# Teas Math portion

What is a simple fraction?

A fraction that is not top heavy like 2/3.

What is an improper fraction?

A fraction that is top heavy like 3/2.

Where is the numerator in a fraction?

The numerator is the top part of the fraction. Thus in � : 1 is the numerator while 2 is the denominator.

Where is the denominator in a fraction?

The denominator is the bottom part of the fraction. Thus in � : 1 is the numerator while 2 is the denominator.

Define the symbol =, <, >

#NAME?

What kind of numbers is 2�, 2�, 3�?

These numbers are examples of mixed numbers.

What is an improper fraction?

It is a fraction where the numerator is greater than the denominator like 23/4.

What are the steps of changing a mixed fraction to an improper fraction? Using example 2�

Using example 2�.
1) Multiply 4 x 2 = 8
2) Add the sum of 8 to numerator thus 8+3= 11
3) Keep the same denominator and the answer is 11/4.

What are the steps of changing an improper fraction to a mixed fraction? Using example 11/4

Using example 11/4
1) Divide the mixed fraction. 11/4 is 2 with a remainder of of 3.
2) Thus it is 2�. *please note that we kept the same denominator when applying the remainder.

How do you change a fraction so you can add like terms? Use example � + � = ?

Use example � + � = ?
1) Determine which fraction you would like to change. In this case it would be �. To add fractions, the denominator must be the same.
2) To change � we multiply both numerator and denominator by 2/2 to equal 2/4. *2/4 and � are the s

Whenever possible, when taking a test, reduce the fractions into ----- ----- ?

Whenever possible, when taking a test, reduce the fractions into LOWER TERMS

What are the steps in reducing a fraction to its lowest term? Use example 8/16.

Use example 8/16.
1) Divide both the numerator and the denominator with the number that you determined will go evenly for both terms.
In this case it would be 8 so 8/16 � 8/8= 1/8

What are the steps in adding fractions with the same denominator? Use example 2/5 + 1/5 =?

Use example 2/5 + 1/5 =?
1) Just add the numerators because both fractions are like terms with the same denominator.
Thus 2/5 + 1/5 = 3/5 or 2+1= 3 then place the denominator back 3/5.

What are the steps in adding fractions with the different denominators? Use example 2/4 + 1/12 =?

Use example 2/4 + 1/12 =?
1) Find a common denominator by reducing a fraction or multiplying a fraction to make it into like terms.
Thus 2/4 x 3/3 = 6/12
2) Add the like terms keeping the denominator the same.
Thus 6/12 + 1/12 = 7/12

What are the steps in subtracting fractions with the same denominator?
Use example 7/8 - 3/8 = ?

Use example 7/8 - 3/8 = ?
1) Just subtract the numerators because both fractions are like terms with the same denominator.
Thus 7/8 - 3/8 = 4/8
*don't forget to reduce the fraction 4/8 � 2/2 = 1/4

What are the steps in subtracting fractions with the unlike denominators?
Use example 5/6 - 3/5 = ?

Use example 5/6 - 3/5 = ?
1) Find a common denominator by reducing a fraction or multiplying a fraction to make it into like terms.
Thus the GCF (greatest common factor) of the denominator 6 & 5 is 30. 5/6 x 5/5 = 25/30, 3/5 x 6/6= 18/30. Using the new te

Can mixed fraction be added or subtracted?

YES. Provided they follow the same like term rules with the denominator being the same.

Can mixed numbers be added or subtracted?

YES. Provided they follow the same like term rules with the denominator being the same. Make your life easier by changing the mixed number into a mixed fraction and then add or subtract to eliminate common mistakes as long as they have like denominators.

What is the general rule when multiplying fractions?

To multiply fractions. multiply the numerator to get the new numerator, and multiply the denominator to get the new denominator.

What is the "shortcut" called cross cancellation when multiplying fractions?

Cross cancellation is where you simply the fractions diagonally from one another. Example *reduced
2
1 X 8* 1 2
__ __ = _ x _ = 2/15
4* X 15 1 15
1

What is the general rule for reading a decimal?

Numbers to the right of the decimal point have a value less than 1 and the numbers to the left of the decimal point have a value greater than 1.

