Praxis 7803 Elementary Education Math

absolute value:
The distance a number is from zero on a number line ( absolute value is always the positive version of the number). 0 is neutral neither positive or negative.

addend:

a number that is added to another number

Adding Decimals:

Align the decimal points and add as you normally would.

Adding Fractions same denominator:
Just add the numerators. Keep the same denominator.

Add to:
Change Unknown:
Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two? 2 + ? = 5

Add to:
Result Unknown:
Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now? 2 + 3 = ?

Add to:
Start Unknown:
Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before? ? + 3 =5

adjacent angles:
Adjacent angles are two angles that have a common vertex and a common side. The vertex of an angle is the endpoint of the rays that form the sides of the angle. When we say common vertex and common side, we mean that the vertex point and the side are shared by the two angles. Here's an example of adjacent angles:


algabraic expression:

A combination of variables, numbers, and at least one operation.

algebraic expression:
A mathematical phrase involving at least one variable and sometimes numbers and operation symbols.

Area of an Irregular shape:
To find the area of irregular shapes, the first thing to do is to divide the irregular shape into regular shapes that you can recognize such as triangles, rectangles, circles, squares and so forth...

Area of a rectangle formula:
A= length x width

Area of a shape:
The amount of space inside an object
Area of a Square = side of square times itself Ex:
6x6
Area of a Rectangle = width x height = w x h
Area of a Triangle =1/2(base?height)
Area of a Semi-Circle = (? x radius2)/2 = (? x r2)/2

ARRAYS2, AREA3-GROUP SIZE UNKNOWN ("HOW MANY IN EACH GROUP?" DIVISION):
If 18 apples are arranged into 3 equal rows, how many apples will be in each row? Area example. A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it?

ARRAYS2, AREA3-NUMBER OF GROUPS UNKNOWN ("HOW MANY GROUPS?" DIVISION):
If 18 apples are arranged into equal rows of 6 apples, how many rows will there be? Area example. A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it?

ARRAYS2, AREA3-UNKNOWN PRODUCT:
There are 3 rows of apples with 6 apples in each row. How many apples are there? Area example. What is the area of a 3 cm by 6 cm rectangle?

Associative Property:

Changing the grouping of numbers will NOT change the value. For example:
(7 + 4) + 8 = 7 + (4 + 8) also works with multiplication

Base 10 Number System:
a number system in which all numbers are expressed using the digits 0-9

Base 10 numerals:
In math, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are base ten numerals. We can only count to nine without the need for two numerals or digits. All numbers in the number system are made by combining these 10 numerals or digits.

benchmark numbers:
Numbers that help you estimate objects without counting them, such as 25, 50, 100

Cardinality:
is a measure of the "number of elements of the set". For example, the set contains 3 elements, and therefore has a cardinality of 3.

Changing a Mixed Number into an Improper Fraction:
When carrying out mathematical operations, it is usually necessary to work with
improper fractions rather than mixed numbers. To change a mixed number into an
improper fraction:

1. Multiply the whole number by the denominator.
2. Add the numerator to the product.
3. Place the sum in the numerator over the original denominator.

Commutative Property:

The property that says that two or more numbers can be added or multiplied in any order without changing the result.

Compare:
Bigger Unknown:
(Version with "more"):
Julie has three more apples than Lucy. Lucy has two apples. How many apples does Julie have? (Version with "fewer"):
Lucy has 3 fewer apples than Julie. Lucy has two apples. How many apples does Julie have? 2 + 3 = ?, 3 + 2 = ?

Compare Difference Unknown:
("How many more?" version):
Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy?("How many fewer?" version):
Lucy has two apples. Julie has five apples. How many fewer apples does Lucy have then Julie? 2 + ? = 5, 5 - 2 = ?

compare-GROUP SIZE UNKNOWN ("HOW MANY IN EACH GROUP?" DIVISION):
A red hat costs $18 and that is 3 times as much as a blue hat costs. How much does a blue hat cost? Measurement example. A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first?

compare-NUMBER OF GROUPS UNKNOWN ("HOW MANY GROUPS?" DIVISION):
A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat? Measurement example. A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first?

