MATH PRAXIS �REVIEW�

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13

REAL NUMBERS

• Natural Numbers– 1, 2, 3,4….
• Whole Numbers– 0, 1, 2, 3, 4…..
• Integers-- …-2, -1, 0, 1, 2….
• Rational– can be written as p/q, ½, -3, 4.3

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REAL NUMBERS

PRIME & COMPOSITE NUMBERS

• A PRIME number is a natural number greater than 1 that has no positive divisors other than itself and 1.
• 2, 3, 5, 7, 11, 13 are the first prime numbers.

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• A COMPOSITE number is a number greater than 1 that is not a prime number.
• 4, 6, 8, 9, 10, 12 are the first composite numbers.

ABSOLUTE VALUE

• Absolute value may be defined as the distance from zero on the number line….

|4| = DEFINED AS ABSOLUTE VALUE OF 4

-4 AND 4 BOTH HAVE AN ABSOLUTE VALUE OF 4

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EXPONENTIAL EXPRESSIONS

• An exponent tells you to multiply repeatedly

a³=a x a x a

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4³= 4 X 4 X 4 = 64

PLACE VALUE� ANY NUMBER RAISED TO ZERO POWER EQUALS ONE: �3⁰ = 1�SO … 5 ( 10⁰ ) = 5 X 1 = 5

REMEMBER 10 RAISED TO 0 EQUALS ONE

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ORDER OF OPERATIONS

Please Excuse My Dear Aunt Sally

• P- Parentheses– grouping
• E- Exponents
• M- Multiply
• D- Divide
• A- Add
• S- Subtract

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4(5-2)² - 2³ =

5 – 2 = 3

3 X 3 = 9

4 X 9 = 36

2 X 2 X 2 = 8

SO

36 – 8 = 28

SQUARES

• SQUARES DEFINED IS THE PRODUCT OF A NUMBER WITH ITSELF, i.e., A NUMBER MULTIPLIED BY ITSELF

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4X4=16

5X5=25

6X6=36 ALSO 6²

CUBES

• A CUBE IS THE PRODUCT OF A NUMBER MULTIPLIED BY ITSELF TWICE

2X2X2=8

3X3X3=27 ALSO 3³

COMMON MATH SYMBOLS

• = IS EQUAL TO
• ≠ IS NOT EQUAL TO
• ˃ IS GREATER THAN: 5 ˃ 3 (5 is greater than 3)
• ˂ IS LESS THAN: 3 ˂ 5 (3 is less than 5)
• ≤ IS LESS THAN OR EQUAL TO
• ≥ IS GREATER THAN OR EQUAL TO
• ǁ IS PARALLEL TO
• IS PERPENDICULAR TO

COMMON MATH SYMBOLS

EXAMPLE

5 ≤ 7 – p

Which of the following is equivalent to the inequality above?

P ≤ 2

P ≥ 2

Since 7 subtract p is greater than or equal to 5 (≤), then 7 subtract ?

(what number) must equal a number equal to or greater than 5.

7 subtract 1 equals 6 (that works) 7 subtract 2 equals 5 (that works), 7 subtract 3 equals 4 (that doesn’t work). So the answer is P ≤ 2 (P is less than or equal to 2).

COMMUTATIVE LAW �OF �ADDITION & MULTIPLICATION

• DEFINED AS “ORDER DOES NOT MATTER.”

2 + 3 = 3 + 2 BOTH EQUAL 5

2 X 3 = 3 X 2 BOTH EQUAL 6

ASSOCIATE LAW�OF ADDITION AND MULTIPLICATION

• DEFINED AS “GROUPING DOES NOT MATTER.”

(2 + 3) + 4 = 2 + (3 + 4) BOTH EQUAL 9

(2 X 3) X 4 = 2 X (3 X 4) BOTH EQUAL 24

IDENTITY ELEMENT �FOR ADDITION AND MULTIPLICATION

• THE IDENTITY ELEMENT FOR ADDITION IS 0

ANY NUMBER ADDED TO 0 GIVES THE ORIGINAL NUMBER.