Review the decimals position as whole numbers into decimal numbers.

Ten thousands 10,000
Thousands 1,000
Hundreds 100
Tens 10
Ones 1
Decimal Point .
Tenths .1
Hundredths .01
Thousandths .001
Ten thousandths .0001

What is the general rule for adding and subtracting decimals?

Place the decimals in a vertical column so the decimals all align and add/subtract.
102.60
3.02
+00.45
-----------
106.07

What is the general rule for multiplying decimals?

The same method for multiplying whole numbers applies to decimals but the location of the decimal in the total depends on the number of places of the original problem. Example
6.3
X 7.6
------
378
4410
---------
4788 ----> 47.88 (original problem has 2 de

Why is multiplying by 10, 100 or 100- fast and easy to calculate?

Multiplying by 10, 100 or 100 is fast and easy to calculate by simply moving the decimal point the same number of places to the right, as there are zeroes in the multiplier.
Example
0.712 X 10 = 7.12 (moving one decimal place to the right)
0.09 X 1000= 90

How do you divide a decimal by a whole number?

Divide a decimal by a whole number, place the decimal point in the quotient directly above the decimal point of the dividend.
Example: 30.5 � 5 = 6.1
6.1
5 ?------
30.5
30.
-----
5
5
--
0

What are the steps to divide two decimals?

Change the decimal number in the divisor to a whole number and move the dividend by the same number of places that you moved the decimal point in the divisor and solve.
1.2 � 0.48 ------> 12. � 04.8 = 0.4

Why is dividing by 10, 100 or 100- fast and easy to calculate?

Dividiing by 10, 100 or 100 is fast and easy to calculate by simply moving the decimal point the same number of places to the left, as there are zeroes in the multiplier.
Example
0.712 � 10 = 0.0712 (moving one decimal place to the left)
9 � 1000= 0.009 (

How do you change fractions into decimals?

Divide the numerator by the denominator and place a decimal point after the dividend.Add zeroes as needed and make sure that the decimal point is directly above the decimal point the dividend and then divide. Example 3/8
0.375
8 ?----------
3.000
2.4
----

How do you change decimals into common fractions?

The decimal expressed becomes the numerator of the fraction. The number of decimal places to the right of the decimal will tell you what the denominator is.
To change 0.75 = 75 � ?
1 place = a denominator of 10
2 place = a denominator of 100
3 place = a d

How do you change a percent (%) into a fraction?

1) Drop the % symbol 20% to 20
2) Divide the number by 100 20 � 100 = 1/5
3) Reduce the fraction to its lowest terms.
4) Change the mixed number is necessary.

How do you change a fraction into percent (%)?

1) Multiply the fraction by 100. 1/2 X 100/1 = 100/2
2) Reduce if necessary. 100/2 = 50/1 = 50
3) Change the improper fraction to a mixed number.
4) Add the % symbol.

How do you change a percent (%) into a decimal?

1) Drop the % symbol. When you drop the % symbol from a whole number, a decimal point takes the place of the symbol. For example, when you drop the % symbol from 68.1%, the decimal point replaces the % symbol.
2) Divide by 100 by moving the decimal point

How do you change a decimal to a percent (%) ?

1) Multiply by 100 by moving the decimal point two places to he right. For 3.19 you would move the decimal point two places to the right, so 3.190 = 319.0
2) Add zeroes as needed.
3) Add the % symbo. 319.0 = 319%

What is a ratio?

A ratio is used to express a relationship between two units or quantities by division. A slash (/) or colon (:) is used to indicate division, and both are read as "is to" or "per". For the ratio of "1 is to 2" you can write 1:2 or 1/2. The numerator is al

What is a proportion?

A proportion states that two rations are equal. A proportion can be written as a common fraction from in which the numerator and denominator of one fraction have the same relationship as the numerator and denominator of another fraction. The equal symbol

How do you verify that two ratios in a proportion are equal?

For a fraction, multiply the numerator of each ration by its opposite denominator. The sum of the product will be equal.
Example : 1/3 : 2/6
2 x 3 = 1 x 6 (by cross multiplying)
6 = 6

How do you solve for x?