Compare:
Smaller Unknown:
(Version with "more"):
Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?(Version with "fewer"):
Lucy has 3 fewer apples than Julie. Julie has five apples. How many apples does Lucy have? 5 - 3 = ?, ? + 3 = 5

compare-UNKNOWN PRODUCT:
A blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost? Measurement example. A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long?

Comparing fractions strategies:
Comparing Fractions Example:

12/32 and 28/40

Do you really need to find a common denominator in order to compare these two fractions? I think not. The first fraction is clearly less than one-half, while the second is greater than one-half. Case closed. Comparing fractions using a benchmark of one-half is just one of the strategies students should have in their toolbox.

Comparing fractions when the denominators are different:
To compare fractions that have different denominators, convert them all to a set of
fractions that have the same denominator. There are three steps to comparing
fractions when the denominators are different.
1. Find the Least Common Denominator (LCD) for the group of fractions you are
comparing.
2. Find the multiplier for each fraction. Multiply both the top and bottom of each
fraction by that multiplier.
3. Compare and order the numerators of each fraction.

Composing Numbers:
Subparts into a whole. (Taking an expanded number and changing it to standard notation).

congruent angles:
Congruent Angles have the same angle (in degrees or radians). That is all.

Considerations in place value:
1. Recognize that in a multi-digit whole number, a digit in one place represents 10 times
what it represents in the place to its right.
2.Recognize that in a multi-digit number, a digit in one place represents 10 times as
much as it represents in the place to its right and 1/10 of what it represents in
the place to its left.
3. Explain patterns in the number of zeros of the product when multiplying a number
by powers of 10.

convert a decimal to a fraction:

First, convert the decimal to fraction using tenths, hundredths, thousandths, etc. depending on the number of decimal places. e.g. 1.75 = 1 75/100.
Next, simplify the fraction part to the lowest common term. e.g. 75/100 = 3/4.

Converting Between Improper Fractions and Whole/Mixed Numbers:
An improper fraction is one in which the numerator is larger than the denominator.
For example, if you were told you had six-fourths (6/4) of a pie left, you would know
that you had one whole pie (4/4) plus one-half of a pie (2/4)

counting on:

Counting up from the lesser number to the greater number.

Covert a decimal to a fraction:
Convert decimal 0.05 to a fraction
0.05 = 1/20 as a fraction

Step by Step Solution
To convert the decimal 0.05 to a fraction follow these steps:


Step 1:
Write down the number as a fraction of one:


0.05 = 0.05/1

Step 2:
Multiply both top and bottom by 10 for every number after the decimal point:


As we have 2 numbers after the decimal point, we multiply both numerator and denominator by 100. So,

0.05/1 = (0.05 x 100)/(1 x 100) = 5/100.

Step 3:
Simplify (or reduce) the fraction:


5/100 = 1/20 when reduced to the simplest form.

Decimal:
A number written on the basis of powers of ten
53.109

Decimal division by powers of 10:
If you are dividing by 10, 100, 1000 then move the decimal to the left the same number as there are zeros.
If you are dividing by 0.1, 0.01, or 0.001 then move the decimal to the right the same number as there are zeroes.
Example 94.56/100=0.9456

Decimal division by tenths:

To divide decimal numbers:


If the divisor is not a whole number, move decimal point to right to make it a whole number and move decimal point in dividend the same number of places.

Divide as usual. Keep dividing until the answer terminates or repeats.

Put decimal point directly above decimal point in the dividend.

Check your answer. Multiply quotient by divisor. Does it equal the dividend?

Decimal multiplication powers of 10:
Move the decimal point right as many places
as there are 0's in the power. If there are not enough digits, add on 0's.