4 + 0 = 4

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• THE IDENTITY ELEMENT FOR MULTIPLICATION IS 1

ANY NUMBER MULTIPLIED BY 1 GIVES THE ORIGINAL NUMBER.

4 X 1 = 4

ADDITIVE INVERSE

• THE ADDITIVE INVERSE IS THE OPPOSITE (NEGATIVE) OF THE NUMBER.
• ANY NUMBER PLUS ITS ADDITIVE INVERSE EQUALS 0.

3 + -3 = 0

RECIPROCAL

MULTIPLICATIVE INVERSE

DISTRIBUTIVE PROPERTY

• THE DISTRIBUTIVE PROPERTY IS THE PROCESS OF DISTRIBUTING THE NUMBER ON THE OUTSIDE OF THE PARENTHESIS TO EACH TERM ON THE INSIDE.

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2(3 + 4) = 2(3) + 2(4)= BOTH EQUAL 14

PLACE VALUE

• WE USE THE BASE 10 PLACE VALUE SYSTEM.

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• IN THE NUMBER 345

5 EQUALS 5 ONES

4 EQUALS 4 GROUPS OF TEN

3 EQUALS 3 GROUPS OF HUNDRED

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IN THIS EXAMPLE THE NUMERAL 3 IS MORE THAN THE NUMERAL 5 BECAUSE THE “5” MEANS 5 ONES, BUT THE “3” MEANS 3 HUNDREDS.

PLACE VALUE

PLACE VALUE

685,321

648,955

THE 8 IN THE TOP NUMBER REPRESENTS

HOW MANY TIMES WHAT THE 8

IN THE BOTTOM NUMBER REPRESENTS?

ANSWER

TEN TIMES

PLACE VALUE

WHICH NUMBER IS THE LEAST?

0.203

0.2041

0.20051

0.21

ANSWER

0.20051

EXPANDED NOTATION

ROUNDING OFF NUMBERS

• UNDERLINE THE DIGIT YOU ARE ROUNDING OFF.
• LOOK TO ITS IMMEDIATE RIGHT (ONE PLACE).
• IF IT IS 5 OR MORE, ROUND UP.
• IF IT IS 4 OR LESS, ROUND DOWN.

345,723 ROUNDS TO 350,000

343,723 ROUNDS TO 340,000

3.4678 ROUNDS TO 3.47

3.4629 ROUNDS TO 3.46

ESTIMATING

• WHEN ESTIMATING THE ANSWER TO AN EQUATION, IT IS APPROPRIATE TO ROUND OFF ONE OR MORE OF THE NUMBERS IN THE EQUATION.

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Example: 34 X 987 (= 33,558)

ANSWER: ROUND 987 TO 1,000

34 x 1,000 = 34,000

ADDING/SUBTRACTING �WITH NEGATIVE NUMBERS

IF TWO LIKE SIGNS

(+) (+) THEN (+3) + (+2) = 5 or just 3 + 2 = 5

(-) (-) THEN (-14) - (-4) = -10 or just -14 + 4 = -10

(subtracting a negative number is similar to adding: 8 – (-3) = 8 + 3 = 11)

IF TWO UNLIKE SIGNS

(+) (-) THEN (+12) + (-4) = 8 or just 12 – 4 = 8

(adding a negative number is similar to subtraction: 8 + (-3) = 8 – 3 = 5)

(-) (+) THEN (-19) - (+6) = -25 or just -19 – 6 = -25

INTEGERS

• 4 – 3 = 1
• 4 – 2 = 2 SUBTRACTING A NEGATIVE
• 4 – 1 = 3 NUMBER IS LIKE ADDING
• 4 – 0 = 4
• 4 – (-1) = 5
• 4 – (-2) = 6
• 4 – (-3) = 7

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MULTIPLYING AND DIVIDING�WITH NEGATIVE NUMBERS

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FRACTIONS

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FRACTIONS

CONVERTING FRACTIONS TO DECIMALS.