1) Write down what is available or known in a fraction format.
2) Complete the proportion by writing down what you desire in a fraction format, making sure that the numerators and the denominators are like units.
3) Cross multiply the numerator of each ra

Using the example solve for X.
75 milligrams of Demerol, a painkiller, is prescribed for a patient following surgery. The medication is available as a liquid solution, with each milliliter of solution containing 100 milligrams of Demerol. To administer th

1) 100mg/ 1ml is known
2) The complete proportion by adding the known and what is desired using X.
100mg/ 1ml = 75mg/ Xml
3) Cross multiply 100X = 75
4) Solve for X.
x= 3/4ml

When letters or numbers are written together without any sign or symbol between them, you should assume that.......

When letters or numbers are written together without any sign or symbol between them, you should assume that...... multiplication should be used between those digits.

What are algebraic terms?

Algebraic terms can be numbers or letter, or combination of letter and numbers in an expression separated + or - signs. The expression 5z + 2 + 4x� has three terms, 5z, 2, and 4x�.

Expression that have only one term are called?

Monomials (mono= one)

Expression that have more than one term are called?

Polynomials (poly=many)

The letters in an algebraic expression are called ?

variable or unknowns

When a variable is multiplied by a number, the number is called?

the coefficient of the variable, In the expression 5x� + 2yz, the coefficient of x� is 5a and the coefficient of yz is 2.

What are the four axioms of algebra?

If you add the same number of expression to each side of an equation, the equation remains equal.
2) Subtraction axiom
If you subtract the same number of expressions from each side of an equation, the equation remains equal.
3) Multiplic

What is the addition axiom of algebra?

If you add the same number of expression to each side of an equation, the equation remains equal.
Example: X - 15 = 30
X- 15 + 15 = 30 + 15
X = 45

What is the subtraction axiom of algebra?

Subtraction axiom
If you subtract the same number of expressions from each side of an equation, the equation remains equal.
Example: X + 15 = 30
X +15 - 15 = 30 - 15
X = 15

What is the multiplication axiom of algebra?

Multiplication axiom
If you multiply by each side of an equation by the same number or expression, the equation remains equal.
Example: X/3 = 12
X/3 x 3/1 = 12/1 x 3/1 or
X/3 x 3 = 12 X 3
X = 36
X = 15

What is the division axiom of algebra?

Division axiom
If each side of an equation is divided by the same number or expression, the equation remains equal.
Example: 3X = 12
3X / 3 = 12 / 3
X = 4

What are the 3 multiplication rules for negative and positive integers?

1) A negative number times a negative number equals a positive integer. (-)(-) = (+)
2) A positive number times a positive number equals a positive integer. (+)(+) = (+)
3) 1) A negative number times a positive number equals a negative integer. (+)(-) = (

What are the 4 division rules for negative and positive integers?

1) A negative number divided by a negative number equals a positive number. (-) � (-) = +
2) A positive number divided by a positive number equals a positive number. (+) � (+) = +
3) A negative number divided by a positive number equals a negative number.

What are the addition and subtraction rules for negative and positive integers?

Change signs as appropriate and solve using addition or subtraction..

What are the rules for simplifying expression into a simpler one?

1) Perform any multiplication or division before performing addition or subtraction.
2) The order in which you multiply numbers and letters in a term does not matter.
3) The order in which you add terms does not matter.
4) If there are roots or powers in

If an expression has more than one set of parentheses, what should you do?

If an expression has more than one set of parentheses, get rid of the inner parenthesis first and then work out through the rest of the parentheses.

True or False. The only algebraic terms which can be combined are like terms?

TRUE

What is an equation?

An equation is a statement that says two algebraic expressions are equal.

What is the order of calculations? *hint My Dear Aunt Sally

Order of operations or calculations.
Multiplication, Division, Addition and Subtraction

Celsius to Fahrenheit

F= 1.8 (C) +32

Fahrenheit to Celsius

C=(F-32)/1.8

Kelvin

K=Celsius + 273.15

Distance Formula

D=rate/time

How much heat is needed to vaporize a liquid?

