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DECIMAL Divide the numerator by the denominator . When there is nothing left to bring down, add a decimal and zero. 0.125 8 1.000 -8 20 -16 40 -40
PERCENTAGE
PERCENTAGE
Convert to
1. Divide numerator by denominator 0 .125 8
1.000
2. Multiply answer by 100 and add a percent sign
0.175 x 100 = 12.5%
Fraction
Or “SHWOOPIE” move the decimal two places to the right
FRACTION
Convert to
1.
Multiply by 100 and add a percent sign
Remove decimal point and write the number as the numerator. .125
2. The denominator is a multiple of 10, depending on the place value of the last digit
or “SWOOPIE” move the decimal two places to the right
1000 3. Write the fraction and reduce to the lowest terms
FRACTION 1.
125 1000
= 25 = 200
1 8
Divide the percentage by 100 and drop the percent sign.
12.5% = .125 Or SHWOOPIE two steps to the left 2.
Decimal
DECIMAL
Convert to 1.
Write the decimal as a fraction and reduce it to lowest terms
Divide the percentage by 100 and drop the percent sign. 12.5% = .125
Or “Swoopie” two decimal places to the left
125 = 1 1000 8
Percentage
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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 0.2 5 1.0 0 10 10 0
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 %
0.375 8 3.000 0 30 24 60 56 40 40 0
0.11111 9 1.00000 -0 10 - 9 10 -9 10 -9 1
To turn a PERCENT into a DECIMAL, move the DECIMAL two times to the LEFT. EXAMPLES: 50% = 0.50
0.124 = 12.4 %
6% = 0.06
1.34 = 134 %
200% = 2.00
To write a DECIMAL as a FRACTION write the number over its place value. EXAMPLES: 0.23 = 23 0.7 = 7 100 10
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
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DECIMAL METHOD: Change the PERCENT into a DECIMAL and then MULTIPLY!
EXAMPLE: 46% of 120 Change the PERCENT into a DECIMAL
PROPORTION STRATEGY: Part = Percent Whole 100 EXAMPLE 46% of 120 X = 46 Write a PROPORTION. 120 100
46% = 0.46
120
Multiply (“of” means multiply in some cases)
x 0.46
720 +4800 5520
Cross Multiply and Divide
100x = 5520 ÷100 ÷100 X = 55.20
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 20 100 EXAMPLE:
x 48 x 48 = 960 =9 60 = 9 3 1
100
100
5
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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 taxes?
STEP 1: Find TAX 6% = 0.06 12.00 x 0.06 Turn the percent .7200 into a decimal STEP 2: Add TAX 12.00 Original price + 0.72 + Tax $12.72 TOTAL
There are four decimal places 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.
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 Change the PERCENT into a DECIMAL Multiply (“of” means multiply in some cases)
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
20% of 45 45 X0.20 000 +900 900
Find the DISCOUNT first
$9.00
Then subtract the discount from the original price
45 X0.20 000 Discount +900 = $9.00 900 $45 - 9 $36
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KILO Kangaroos
HECTO HOP DEKA DOWN BASE BANKS
DECI DRINKING
CENTI To convert move the decimal in the direction CHOCOLATE of the step you are moving to. MILLI For example: MILK To change Meters to Centimeters move the decimal to the right 2 times.
CUSTOMARY SYSTEM: 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.
X = 10 pts
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 = 30 yds
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
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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”
Similar Figures: Figures that are the same shape, but not always the same size The ratio of corresponding sides must be equal for the rectangles to be similar.
80 cm
80 cm = 30 cm 16 cm 6 cm
CONGRUENT: Same shape, Same size
3 = x 6 10
NOT SIMILAR:
Example: Scale factor 6=2 3 The triangles at right have a scale factor of 2, because the corresponding sides are 6 and 3. 6 ÷ 3 = 2. The larger triangle is 2 times the size of the smaller triangle.
Step 1: Write a Proportion using corresponding parts (2nd Shape to 1st shape) Step 2: Cross Multiply and Divide to find the missing side
6x 6ft
The missing side is 5 ft.
The scale factor for the two triangles is 2, because 6 ÷ 3 = 2. So divide the side that corresponds 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
25 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 represents 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 50 real
18 model x real
Use x to represent the length of the real building because this is the unknown value, or what we are solving to find!
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 3 miles
x in 4.5 miles
4.5 = 3x 3 3 1.5 = x
The distance on the map will be 1.5 inches.
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Proportion- an equation that states that two ratios are EQUIVALENT EXAMPLE:
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!
X3
X3
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:
9 6 = 18 n
n 3
9 6 = 18 n
n 27 = 3 9
18 x 6 = 9 n 108 = 9n 9 9 12 = n
27 x 3 = 9 n 81 = 9n 9 9 9=n
=
ANOTHER WAY IS TO LOOK FOR THE CONSTANT!
27 9
3 4
=
n 16
X4
3 4
X4
= X4
n 16
You can multiply 4 times 4 to get 16. So multiply 4 times 3 to get n = 12!
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 proportional 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 exchange rate is 8 Tala for $2. How many Tala would she get if she exchanged $6?
Tala Tala = $ $ 8= $2
x $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.
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Coordinate plane- an area defined by the X AXIS and the Y AXIS. Points are plotted using coordinates from the ORIGIN.
Using formulas to graph equations in the form y = kx will help you see a relationship between two variables. EXAMPLE: Graph the equation y = 7 x 2
The point (2,3) is OVER 2 and UP 3 from the ORIGIN. x
7 2
far w ) ho wn lls do T e (o r up
w ho lls er Te r ov fa
X
Y
1
3.5
2
7
3
10.5
4
14
0
0
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”
CONSTANT: to find DIVIDE y ÷ x
EXAMPLE: The equation below can be used to determine how many boys, y, are in a class that has x girls. 5 y= x 6 If there are 12 girls in the class, how many boys are in the class? A. 8 B. 10 C. 12 D. 18
y= boys
5 x 6
5 y = 6 • 12 60 y= 6 y = 10 boys
girls
STEP 1: Label variables STEP 2: Plug in what you know STEP 3: Solve STEP 4: Check answer.
