Fractions, Decimals and Percent

Formula for Percent Change

Change in Value/Original Value

50% of 10% of a number is what percent of that number? A.1% B. 5% C. 10%

Choose 100 instead of "number". 100 is good for percent questions. (For fractions, choose a common denominator of the fractions given in the problem) 1. 50% of 10% of 100 is what percent of 100. 2. Solve. 50% of 100 is 50. 10% of 50 is 5. 3. Correct answer is B

0.8 x 0.5

If the product ends with 0. that 0 still counts as a place value. 8x5=40 40 and move the decimal 2 places to the left. = 0.40

What number is 62.5% of 192?

If you simply recognize that 62.5%= 0.625= 5/8: 5/8 x 192= 5/1 x 24 = 120

Express the following as percents: 80.4, 0.0007

To convert a decimal to a percent, shift the decimal point two places to the right. 80.4= 8,040% 0.0007= 0.07%

"Of" can be referred as:

multiply or x

"What" can be referred as:

unknown value or (x, y, any variable)

What is 37.5% of 240?

Recognize that 0.375 = 3/8 (3/8)(240)= 3(30)=90

1/50

0.02 or 2%

1/25

0.04 or 4%

1/20

0.05 or 5%

1/9

0.111 or 11.1%

1/8

0.125 or 12.5%

1/6

0.167 or 16.7%

1/3= 2/6

0.333 or 33.3%

3/8

0.375 or 37.5%

5/8

0.625 or 62.5%

2/3=4/6

0.6666 or 66.7%

5/6

0.833 or 83.3%

7/8

0.875 or 87.5%

If a ticket increased in price by 20%, and then increased again by 5%, by what percent did the ticket price increase in total?

1. Answer is NOT 25% 2. Walk through this with real numbers. If the ticket originally cost $100, then the first increase would bring the ticket price up to 100 plus 20% of 100 for a total of $120. 3. The second increase of 5% is now based on the new ticket price of $120 4. 120 + (0.05)(120)= $126 5. The plan increased by 26% (126 is 26 more than the original 100

When Karen bought a new television, originally priced at $700, she used a coupon for a 12% discount. What price did she pay for the TV? A. $630 B. $616 C. $560

1. Because 10% of 700 is 70, you know Karen receieved something more than a $70 discount. She must have paid a bit less than $630 so A cannot be correct. 2. A 20% discount would have resulted in another 70% off, for a total $140 discount, or $560. C would be too small. Therefore, B is the answer.

0.02 x 1.4

1. Count the degits to the right of the decimal- 3 2. Multiply normally- 14 x 2= 28 3. Move the decimal 3 places to the left. 28= 0.028

Steps for Problem Solving/Data Sufficiency

1. Glance, Read, Jot. (If numbers are far apart, you can estimate. 2. Reflect, Organize 3. Work

0.0003 x 40,000

1. If you are multiplying a very large number and a very small number, move the decimals he same number of places, but in the opposite direction! 2. Move the decimal point right 4 places on the 0.0003 = 3 3. Move the decimal point left 4 places on the 40,000=4 4. 0.0003 x 40,000= 3x4=12

0.0045/0.09

1. Move the decimal 4 spaces to the right to make both the numerator and the denominator whole numbers. 2. 45/900

12.42/0.3

1. Move the decimal one space to the right to make 0.3 a whole number. 2. Then, move the decimal one space to the right in 12.42 to make it 124.2 3. 124.2/3= 41.4

Strategy: Estimation Ex: 7/13+5/11 is approximately equal to a. 0 B.1 C. 2

1. Round fractions up to easier ones. Make sure if you go up on one fraction, you go less on the other. 2. 7/14+5/10= 0.5+0.5=1.

Of 450 employees at a company, 20% are managers are the rest are not managers. If 60% of the managers work in the engineering department, how many managers do not work in the engineering department? a. 36 b. 54 C. 90

1. The qustion asks for the number of managers who do not work in engineering. First, find the number of managers, which is 20% of 450: 10% of 450 is 45, so 20% is twice as much, or 90. 2. There are 90 managers total, so C cannot be the answer. Further, if 60% of those managers work in engineering, then 40% or less than hald do not. Half of 90 is 45 so the numbers of managers not in engineering must be less than 45. 3. only possible answer is A. 36

30 is what percent of 50?

1. Translate the question into an equation. 2. 30= x/100 x 50 30= x/100 x50 30= x/2 x=60

What is 70 percent of 120?

1. Translate the question into equation. 2. x=70/100x120 x= 7/10 x 120= 84

Step 1 when testing cases. (Data Sufficiency)

1. What possible cases are allowed? -Before you start solving, make sure you know what restrictions have been placed on the basic problem in the question stem. You may be told to use the 10 digits, or that the particular number is positive, or odd, and so on. Follow these restrictions when choosing numbers to try later in your work.