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CONVERTING DECIMALS TO PERCENTS.

SIMPLY MOVE DECIMAL TWO PLACES OVER.

.60 EQUALS 60%

CONVERTING IMPROPER FRACTIONS TO PROPER FRACTIONS.

FACTORS

• THE FACTORS OF A NUMBER ARE THOSE NUMBERS (whole numbers) WHEN MULTIPLIED TOGETHER YIELD THAT NUMBER:

EXAMPLE

8 = 2 X 4 ALSO 8 = 1 X 8

THEREFORE

THE FACTORS OF 8 ARE 1,2,4,& 8

COMMON FACTORS

• COMMON FACTORS ARE THOSE FACTORS WHICH ARE THE SAME FOR TWO OR MORE NUMBERS.

24: 1,2,3,4,6,8,12,24

36: 1,2,3,4,6,9,12,18,36

COMMON FACTORS ARE

1,2,3,4,6,& 12

GREATEST COMMON FACTOR

• THE GREATEST COMMON FACTOR IS THE LARGEST FACTOR THAT IS COMMON TO THE NUMBERS BEING COMPARED:

12: 1,2,3,4,6,12

30: 1,2,3,5,6,10,15,30

THEREFORE

1,2,3,& 6 ARE ALL THE COMMON FACTORS

BUT 6 (SIX) IS THE GREATEST COMMON FACTOR.

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MULTIPLES

• MULTIPLES OF A NUMBER ARE FOUND BY MULTIPLYING THE NUMBER BY 2,3,4,ETC.

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EXAMPLE

THE MULTIPLES OF 8 ARE 8,16,24,32,…

LEAST COMMON MULTIPLE

• THE LEAST COMMON MULTIPLE IS THE SMALLEST NUMBER WHICH IS COMMON TO TWO NUMBERS:

3: 3,6,9,12,15,18,21,24

4: 4,8,12,16,20,24,28

THE LEAST COMMON MULTIPLE OF THREE (3) AND FOUR (4) IS 12

ADDING�FRACTIONS

ADDING FRACTIONS

ADDING FRACTIONS

SUBTRACTING�FRACTIONS

SUBTRACTING FRACTIONS

SUBTRACTING FRACTIONS

MULTIPLYING FRACTIONS

DIVIDING FRACTIONS�TO DIVIDE A FRACTION YOU SIMPLY MULTIPLY THE NUMBER BY THE RECIPROCAL OF THE FRACTIONS.

ADDING�MIXED FRACTIONS EXAMPLE

SUBTRACTING �MIXED FRACTIONS EXAMPLE

MULTIPLYING �MIXED FRACTIONS

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DIVIDING MIXED FRACTIONS

ADDING AND SUBTRACTING�DECIMALS

EXAMPLE

4.316 + 179.5 =

4.316

+ 179.5

183.816

MULTIPLYING DECINALS

25.35 (TWO DECIMAL PLACES)

X 0.12 (TWO DECIMAL PLACES)

5070

25350

3.0420 (TWO PLUS TWO EQUALS FOUR DECIMAL PLACES)

DIVIDING DECIMALS

.2 12.64�

2. 126.4

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2 126.4

63.8

2 126.4

MAKE THE DIVISOR A WHOLE NUMBER BY MOVING THE DECIMAL POINT TO THE RIGHT. MOVE THE DECIMAL IN THE DIVIDEND AN EQUAL NUMBER OF SPACES.