Decimal multiplication powers of 10:
...

decimal multiplication powers of 10:

if you are multiplying by 10, 100, 1000 then move the decimal to the right the same numbers as there are zero.
if you are multiplying by 0.1, 0.01, or 0.001 then move the decimal to the left the same number there are zeros.
Example:
6.3 x 1000=6.300.0

Decimal point:
:
A dot noting the change from positive powers of
ten (left of point) to negative powers of ten (right of point)
Ex:
53.109

Decimals and place values:


Decimals and their Equivalent Fractions:
The decimal equivalent of any fraction can be found by dividing the numerator of the by the denominator.
For example:
2/100 is equivalent to 0.02, 20/100 and 2/10 are equivalent to 0.2

Decimals Explained:
As you move right from the decimal point, each place value is 1/10 the value of the number to its left. The first number to the right of the decimal point is in the tenths place. Tenths are tenths of one whole. Ten tenths are equal to one whole.

The second number to the right of the decimal point is in the hundredths place. A hundredth is one hundredth of a whole. One hundred hundredths make up a whole.

The third number to the right of the decimal point is in the thousandths place. A thousandth is one thousandth of a whole. One thousand thousandths make up a whole.

Decomposing Numbers:
Break down numbers into their sub-parts. (Taking a standard number and changing it into expanded form). process of breaking a number into smaller units to simplify problem solving ex. 15 can be 10+5 or 10 can be 6+ 4

Define a square in terms of other two-dimensional geometric figures:
A square is a quadrilateral with 4 sides of equal length and 4 angles of equal measure, whereas a rectangle is a quadrilateral with 4 angles of equal measure, a rhombus is a quadrilateral with 4 sides of equal length, and a parallelogram is a quadrilateral where opposite sides are parallel. Therefore, a rectangle that has 4 sides of equal length is a square, and a rhombus that is also a rectangle is a square,

diameter of a circle:
2 x radius

The difference between and equation and expression:
Expression:
4y + 2
Equation:
4y + 2 = 14

Digit:
a symbol used to show a number
0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Direction in Place Value:
place value increases ten times with each shift to the left in a multi-digit number

Distributive Property:

a property indicating a special way in which multiplication is applied to addition of two or more numbers in which each term inside a set of parentheses can be multiplied by a factor outside the parentheses, such as a(b + c) = ab + ac

The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

dividend:

A number that is divided by another number.

Dividing Decimals:

Move the decimal to the right on both numbers until there is nothing to the right of the decimal

dividing decimals by whole numbers:

send decimal straight up above, then divide like normal numbers

Dividing Fractions:
:
Invert (reciprocal) the second fraction to the right of the division symbol (cancel if possible and multiply

Dividing fractions by whole numbers:

Step 1. Multiply the bottom number of the fraction by the whole number
Step 2. Simplify the fraction (if needed)

Diving a number by 0:
equals 0

Division Key words:
as much
cut up
each group has
equal sharing
half (or other fractions)
how many in each
parts
per
percent
quotient of
ratio of
separated
share something equally

divisor:

the number you divide by in a division problem

Equal groups GROUP SIZE UNKNOWN ("HOW MANY IN EACH GROUP?" DIVISION):
If 18 plums are shared equally into 3 bags, then how many plums will be in each bag? Measurement example. You have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be?

Equal groups NUMBER OF GROUPS UNKNOWN ("HOW MANY GROUPS?" DIVISION):
If 18 plums are to be packed 6 to a bag, then how many bags are needed? Measurement example. You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have?

Equal Groups - Unknown Product:
There are 3 bags with 6 plums in each bag. How many plums are there in all? Measurement example. You need 3 lengths of string, each 6 inches long. How much string will you need altogether?

equivalent decimals:

Equivalent decimal fractions are unlike fractions which are equal in value.
Let us consider the following examples:


(i) 0.4, 0.40, 0.400, 0.4000

Each of the above is equal to 0.4 or 4/10.


(ii) 1.9, 1.90, 1.900, 1.9000

Each of the above is equal to 1.9 or 19/10.


(iii) 10.14, 10.140, 10.1400, 10.14000

Each of the above is equal to 10.14 or 1014/100.

Equivalent decimal fractions are unlike fractions which are equal in value.



(iv) 0.94, 0.940, 0.9400, 0.94000

Each of the above is equal to 0.94 or 94/100.


