268.3457 = (1 × 000) + (2 × 100) + (6 × 10)POSITIVE, SO THE ANS...

1,268.3457 = (1 × 1,000) + (2 × 100) + (6 × 10)

positive, so the answer is positive 1.

+ (8 × 1) + (3 × .1) + (4 × .01) + (5 × .001) +

(7 × .0001)

1

Comparing Decimals

3 = ³ ₁ = 3 x = ¹ _x ⁴ ₅ = ⁵ ₄ 5 = ¹ ₅

Comparing decimals is actually quite simple. Just line

up the decimal points and fill in any zeroes needed to

When dividing fractions, simply multiply either

have an equal number of digits.

fraction by the other’s reciprocal to get the answer.

Example:

Compare .5 and .005.

2

Line up decimal points .500

1 ÷ ³ ₄ = ¹ ₂ ² ₁ × ⁴ ₃ = ⁴ ₆ ⁸ ₃ = ¹ ₂ ⁶ ₁

and add zeroes. .005

Adding and Subtracting Fractions

Then ignore the decimal point and ask, which is

To add or subtract fractions with like denomina-

bigger: 500 or 5?

tors, just add or subtract the numerators and

leave the denominator as it is. For example,

500 is definitely bigger than 5, so .5 is larger

than .005.

7 + ⁵ ₇ = ⁶ ₇ and ⁵ ₈ – ² ₈ = ³ ₈

To add or subtract fractions with unlike denomi-

nators, you must find the least common

Fractions

denominator, or LCD.

To do well when working with fractions, it is necessary

to understand some basic concepts. Here are some

math rules for fractions using variables:

For example, if given the denominators 8 and 12, 24

would be the LCD because 8 × 3 = 24 and 12 × 2 = 24.

a

In other words, the LCD is the smallest number divis-

b × _d ^c = _b ^a _× ^× _d ^{c a} _b + _b ^c = ^{a +} _b ^c

ible by each of the denominators.

Once you know the LCD, convert each fraction to

its new form by multiplying both the numerator and

b ÷ _d ^c = ^a _b × ^d _c = ^a _b ^× _× ^d _c ^a _b + _d ^c = ^ad _b ⁺ _d ^bc

denominator by the necessary number to get the LCD,

Multiplying Fractions

and then add or subtract the new numerators.

Multiplying fractions is one of the easiest operations to

perform. To multiply fractions, simply multiply the

numerators and the denominators, writing each in the

3 + ² ₅ = ⁵ ₅ ⁽ ₍ ¹ ₃ ⁾ ₎ + ³ ₃ ⁽ ₍ ² ₅ ⁾ ₎ = ₁ ⁵ ₅ + ₁ ⁶ ₅ = ¹ ₁ ¹ ₅

respective place over or under the fraction bar.

Sets

Sets are collections of numbers and are usually based on

4

certain criteria. All the numbers within a set are called

5 × ⁶ ₇ = ² ₃ ⁴ ₅

the members of the set. For example, the set of integers

Dividing Fractions

looks like this:

Dividing fractions is the same thing as multiplying

fractions by their reciprocal. To find the reciprocal of

{ . . . –3, –2 , –1, 0, 1, 2, 3, . . . }

any number, switch its numerator and denominator.

For example, the reciprocals of the following

The set of whole numbers looks like this:

numbers are:

{ 0, 1, 2, 3, . . . }

When you find the elements that two (or more)

sets have in common, you are finding the intersection

Find the median of the number set: 1, 5, 3, 7, 2.

of the sets. The symbol for intersection is: ∩.

First, arrange the set in ascending order: 1, 2, 3,

For example, the intersection of the integers and