PLACE THE DECIMAL POINT IN THE ANSWER LINED UP WITH THE DECIMAL POINT IN THE DIVIDEND

DIVIDE THE NUMBER MAKING SURE THE DECIMAL POINTS REMAIN LINED UP

HOW TO COMPARE AND ORDER FRACTIONS, SMALLEST TO LARGEST

FUNCTION RULES FOR DATA

A FUNCTION IS A RULE (AN EQUATION) THAT SHOWS A RELATIONSHIP BETWEEN AN INPUT AND THE OUTPUT

IT IS OFTEN

GIVEN AS A FORMULA

F(x) = 3x + 5

Meaning

TAKE AN INPUT

(FOR EXAMPLE … 7)

MULTIPLY IT (7) BY 3

AND ADD 5

EQUALS 26

FUNCTION RULES FOR DATA

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CONSIDER THEN THAT IF YOU TAKE 60

AND APPLY THE FUNCTION RULE

AND YOU GET 24

SO WE KNOW THEN THAT . . .

60 x ? = 24

TO FIND THIS YOU SIMPLY DIVIDE 24 BY 60

YOU GET .4

SO

30 x .4 = 12

FUNCTION RULES FOR DATA

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IN THIS CASE THE FUNCTION RULE

COULD BE Y = -X² - 2X

BECAUSE (SUBSTITUTING THE VARIABLES)

-(-1)² - 2(-1) = -1 + 2 = 1

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STATISTICAL QUESTIONS

IN ORDER FOR A MATH PROBLEM TO TYPICALLY BE CONSISDERED A STATISTICAL QUESTION, THE ANSWER MUST REQUIRE THE COLLECTING OF DATA AND WHERE THERE WILL ALSO BE A VARIABILITY OF DATA — THE PROBLEM CAN’T JUST BE ANSWERED BY COUNTING, FOR EXAMPLE.

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RATIO

SOLVING RATIO PROPORTIONS

• A proportion is two ratios with an equal sign between them.

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FINDING PERCENT

• Because "Percent" means "per 100" think:

"this should be divided by 100“

• So 75% really means ⁷⁵/₁₀₀
• And 100% is ¹⁰⁰/₁₀₀ or exactly 1 (100% of any number is just the number, unchanged)
• And 200% is ²⁰⁰/₁₀₀ or exactly 2 (200% of any number is twice the number)
• 5% = .05 and 50% = .5

2% = .02 and 20% = .2

1% = .01 and 10% = .1 and 100% = 1

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WHAT IS 15% OF 60?

.15 X 60 = 9

70% OF WHAT NUMBER

IS 35?

70 35

----- = -----

100 X

CROSS MULTIPLY

100 X 35 ÷ 70 = 50

50 IS THE ANSWER

PERCENT CHANGE FORMULA

.2

5 1.0 or 20% decrease

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PERCENT PROBLEMS

IF 5 PERCENT OF 300 STUDENTS HAVE PERFECT ATTENDANCE. WHICH EQUATION CAN BE USED TO DETERMINE THE NUMBER OF STUDENTS WITH A PERFECT ATTENDANCE RECORD?

1/4 X 300

1/20 X 300

1/5 X 300

5 X 300

ANSWER

1/20 X 300= 15 (15 STUDENTS)

FOR 1/20 EQUALS 5 PERCENT (1 DIVIDED BY 20 EQUALS .05, OR 5%)

. 05

20 1.00

CONVERTING A FRACTION TO A PERCENT

FINDING AVERAGES

MODE

THE MODE IS THE NUMBER THAT

APPEARS THE MOST OFTEN.

Example: 3,4,8,9,9,2,8,9

9 is the mode.

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FINDING AVERAGES

MEDIAN

THE MEDIAN OF A SET OF NUMBERS

(ARRANGED IN ASCENDING ORDER)

IS THE MIDDLE NUMBER (if there is an

odd number of items in the set). If there is an even number in the set, the median is the mean of the middle two numbers.

Example: 3,4,6,9,21,24,56

9 is the median.

FINDING AVERAGES

THE MEAN IS WHAT IS USUALLY CALLED AVERAGE.

TO CALCULATE THE MEAN

ADD ALL OF THE NUMBERS.

THEN DIVIDE BY THE TOTAL NUMBER OF NUMBERS ADDED.

Example: 2,8,15,23

The mean is 48 ÷ 4 = 12

12 is the average.