(v) 9.1, 9.10, 9.100, 9.1000

Each of the above is equal to 9.1 or 91/10.


(vi) 60.49, 60.4900, 60.490

Each of the above is equal to 60.49 or 6049/100.


Similarly, we have

0.300 = 0.30 = 0.3

0.700 = 0.70 = 0.7

0.200 = 0.20 = 0.2

Thus, by adding any number of zeros after the extreme right digit in the decimal part of a decimal number does not change the value of the number.

equivalent expressions:
expressions that have the same value

Equivalent Fractions:
fractions that have the same value but may look different. Ex, 1/2, 2/4, 3/6,etc.

equivalent fractions:
You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.
You only multiply or divide, never add or subtract, to get an equivalent fraction.
Only divide when the top and bottom stay as whole numbers.

Expanded notation:
:
Writing a number and showing the place
value of each digit
EX:
40,000 + 2,000 + 100 + 3

Finding fractions of whole number:
For finding a fraction of a whole number, we multiply the numerator of the fraction by the given number and then divide the product by the denominator of the fraction.

Find 2/5 of 15.

To find 2/5 of 15, we multiply the numerator 2 by the given whole number 15 and then divide the product 30 by the denominator 5.

2/5 × 15 = 2 × 15/5 = 30/5 = 6

So, 2/5 of 15 = 6.

Fraction Rules:

Addition and Subtraction = common denominator
multiplication = straight across
Division = To divide one fraction by another, invert (turn upside-down) the second fraction, then multiply.

Fractions as ratios:
To convert a fraction to a ratio, first write down the numerator, or top number. Second, write a colon. Thirdly, write down the denominator, or bottom number. For example, the fraction 1/6 can be written as the ratio 1:
6.

Fundamental Theorem of Arithmetic:
Every composite number can be expressed as a unique product of prime numbers.

How do we represent numbers using base 10 blocks:


How to calculate the least common denominator:
The same fraction can be expressed in many different forms. If the ratio between numerator and denominator is the same, the fractions represent the same rational number.

The least common denominator of a set of fractions is the least number that is a multiple of all the denominators:
their "least common multiple".
Method of calculating the LCD is the same as calculation least common multiple of fractions denominators.
The simple method for computing common denominator (not least at all) is multiply all denominators.

Intergers:
An integer (pronounced IN-tuh-jer) is a whole number (not a fractional number) that can be positive, negative, or zero.

kilometer:
1000 meters

least common multiple:
The smallest multiple (other than zero) that two or more numbers have in common.

The least common multiple, or LCM, is another number that's useful in solving many math problems. Let's find the LCM of 30 and 45. One way to find the least common multiple of two numbers is to first list the prime factors of each number.

30 = 2 × 3 × 5
45 = 3 × 3 × 5

Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

2:
one occurrence
3:
two occurrences
5:
one occurrence
2 × 3 × 3 × 5 = 90 <— LCM

Like terms in algebraic expression:
Like terms are terms that contain the same variables raised to the same power. Only the numerical coefficients are different.

lowest common denominator:
The lowest common denominator or least common denominator (abbreviated LCD) is the least common multiple of the denominators of a set of fractions. It is the smallest positive integer that is a multiple of each denominator in the set.

Make 10 strategy:

Make Ten Strategy for Addition
Step 1:
The first addend and what make ten?
Step 2:
Write the number below the second addend
Step 3:
The number below the second addend and what make the second addend?
Step 4:
Add the rest to 10

metric system:
a system of measurement based on the number 10

metric units of length:

Kilometer (km)1000
Meter (m)
Decimeter (dm)
Centimeter (cm)
Millimeter (mm)
Micrometer (um)
Nanometer (nm)

millimeter, centimeter, meter, kilometer:
metric units of length

minuend:

The number from which another number is subtracted; the first number in a subtraction problem

mixed number:

a number made up of a whole number AND a fraction
2 1/3
-Divide the numerator by the denominator.
-Write down the whole number answer
-Then write down any remainder above the denominator.