(Formula)
H=ML
h: heat needed
m: mass
l: latent heat

How much heat is needs to be removed in order to condense a gas to a liquid? (Formula)

H=-ML
h:heat needed
m: mass
l: latent heat

Percent increase formula

[(new value-original value)/original value] x 100

Percent decrease formula

[(original value-new value)/original value] x 100

1 Kilometer

1,000 meters

1 Meter

100 centimeters

1 Centimeter

10 millimeters

1 Mile

1760 yards

1 Mile

5280 feet

1 Yard

3 meters

1 Foot

12 inches

1 Inch

2.54 centimeters

1 Liter

1,000 milliliters

1 Milliliter

1 Cubic Centimeter

1 Gallon

128 ounces

1 Gallon

4 quarts

1 Quart

2 pints

1 Quart

946 ounces

1 Pint

2 cups

1 Cup

8 ounces

1 Ounce

30 milliliters

1 Kilogram

1,000 grams

1 Kilogram

2.2 pounds

1 Gram

1,000 milligrams

1 Ton

2,000 pounds

1 Pound

16 ounces

1 Ounce

2 Tablespoons

1 Teaspoon

5 milliliters

What are bar graphs or histograms used for?

compare frequencies of an event
histograms are for continuous events
bar graphs are for noncontinuous events

What are line graphs used for?

show changes over a period of time or compares the relationship between two quantities

What is a mode?

Mode is the number that appears most often in a set. There could be more than one.
Example: 122234445 The mode would be 2 & 4.

What are the equations for rectangles?

Rectangles
PERIMETER= 2L + 2W
AREA= LW
=360�

What are the equations for squares?

Squares
PERIMETER= 4S
AREA= S2
=360�

What are the equations for triangles?

triangles
PERIMETER= S1 + S2 + S3
AREA+ 1/2 BxH
=180�

What are the equations for circles?

Circles
DIAMETER: 2R
CIRCUMFERENCE= 2?R
AREA= ?R�
=360�

What are the equations for hypotenuse and diagonals?

Hypotenuse and diagonals
A�+B�=C�
WITH C ALWAYS BEING THE DIAGONAL

What is the formula for the SLOPE?

S= Y?-Y?
_______
X?-X?

What is the slope intercept formula?

SLOPE INTERCEPT FORMULA
Y= MX + B

What can u tell about the slope after looking at it?

�A POS SLOPE WILL ALWAYS POINT UP
�A NEG SLOPE WILL ALWAYS POINT DOWN
� A 0 SLOPE RUNS PARALLEL TO THE X AXIS

Review the US measurement chart.

US MEASUREMENTS: FLUID
8 OZ= 1 CUP
2 CUPS= 1 PINT
2 PINTS= 1 QRT
4 QRTS= 1 GALLON

Review the US Measurement weights.

US MEASUREMENTS: WEIGHT
16 OZ= 1 POUND
2000 LBS= 1 TON

Review the US measurement in lengths.

US MEASUREMENTS: LENGTH
12 INCHES= 1 FOOT
3 FEET= 1 YARD
5280 FEET = 1 MILE

Review Mass in the metric system.

METRIC: MASS
1 GRAM=
�1000 MG
�100 CG
�10 DECIGRAMS
�1/10 DECAGRAMS (1DECA=10GRAMS)
�1/100 HECTOGRAMS (1 HECT= 100 GRAMS)
�1/1000 KG (1 KG= 1000 GRAMS)

Review the lengths in the metric system.

METRIC: LENGTH
1 METER=
�1000 MM
�100 CM
�10 DECIMETERS
�1/10 DECAMETERS (1DECA=10M)
�1/100 HECTOMETERS (1 HECT= 100 M)
�1/1000 KMETERS (1 KG= 1000 M)

Review fluids in the metric system.

METRIC: FLUID
1 LITER=
�1000 ML
�100 CL
�10 DECILETERS
�1/10 DECALITER (1DECA=10L)
�1/100 HECTOLITER (1 HECT= 100 L)
�1/1000 KL (1 KG= 1000 L)

Review metric to US conversions.

METRIC/US CONVERSIONS
1 M= 1.09 YARDS
2.54 CM = 1 INCH
28 GRAMS= 1 OZ
1 KG= 2.2 LBS
1L= 1.06 QRTS