meters to Centimeters move the decimal to the right 2 times.

1) Write a ratio using the question.

2) Write the units by the ratio.

3) Write the ratio of the conversion.

4) Solve the proportion by cross multiplying, then dividing.

EXAMPLE: How many inches are in 12 feet?

X in 12 ft

X in = 12 in

12 ft 1 ft 1x = 144 1 1 X = 144

X = 10 pts X = 30 yds

23

Scale factor: The ratio of corresponding sides for a pair of similar figures. Corresponding sides: Sides that have the same relative position on similar figures. Sides that “match” Example: Scale factor 6 = 2 3

The triangles at right

have a scale factor of 2, because the correspond-

ing sides are 6 and 3. 6

÷ 3 = 2. The larger tri-angle is 2 times the size

of the smaller triangle.

Similar Figures: Figures that are the same shape, but not always the same size

CONGRUENT: Same shape, Same size

The ratio of corresponding sides must be equal for the rectangles to be similar. 80 cm 30 cm 16 cm 6 cm

80 cm

=

NOT SIMILAR:

Step 1: Write a Proportion using

corresponding parts

(2nd Shape to 1st shape)

Step 2: Cross Multiply and Divide

to find the missing side

3 x

=

10 6

The missing side is 5 ft.

The scale factor for the two tri-angles is 2, because 6 ÷ 3 = 2. So divide the side that corre-sponds to x, 10 ft, by 2. The missing side is 5 ft!

÷2

Sometimes the corresponding sides

are rotated.

3 in corresponds to 6 in cdfdffdfsdfds

5 in corresponds to

10 in cdfdffdfsdfds

4 in corresponds to n in cdfdffdfsdfds

6x 6ft

24

Scale Drawings- Drawings that represent real objects or places and are drawn to proportion

Identify the drawing/model length and actual length.

Write a ratio of the model over the drawing/model length to the actual length.

EXAMPLE: The length of a car measures 240 inches. The length of the drawing is 12 inches. What is the scale factor of the drawing?

= = ÷12

9÷ 12

The scale factor for the drawing of the car is 1:20, or one inch on the drawing repre-sents 20 inches on the real car.

Identify the scale.

Set up a proportion with the scale on the left and the problem on the right. Set it up each ratio

with the model or drawing to the real lengths.

EXAMPLE:

Avery has a model of a building for his architecture class. The model is 18 inches high. The scale factor of the model is 1:50. How many inches tall is the building that the model represents?

1 model 18 model

50 real x real 18 x 50 = 1x

900 = 1x

900 = x

The real building will be 900 inches.

Identify

the scale.

Set up a proportion with the scale on the left and the problem on the right. Set it up each ratio

with the model or drawing to the real lengths.

EXAMPLE:

Max is making a map of his hometown. The scale for the map will be 1 in on the map represents 3 miles. The distance between his house and his school is 4.5 miles. How far apart will Max need to draw his house and his school on the map?

1 in x in 4.5 = 3x The distance on the

3 miles 4.5 miles 3 3 map will be 1.5 inches.

1.5 = x

25

Use x to represent the length of the real build-ing because this is the unknown value, or what we are solving to find!

Proportion- an equation that states that two ratios are EQUIVALENT

EXAMPLE:

When one of the four numbers in a proportion is unknown, cross products may be used to find the

unknown number. Question marks or letters are frequently used in place of the unknown number.

To SOLVE a PROPORTION with an unknown, CROSS MULTIPLY and DIVIDE!

EXAMPLES:

We know these ratios are equal because 3 x 3 = 9 and 8 x 3 = 24. The numerator and denominator are both multiplied by

3. 3 is the CONSTANT

OF PROPORTIONALITY!

X 3

X 3

9 6

18 n=

9 6

18 n

=

18 x 6 = 9 n

108 = 9n

9 9

12 = n

n 27

3 9 =

n 27

3 9=

27 x 3 = 9 n

81 = 9n

9 9

9 = n

ANOTHER WAY IS TO LOOK FOR THE CONSTANT!

3 n

4 16 =

X 4

3 n

4 16 =

X 4

X 4

n = 12

You can multiply 4 times 4 to get 16. So multiply 4 times 3 to get n = 12!

When you are given the value of two items which are related and then asked to figure out what

will be the value of one of the item if the value of the other item changes, you have a propor-

tional relationship!

It is helpful to set up the ratios in words before using numbers so that you are consistent.

Ming was planning a trip to Western Samoa. Before going, she did some research and learned that the ex-change rate is 8 Tala for $2. How many Tala would she get if she exchanged $6?

Tala Tala

$ $

8 x

$2 $6

48 = 2x

24 = x

She will get 24 Tala.

=

STEP 1: Underline keywords

STEP 2: Set up ratios in WORDS.

STEP 3: Plug in numbers.

(“how many” is

represented by x)

STEP 4: Solve proportion

STEP 5: Check answer.

=

26

Coordinate plane- an area defined by the X AXIS

and the Y AXIS. Points are plotted using coordinates

from the ORIGIN.

Tells how

far over

Tells how

far

up (or down)

Using formulas to graph equations in the form

y = kx will help you see a relationship between

two variables.

EXAMPLE: Graph the equation y = x

The point (2,3) is

OVER 2 and UP 3

from the

ORIGIN.

Direct Proportion: The relation between two quantities whose ratio remains

constant. When one variable increases the other increases proportionally:

When one variable doubles the other doubles, when one variable triples the

other triples, and so on. When A changes by some factor, then B changes by

the same factor: A=kB, where k is the constant of proportionality.

Constant of Proportionality: In a proportional relationship, y=kx, k is the constant of

proportionality, which is the value of the ratio between y and x. “MULTIPLIER”

EXAMPLE:

CONSTANT:

to find

DIVIDE y ÷ x

The equation below can be used to determine how many

boys, y, are in a class that has x girls.

y = x

If there are 12 girls in the class, how many boys are in

the class?

A. 8 B. 10 C. 12 D. 18

5

6

y = x

y = • 12

y =

y = 10 boys

5

6

girls boys 5

6 60

6

STEP 1: Label

variables

STEP 2: Plug in

what you

know

STEP 3: Solve

STEP 4: Check

answer.

7

2

X Y

1 3.5

2 7

3 10.5

4 14

0 0

x

7

2

27