Multiplication key words:
by (dimension)
double
each group
every
factor of
increased by
multiplied by
of
product
times
triple
twice

Multiplying Decimals:

ignore decimal points and multiply the two numbers, then count the digits to the right of the decimal points in the original numbers and place the decimal so there are the same number of digits to the right of the decimal

Multiplying Fractions:
1. Multiply the numerators.
2. Multiply the denominators.

Multiplying Fractions:
When multiplying fractions, simply multiply the the numerators together and multiply the denominators together. It is good practice to see if and numbers can cancel.
Canceling is done when the numerator and denominator can be divided evenly by the same number. Note:
canceling happen top to bottom and or diagonally but never across.

Multiplying mixed numbers:
1. Change the mixed number into an improper fraction by multiplying the denominator by the whole number. Then add the numerator in. Your denominator stays the same.
2. Multiply the numerators.
3. Multiply the denominators.
4. Simplify

Order of Operations (PEMDAS):

the sequence in which operations are
performed when evaluating an expression:
Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction.
Parentheses (simplify inside 'em)
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

Ordinal:
Ordinal numbers indicate the order or rank of things in a set rank, order 1st, 2nd, 3rd......

partitive division:

If the number of groups is known, and you are trying to find the number in each group, then the problem is referred to as a partitive division problem. Partitive division may also be called equal groups, or sharing and distribution. You are, in effect, partitioning the dividend into the number of groups indicated by the divisor and then counting the number of items in each of the groups.

perimeter:
The distance around a figure

Perimeter (circumference) of a circle:
C=2?r

Perimeter formula for a rectangle:
P=2l+2w

Perimeter of a rectangle:
P= 2L + 2w

Perimeter of a square:
P = 4s

Place:
The position of a digit relative to the decimal
Ones, tens, hundreds, etc.

Place Value:
The value of a digit based on its position within a number

place value:
The value of each digit in a number based on the location of the digit

Place Value and 10 blocks:


Place Value Decimals:
Decimals are a shorthand way to write fractions and mixed numbers with denominators that are powers of 10 , like 10,100,1000,10000, etc.

If a number has a decimal point , then the first digit to the right of the decimal point indicates the number of tenths.

For example, the decimal 0.3 is the same as the fraction 3/10 .

The second digit to the right of the decimal point indicates the number of hundredths.

For example, the decimal 3.26 is the same as the mixed number 3 26/100 . (Note that the first digit to the left of the decimal point is the ones digit.)

You can write decimals with many places to the right of the decimal point. For example, this is a representation of the mixed number 51480531000000 , with the place values named:


polygon:
Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up).

Polygon (convex):
A convex polygon is defined as a polygon with all its interior angles less than 180°. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Think of it as a 'bulging' polygon. Note that a triangle (3-gon) is always convex.

proportion:
1. The relationship of one thing to another in size, amount, etc. 2. Size or weight relationships among structures or among elements in a single structure.

put together/take apart addend unknown:
Five apples are on the table. Three are red and the rest are green. How many apples are green? 3 + ? = 5, 5-3 = ?

put together/take apart both addends unknown:
Grandma has five flowers. How many can she put in the red vase and how many in her blue vase? 5 = 0 + 5, 5 + 0 5 = 1 +4, 5 = 4 +1, 5 = 2 + 3, 5 = 3 + 2

Put Together/Take Apart, Total Unknown:
Three red apples and two green apples are on the table. How many apples are on the table? 3 + 2 = ?

quadrilateral:
Quadrilateral just means "four sides"
(quad means four, lateral means side).

A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides.

A quadrilateral has:


four sides (edges)
four vertices (corners)
interior angles that add to 360 degrees:


quadrilateral:
A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides.
four sides (edges)
four vertices (corners)
interior angles that add to 360 degrees:


quadrilateral:

a four-sided polygon.

quotative division:
If the number in each group is known, and you are trying to find the number of groups, then the problem is referred to as a quotative division problem. Quotative division may also be called measurement, or repeated subtraction. You are, in effect, counting or measuring the number of times you can subtract the divisor from the dividend. Long division (remember long division?!) uses this concept.

quotient:

the answer to a division problem

Ratio:
The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

rational numbers:

All positive and negative integers, fractions and decimal numbers.