Quick Calculations with Percents

1. You can calculate most percentages quickly using a combination of 50%, 10%, 5% and 1% of the original number. 2. Ex: what is 70% of 120 3. Split 70% into 50%, 10% and 10% 4. Calculate 50%, 10%, 10% of 120. 5. 60+12+12=84

In the decimal, 2.4d7, d represents a digit from 0 to 9. If the value of the decimal rounded to the nearest tenth is less than 2.5, what are the possible values of d?

1. { 0, 1, 2, 3, 4)

4/3

1.33 or 133%

7/4

1.75 or 175%

10% increase and 10% greater than means:

110% of the original. Always think of the original number as 100%

2.57 x 10^6 and 14.29 /10^5

2,570,000 Add 4 Zeroes at the end. 0.0001429 Add 3 zeroes at the beginning

Step 2 when testing cases

2. Choose numbers that work for the statement. - Pause for a moment to remind yourself that you are only allowed to choose numbers for each statement that make the particular statement true. With enough practice, this will begin to become second nature. If you answer a Testing case problem incorrectly but aren't sure why, see whether you accidently tested cases that weren't allowed because they didn't make the statement true.

3.9742 x 10^3 and 89.507 x 10

3,974.2 Move the decimal to the right 3 spaces. 895.07 Move the decimal to the right 1 space.

Step 3 when testing cases

3. Try to prove the statement insufficient. Value: Sufficient- single numerical answer Not Sufficient- two or more possible answers Yes/No: Sufficient- Always yes or always no Not sufficient- maybe or sometimes yes, sometimes no.

The price of a cup of coffee increases from 80 cents to 84 cents. By what percent did the price change?

4/80= 1/20 x/100= 1/20 x=5

4,169.2 / 10^2 and 89.507 /10

41.692 Move the decimal to the left 2 spaces. 8.9507 Move the decimal to the left 1 space.

What number is 50% of 60?

50% greater than is the same as %150. Rewrite. What number is 150% of 60. x=1.5x60 x=90

Benchmark values for percents and fractions

50%, 10%, 1%, 1/2, the quarters(1/4, 3/4), and the thirds (1/3, 2/3)

45% decrease and 45% less than means:

55% of the original.

6,782.01 x 10^-3 and 53.0447 / 10^-2

6.78201 Negative reverses the regular process so move the decimal to the left 3 spaces. 5,3407.47 Move the decimal to the right 2 places.

Analyze just the decimal portion of the number: 0.8347:

8 is in the tenths place, giving it a value of 8 tenths, or 8/10 3 is in the hundredths place 4 is in the thusandths place 7 is in the ten-thousandths place.

Converting Percents into Decimals

Move the decimal point two spaces to the left 525%= 5.25 5.25%= 0.0525

Converting Decimals into Percents

Move the decimal point two spaces to the right. 0.6=60% 0.459= 45.9%

A dress is marked up (16)2/3% to a final price of $140. What is the original price of the dress?

Set up equation. x+1/6x=140 7/6(x)= 140 x=120

Express the following as decimals: 9/2, 3000/10,000

Simplify the fraction before you divide 9/2= 4.5 3000/10,000= 3/10= 0.3

200 is 16% of what number?

This is a percent vs. decimal conversion problem. If you simply recognize that 16%= 0.16= 16/100= 4/25, this problem will be a lot easier: 4/25(x)=200, do x=200 x 25/4 50 x25= 1250.

Express the following as fractions and simplify: 2.45, 0.08

To convert a decimal to a fraction, write it over the appropriate power of 10 and simplify. 2.45= (2)45/100= (2)9/20 (mixed) or 49/20 (improper) 0.008= 8/1000= 1/125

Express the following as percents: 1,000/10, 25/8

To convert a fraction to a percent, rewrite the fraction with a denominator of 100: 1000/10= 10,000/100= 10,000% Or, convert the fraction to a decimal and shift the decimal point two places to the right: 25/8= (3)1/8= 3.125= 312.5%

Express the following as decimals: (1)27/4, (12)8/3

To convert a mixed number to a decimal, simplify the mixed number first, if needed. (1)27/4= 1+ (6)3/4= 7.75 (12)8/3= 12+(2)2/3= (14)2/3= 14.66

Express the following as fractions and simplify: 420% , 8%

To convert a percent to a fraction, write it over a denominator of 100 and simplify: 420%= 420/100= 21/5 8%= 8/100= 2/25

Compound interest Formula

Total Amount= P(1+(r/n))^nt P=principal r= rate in decimal form n= number of times per year t= number of years.

What is 75% of 20

Use fraction skills to convert 75% to 3/43 3/4 x 20= (3)(5)= 15

Percent can be referred as:

divide by 100 or (/100)

"Is" can be referred as:

equals or =