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BASIC COLLEGE
MATH
MT102
Whole Number Objectives
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Standard and expanded form
Write a standard numeral in words
Determine if a given number is less than or greater than another.
Round a number to the nearest ten, hundred, or thousand
Be able to add, subtract, multiply and divide
Determine if a number is prime or composite
Find the prime factors of a number
Write a number as the product of primes
Order of operations
Solving simple equations
Standard and expanded form
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Examples of standard form:
 406
 5143
 98
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Examples of expanded form:
 400
+0+6
 5000 + 100 + 40 + 3
 90 + 8
Write a standard numeral in words
using place value
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Know your place value chart!
 Pg.
7
The “and” is only used to hold the decimal
point
 The place values behind the decimal end
with a “th”
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Determine if a given number is less
than or greater than another.
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A < B (A is less than B)
 Example:
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5<9
A > B (A is greater than B)
 Example:
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12 > 5
Round a number to the nearest ten,
hundred, or thousand
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Rules for rounding:
 Step
1: Underline the place to which you are
rounding.
 Step 2: If the first number to the right of the
underlined place is 5 or more, add one to the
underlined number. Otherwise do not change
the underline number.
 Step 3: Change all the numbers to the right of
the underlined number to zeros.
Be able to add, subtract, multiply
and divide
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The definitions:
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Addend = numbers to be added
Sum = the result or total in an addition problem
Minuend = the larger of the numbers in a subtraction problem
Subtrahend = the number being subtracted
Difference = the result in a subtraction problem
Multiplier, multiplicand, factor = numbers being multiplied
Product = the result in a multiplication problem
Dividend = the number being divided
Divisor = the number used to divide
Quotient = the result in a division problem
Be able to add, subtract, multiply
and divide
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Practice, practice, practice
Determine if a number is prime or
composite
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A prime number is a number having
exactly two different factors, itself and 1.
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examples: 2, 3, 5, 7, and 11
A composite number is any number that is
greater than one and not prime.
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example: 4, 6, 8, 9, and 12
Find the prime factors of a number
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Take the number and divided by the first
few primes
 2,
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3, 5, 7, 11, and so on
For help look at the rules of divisibility
 Pg.
73 & 74
Write a number as the product of
primes
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You can write in the form of a factor tree or
in base and exponent form.
 Pg.
75
Order of operations
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PEMDAS
 Do
all calculations inside grouping symbols
like parentheses, brackets, or braces
 Evaluate all exponential expressions
 Do all multiplications and divisions in order
from left to right
 Do additions and subtractions in order left to
right.
Solving simple equations
The solution of an equation is the
replacement that makes the equation a
true statement. When we find the solution
of an equation we say that we have solved
the equation.
 Examples:
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X – 7 = 14
 X + 13 = 26
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Fractions p.111
Diagrams
 http://www.visualfractions.com/index.htm
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Proper and Improper Fractions
p.111
A proper fraction is a fraction in which the
numerator is less than the denominator.
 An improper fraction is a fraction in which
the numerator is equal to or greater than
the denominator.
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Improper Fractions as Mixed
Numbers p.112
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A mixed number is a number representing the sum of a
whole number and a proper fraction.
To write an improper fraction as a mixed number:
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Divide the numerator by the denominator. This will be your whole
number in your mixed number
The fractional part uses the remainder as the numerator and the
same denominator as the original fraction.
Example:
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17/2 = 8 1/2
Mixed Numbers as Improper
Fractions p.1113
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To write a mixed number as an improper
fraction:
 Multiply
the denominator by the whole number
and add the numerator.
 Use the number obtained above as the
numerator and the same denominator as the
denominator.
Equivalent Fractions p.121
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Equivalent fractions
 Fraction A can
 15/30
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be reduced to equal fraction B
=½
To obtain an equivalent fraction you
multiply the numerator and denominator
by the same number.