FINDING RANGE

THE RANGE IS SIMPLY THE DIFFERENCE BETWEEN THE HIGHEST AND LOWEST NUMBERS IN A DISTRIBUTION.

FOR EXAMPLE

4,6,9,3,7

The lowest number is 3. The highest number is 9. The range is 9 – 3 = 6

So the range is 6 in this example.

AVERAGES

EXAMPLE

13. 13 13 13 14 14 15 18 21

MEAN: 15

MEDIAN: 14

MODE: 13

RANGE: 8

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PROBABILITY FORMULA

NUMBER OF FAVORABLE

OUTCOMES

PROBABILITY = -----------------------

NUMBER OF POSSIBLE

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OUTCOMES

Example: Using the above spinner, what is the probability that you will spin a 6?

ANSWER 1 IN 8

WHEN TWO EVENTS ARE

INDEPENDENT OF ONE ANOTHER,

YOU HAVE TO MULTIPLY

Example: What is the probability of spinning a red and the number 2?

ANSWER: 1/4 X 1/8 = 1/32

COMBINATIONS

• IF THERE ARE A NUMBER OF SUCCESSIVE CHOICES TO MAKE AND THE CHOICES ARE INDEPENDENT OF EACH OTHER (ORDER MAKES NO DIFFERENCE) THE TOTAL NUMBER OF CHOICES IS THE PRODUCT OF EACH OF THE CHOICES.

Example: How many combinations of shirts and ties are there if there are 5 different color shirts and 3 different color ties?

ANSWER: 5 X 3 = 15

SIMPLE PERMUTATIONS

• IF THERE ARE A NUMBER OF SUCCESSIVE CHOICES TO MAKE AND THE CHOICES ARE AFFECTED BY THE PREVIOUS CHOICE OR CHOICES THEN PERMUTATIONS ARE INVOLVED

Example: How many ways can you arrange the letters

L O V E in a row?

ANSWER: 4 X 3 X 2 X 1 = 24

Example: How many ways can you arrange 5 boxes of cereal in a row?

ANSWER: 5 X 4 X 3 X 2 X 1 = 120

TYPES OF POLYGONS

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CONVEX & CONCAVE

CONVEX HEXAGON: Any 2 points

of this figure can be connected

with a straight line with all parts

of the line staying within the figure.

For a

CONCAVE HEXAGON

this is not true.

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A POLYGON is a closed plane figure, having three or more, usually straight, sides; triangle, square, hexagon�An “irregular” polygon is one that does not have all sides equal and all angles equal.�A polygon is "regular" only if all angles are equal and all sides are equal otherwise it is irregular.�

• Triangle is a three-sided polygon.
• Equilateral triangle has all sides of equal length.
• Isosceles triangle has two side of equal length.
• Scalene triangle has no sides that are of equal length.
• Quadrilateral is a four-sided polygon. TRIANGLES
• Pentagon is a five-sided polygon.
• Hexagon is a six-sided polygon.
• Octagon is an eight-sided polygon.
• Decagon is a ten-sided polygon.

TYPES OF�TRIANGLES

TYPES OF QUADRILATERALS

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COORDINATE GEOMETRY

�GRAPHS�

TYPES OF ANGLES

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�INTERSECTING LINES AND ANGLES MOVING ACROSS PARALLEL LINES�

• IN THE DRAWING BELOW, THE TWO BLACK LINES ARE PARALLEL. THE RED LINE INTERSECTS THE PARALLEL LINES AND IS CALLED THE TRANSVERSAL.
• WHEN TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL LINE, THE ANGLES BETWEEN THE PARALLEL LINES ARE CALLED THE INTERIOR ANGLES (ANGLES 3,4,5,6). THE LINES THAT ARE OUTSIDE THE PARALLEL LINES ARE CALLED THE EXTERIOR ANGLES (1,2,7,8).
• CORRESPONDING ANGLES ARE CONGRUENT (THE SAME). BELOW ARE FOUND FOUR PAIRS OF CORRESPONDING (CONGRUENT )ANGLES: 1 & 5, 2 & 6, 3 & 7, 4 & 8

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ANGLES 1 & 2 EQUALS

180 DEGREES

ANGLES 1,2,3, & 4

EQUALS 360 DEGREES

ANGLES

AN ANGLE IS FORMED BY TWO RAYS THAT SHARE THE SAME END POINT (THE END POINT IS CALLED THE VERTEX).

