The gre anlytycal writting section 5 ppt

Operations with DecimalsTo add and subtract decimals, you must always remember to line up the decimal points: To multiply decimals, it is not necessary to align decimal points.. Then, to

Operations with Decimals

To add and subtract decimals, you must always remember to line up the decimal points:

To multiply decimals, it is not necessary to align decimal points Simply perform the multiplication as if there were no decimal point Then, to determine the placement of the decimal point in the answer, count the numbers located to the right of the decimal point in the decimals being multiplied The total numbers to the right of the decimal point in the original problem is the number of places the decimal point is moved in the product For example:

To divide a decimal by another, such as 13.916 .916, move the decimal point in the divisor to the right until the divisor becomes a whole number Next, move the decimal point in the dividend the same number of places:

This process results in the correct position of the decimal point in the quotient The problem can now be solved by performing simple long division:

Percents

A percent is a measure of a part to a whole, with the whole being equal to 100

■ To change a decimal to a percentage, move the decimal point two units to the right and add a percent-age symbol

245 1391.6

5.68 –1225

166 6

–1470

1960

1391.6

245

1 2.3 4

2 2

x 5 6

1 2

3 4

7 4 0 4

6 1 7 0 0

6.9 1 0 4

1 2 3

4

= TOTAL #'s TO THE RIGHT OF THE DECIMAL POINT = 4

■ To change a fraction to a percentage, first change the fraction to a decimal To do this, divide the numerator by the denominator Then change the decimal to a percentage by moving the decimal two places to the right

Examples:

4

8 = 125 = 12.5%

■ To change a percentage to a decimal, simply move the decimal point two places to the left and elimi-nate the percentage symbol

Examples:

■ To change a percentage to a fraction, divide by 100 and reduce

Examples:

64% = 16040 = 1265 75% = 17050 = 34 82% = 18020 = 4510

■ Keep in mind that any percentage that is 100 or greater will need to reflect a whole number or mixed number when converted

Examples:

125% = 1.25 or 114

350% = 3.5 or 312

Here are some conversions with which you should be familiar:

1

1

1

2

 1

1 0

1

1

1

Order of Operations

An order for doing every mathematical operation is illustrated by the following acronym: Please Excuse My

Dear Aunt Sally Here is what it means mathematically:

P: Parentheses Perform all operations within parentheses first.

E: Exponents Evaluate exponents.

M/D: Multiply/Divide Work from left to right in your subtraction.

A/S: Add/Subtract Work from left to right in your subtraction.

Example:

5 + (32–02)2 = 5 + 

(

2 1

0 ) 2



= 5 + 210

= 5 + 20

= 25

Exponents

An exponent tells you how many times the number, called the base, is a factor in the product

Example:

25 – exponent= 2 2 2 2 2 = 32

⇑

base

Sometimes, you will see an exponent with a variable: b n The b represents a number that will be multiplied by itself n times.

Example:

b n where b = 5 and n = 3

b n= 53= 5 5 5 = 125

Don’t let the variables fool you Most expressions are very easy once you substitute in numbers

Laws of Exponents

■ Any nonzero base to the zero power is always 1

Examples:

■ When multiplying identical bases, you add the exponents.

Examples:

22 24 26 212 a2 a3 a5 a10

■ When dividing identical bases, you subtract the exponents

Examples:

2253= 22 a a74 = a3

Here is another method of illustrating multiplication and division of exponents:

b m b n  b m n

b b mn = b m – n

■ If an exponent appears outside of parentheses, you multiply the exponents together

Examples:

(33)7  321 (g 4)3  g12

■ Exponents can also be negative The following are rules for negative exponents:

m–1

5

1 1

1

5 

m–2

m

1 2

5

1 2

 2

1 5



m–3

m

1 3

5

1 3

 1

1

25 

m –n

m

1

n

for all integers n.

If m 0, then these expressions are undefined

Squares and Square Roots

The square of a number is the product of a number and itself For example, in the expression 32 3 3  9,

the number 9 is the square of the number 3 If we reverse the process, we can say that the number 3 is the

square root of the number 9 The symbol for square root is  and is called the radical The number inside

of the radical is called the radicand.

Example:

52= 25; therefore,25 = 5

Since 25 is the square of 5, we also know that 5 is the square root of 25

Perfect Squares

The square root of a number might not be a whole number For example, the square root of 7 is 2.645751311

It is not possible to find a whole number that can be multiplied by itself to equal 7 A whole number is a

perfect square if its square root is also a whole number Examples of perfect squares: 1, 4, 9, 16, 25, 36, 49, 64,

81, 100,

Properties of Square Root Radicals

■ The product of the square roots of two numbers is the same as the square root of their product

Example:

a × b = a × b

5 × 3 = 15

■ The quotient of the square roots of two numbers is the square root of the quotient

Example:

( b 0)

 5

■ The square of a square root radical is the radicand

Example:

(n)2= n

(3)2= 3 · 3 = 9 = 3

■ To combine square root radicals with the same radicands, combine their coefficients and keep the same radical factor You may add or subtract radicals with the same radicand

Example:

a b + cb = (a + c)b

43 + 23 = 63

■ Radicals cannot be combined using addition and subtraction

Example:

a + b  ≠ a + b

4 + 11 ≠ 4 + 11

15

 3

15 

3

a



b

a



b

■ To simplify a square root radical, write the radicand as the product of two factors, with one number being the largest perfect square factor Then write the radical of each factor and simplify

Example:

8 = 4 2 = 22

Ratio

The ratio of the numbers 10 to 30 can be expressed in several ways, for example:

10 to 30 or

10:30 or

1

3

0

0



Since a ratio is also an implied division, it can be reduced to lowest terms Therefore, since both 10 and 30 are multiples of 10, the above ratio can be written as:

1 to 3 or

1:3 or

1

3 

 A l g e b r a R e v i e w

Congratulations on completing the arithmetic section Fortunately, you will only need to know a small por-tion of algebra normally taught in a high school algebra course for the GRE The following secpor-tion outlines only the essential concepts and skills you will need for success on the GRE Quantitative section

Equations

An equation is solved by finding a number that is equal to a certain variable

S IMPLE R ULES FOR W ORKING WITH E QUATIONS

1 The equal sign seperates an equation into two sides.

2 Whenever an operation is performed on one side, the same operation must be performed on the other side.

3 Your first goal is to get all the variables on one side and all the numbers on the other.

4 The final step often is to divide each side by the coefficient, leaving the variable equal to a number.