Regroup:
Exchange equal amounts of tens and ones, hundreds and tens, thousands and hundreds, etc.
10 ones = 1 ten
1,000 = 10 hundreds

regular quadrilateral:
4 sided polygon. All sides and angles are equal. (Square)

Round:
Substitute an approximate value (usually to the
nearest 10, 100, 1,000, etc.)

Rule for dividing fractions:
When you divide two fractions, take the reciprocal of the second fraction and
multiply. (Taking the reciprocal of a fraction means to flip it over.)

Rule for Multiplication of Fractions:
When multiplying fractions, simply multiply the numerators together and then multiply the denominators together. Simplify the result.

The rules for adding and subtracting fractions can be broken down into several steps:
:
1. Determine whether the fractions have the same denominator. If the denominators
are the same, move to step 4.
2. If the denominators are different, find the LCD for the fractions being added or
subtracted.
3. For each of the original fractions, find its equivalent fraction with the LCD in the
denominator.
4. Add or subtract the numerators of the fractions.
5. Simplify the resulting fraction.

Standard notation:
Writing a number with one digit in each place value
example:
42,103

Subitizing:
The ability to instantly "see" the number of objects in a small set without having to count them.

Subtracting Decimals:

Line up the decimal points and subtract normally (ex. 20.02-1.36=18.66)

subtrahend:
A number that is subtracted.

Take From:
Change Unknown:
Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?5 - ? = 3

Take From:
Result Unknown:
Five apples were on the table. I ate two apples. How many apples are on the table now?5-2 = ?

Take From:
Start Unknown:
Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before?? -2 = 3

To find the value of a set of fractions:
You can turn the fraction into a decimal by diving the numerator by the denominator.

using a grid to find perimeter and area:
The perimeter of a figure is the total length of its outline or boundary and this is found by counting the number of unit lengths along the boundary of the figure.
The area of a figure on grid is found by counting the total number of unit squares it occupies (inside the figure).

Value:
Quality of a digit
2 = 2 ones
39 = 3 tens and 9 ones

Value of a fraction:
-When the numerator stays the same, and the denominator increases, the value of the fraction decreases.
-When the denominator stays the same, and the numerator increases, the value of the fraction increases.

Value of decimals to the right of the decimal:

When comparing decimals, begin on the left and compare the digits in each place. Example:

Compare 0.11 and 0.12.
In the tenths place the digits are the same. Look at the hundredths. 2 is greater than 1, so 0.12 > 0.11.

Compare 0.02 and 0.120.
The ones are the same. 1 is greater than 0 in the tenths place, so 0.120 > 0.02.

Compare 2.17 and 0.99.
The ones are different. Since 2 is greater than 0, 2.17 > 0.99.

Remind students that when there are non-zero digits on both sides of the decimal point, they should say, "and," where they see the decimal point. For example, 2.17 is read, "two and seventeen hundredths."
Use models on a 10 x 10 grid as necessary to guide the class in comparing decimals numbers using > and <.>
1. 0.1 (>) 0.01
2. 0.51 (>) 0.509
3. 0.183 (>) 0.083
4. 1.003 (>) 0.339
5. 1.06 (>) 1.007

Word form:
Writing a number using words.
Forty-two thousand, one-hundred
three.

Writing Fractions in it's simplest form:
-Fractions can be simplified when the numerator and denominator have a common
factor in them. If both the numerator and denominator have common factors, then
we can cancel these factors out. For example, in the fraction 8/12, 4 is a common
factor of both 8 and 12.
-We can simplify the fraction by canceling the 4 from both the numerator and
denominator of the fraction. Canceling is equivalent to dividing both the numerator
and denominator by the same number.

Zero:
A digit representing the absence of quantity. Zero is necessary in holding place value.
Ex:
402,005

Zero multiplied or divided by any number:
equals 0