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ANGLES

ADJACENT ANGLES SHARE A COMMON SIDE AND A COMMON VERTEX. ANGLES 1 & 3 ARE ADJACENT ANGLES AS ARE ANGLES 2 & 4.

VERTICLE ANGLES ARE FOUND OPPOSITE ONE ANOTHER. ANGLES 1 & 4 ARE VERTICLE ANGLES AS ARE ANGLES 2 & 3.

SUPPLEMENTARY ANGLES HAVE A SUM OF 180 DEGREES (MAY FORM A STRAIGHT LINE). ANGLES 1 & 3 ARE SUPPLEMENTARY.

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1

2

3

4

ANGLES

A RIGHT ANGLE HAS A MEASURE OF 90 DEGREES.

AN ACUTE ANGLE HAS A MEASURE LESS THAN 90 DEGREES.

AN OBTUSE ANGLE HAS A MEASURE OF MORE THAN 90 DEGREES.

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RIGHT ACUTE OBTUSE

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�PYTHAGOREAN THEOREM�

The Pythagorean Theorem is the relationship that exists among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, i.e., A squared plus B squared equals C squared.

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POLYGON�A TWO-DIMENSIONAL SHAPE WITH STRAIGHT SIDES: TRIANGLE, RECTANGLE, PENTAGON

REGULAR POLYGON

SIDES WITH THE SAME LENGTH

IRREGULAR POLYGON

SIDES OF DIFFERENT LENGTHS

RECTANGLE

7

3

RECTANGLE

AREA = LENGTH X WIDTH

PERIMETER = 2 X LENGTH + 2 X WIDTH

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EXAMPLE

AREA = 21

PERIMETER = 20

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TRIANGLE

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CIRCLE

AREA = π X R² (pi X radius squared)

CIRCUMFERENCE = 2 X π X R

(2 X pi X radius)

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EXAMPLE

AREA = 3.14 X 9 = 28.26

CIRCUMFERENCE = 2 X 3.14 X 3 = 18.84

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RECTANGULAR SOLID

5

4

6

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RECTANGULAR SOLID

SURFACE AREA EQUAL

2 X LENGTH X WIDTH + 2 X LENGTH X HEIGHT + 2 X WIDTH X HEIGHT

VOLUME EQUALS

LENGTH X WIDTH X HEIGHT

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EXAMPLE

SURFACE AREA = 2(24) + 2(30) + 2(20)= 148

VOLUME = 5 X 6 X 4 = 120

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CYLINDER

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10

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3

CYLINDER

SURFACE AREA = 2 X π (PI) X RADIUS X HEIGHT + 2 X π (PI) X RADIUS SQUARED

VOLUME = π (PI) X RADIUS SQUARED X HEIGHT

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EXAMPLE

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SURFACE AREA

(2 X 3.14 X 3 X 10) + (2 X 3.14 X 9) = 244.9

VOLUME

3.14 X 9 X 10 = 282.6

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FLIP (also called reflection)…SLIDE (also called translation)…TURN (also called rotation)

SHAPES

SPHERE CONE TRIANGULAR PRISM CUBE CYLINDER

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TRIANGULAR PYRAMID

�MEASUREMENT�

• 1 GALLON = 4 QUARTS
• 4 CUPS = 1 QUART
• 1 CUP = 8 OUNCES

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• 1 TEASPOON OF LIQUID

IS ABOUT 5 MILLILITERS

• 1,000 MILLILITERS

EQUAL 1 LITER

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• 12 INCHES = 1 FOOT
• 3 FEET = 1 YARD
• 5,280 FEET = 1 MILE

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• 1 CENTIMETER IS ABOUT THE WIDTH OF A FINGERNAIL
• 100 CM = 1 METER
• 1,000 METERS = 1 KILOMETER
• 1 KILOMETER = 62% OF 1 MILE

MEASUREMENT

• 16 OUNCES = 1 POUND
• 2,000 POUNDS = 1 TON

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• 1 PAPERCLIP = 1 GRAM
• 1,000 GRAMS =1 KILOGRAM
• 1 KILOGRAM = 2.2 POUNDS

FAHRENHEIT

• 212 DEGREES BOILING
• 32 DEGREES FREEZING

CELSIUS

• 100 DEGREES BOILING
• 0 DEGREES FREEZING

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• 70 FAHRENHEIT= 21 CELSIUS
• AVERAGE BODY TEMPERATURE IS 98.6 FAHRENHEIT OR 37 CELSIUS

METRIC SYSTEM

EXAMPLES

1 KILOMETER EQUALS 1,000 METERS

1 METER EQUALS 1,000 MILLIMETERS

1 LITER IS 1,000 MILLILITERS

1 KILOGRAM EQUALS 1,000 GRAMS

CONVERSION TO STANDARD

1 METER EQUALS 3.26 FEET

1 KILOMETER EQUALS 0.62 MILES

1 LITER EQUALS 0.26 GALLONS

1 KILOGRAM EQUALS 2.2 POUNDS

METRIC SYSTEM

A pencil is 15 centimeters long.

How long is the pencil in millimeters?

ANSWER

150

Why?

1 centimeter equals 10 millimeters.

ALGEBRA

PROBLEM

x + 6 = 10

SOLUTION

x + 6 – 6 = 10 – 6

x = 4

ALGEBRA

PROBLEM

x ÷ 3 = 4

SOLUTION

x ÷ 3 = 4

x ÷ 3 X 3 = 4 X 3

x = 12

ALGEBRA

PROBLEM

6y = 24

SOLUTION

6y = 24

6y ÷ 6 = 24 ÷ 6

y = 4

ALGEBRA

PROBLEM

8x + 3 = 27

SOLUTION

8x + 3 = 27

8x + 3 – 3 = 27 – 3

8x = 24

8x ÷ 8 = 24 ÷ 8

x = 3

ALGEBRA

BELOW THE EXPONENTS (ALSO CALLED THE DEGREES OF THE TERMS) ARE… 2 AND 3

THE COEFFICIENTS ARE … 6, 4, 7, AND - 5

6xy² - 4x + 7y³ - 5

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TERMS

POLYNOMIALS

5xy² MONOMIAL (1 TERM)

5x - 2 BINOMIAL (2 TERMS)

4x + 5y² - 7 TRINOMIAL (3 TERMS)

ALGEBRA

MONOMIALS

DEGREE OF A MONOMIAL IS THE SUM OF THE EXPONENTS FOUND IN THE DIFFERENT VARIABLES INVOLVED.

A CONSTANT TERM HAS A DEGREE OF 0 (ZERO) UNLESS THE TERM IS 0 (THIS IS CONSIDERED AN UNDEFINED DEGREE).

THE NUMERIC CONSTANT IN A MONOMIAL IS CALLED THE COEFFICIENT.

BELOW IS THE DEGREE AND THE COEFFICIENT OF A FEW MONOMIALS.

ALGEBRAIC EXPRESSION AND EQUATIONS (difference between)

A MATHEMATICAL PHRASE GROUPING NUMBERS AND VARIABLES TOGETHER IS AN ALGEBRAIC EXPRESSION

7X + 4

AN ALGEBRAIC EQUATION IS A MATHEMATICAL PHRASE WITH

TWO EXPRESSIONS SET TO EQUAL ONE ANOTHER

7X + 4 = 50