 3/5
= 3(2)/5(2) = 6/10
Reducing Fractions p. 123
A fraction is reduced to lowest terms when
there are no common factors in the
numerator and denominator.
 You can usually start by dividing the
numerator and denominator by 2 or 3
(primes)
 This is done quickly by finding the GCF
(greatest common factor)
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Comparing Fractions p.124
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To compare fractions write both fractions
with the same denominator.
 Easiest:
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product of both denominators
Example: 3/5, 10/30
3(30)/5(30) = 90/150, 10(5)/30(5) = 50/150
 Which fraction is larger?
 3/5 > 10/30
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Multiplication of Fractions and
Mixed Numbers p.134
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Multiply fractions across
 Products
of numerators
 Products of denominators
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Multiply mixed numbers
 turn
all mixed numbers into improper fractions
 Multiply away
Fractions and exponents p.134
(2/3)2
 2/3(2/3) = 4/9
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Division of Fractions and Mixed
Numbers p.135
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Flip and multiply!
Flip and multiply!
Flip and multiply!
3/5 divided by 2/3
(3/5)3/2 = 9/10
Dividing mixed numbers
 turn
all mixed numbers into improper fractions
 Divide away
Adding and Subtracting Fractions
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When adding/subtracting fractions:
 The
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fractions must have the same denominator
Finding the lowest common denominator
 You
can list multiples p. 145
 You can divide each denominator by primes (factor
tree)
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Finding the greatest common denominator
 Multiply
the denominators
 REDUCE!
Adding and Subtracting Mixed
Numbers
Convert mixed numbers in to improper
fractions
 Find a common denominator
 Add or subtract away!
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Order of operations
Please
 Excuse
 My
 Dear
 Aunt
 Sally
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Decimals p.192
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Write the word name for a decimal
Write a decimal in expanded form
Add two or more decimals
Subtract one decimal from another
Multiply two or more decimals
Divide one decimal by another
Round decimals
Write a fraction as an equivalent decimal
Write repeating decimal as a fraction
Compare two or more decimals
Compare fractions to decimals
Order of operations for decimals
Write the word name for a decimal
p.192
Remember the decimals point means
“and”
 Example
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 567.89
 Five
hundred sixty seven and eighty nine
hundredths
Write a decimal in expanded form
p.193
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Example
 245.34
 200
+ 40 + 5 + 3/10 + 4/100
Add two or more decimals p.193
The decimal points need to be lined up
 Remember to add from right to left
 Example
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245.67
 + 32.23
 277.9
Subtract one decimal from another
p.196
The decimal points need to be lined up
 Remember to subtract from right to left
 Example
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145.67
 - 22.20
 123.47
Multiply two or more decimals
p.204
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Multiply the two decimal numbers as if they were whole
numbers.
The number of decimal digits in the product is the sum if
the number of decimals digits in the factors
Example
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2.29 → two decimal digits
x 3.5 → + one decimal digit
1145
687
8.015 → three decimal digits
Divide one decimal by another
p.206
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Write the problem in long division form
Move the decimal point in the divisor until a
whole number is obtained
Move the decimal point in the dividend the same
number of places as you moved in the divisor
Place a decimal point directly above the decimal
point in the dividend
Divide
Divide one decimal by another
p.206
6.5 √52
 65 √52
 65 √520.
 65 √520.
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Round decimals p.208
Same principle as rounding whole
numbers
 Example
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 Round
 45.68
45.6783 to the nearest hundredth
Write a fraction as an equivalent
decimal p.215
You need to do the division in the fraction
to get the equivalent fraction
 Example
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2
⅜ = 19/8 = 2.375
Write repeating decimal as a
fraction p.218
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Write the repeating part as the numerator of the
fraction
The denominator consist of as many nines as
there are digits in the repeating decimal
Example
 .¯9
 9/9
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Another example
 .¯324
 324/999
Compare two or more decimals
p.224
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To compare decimals make sure all decimals
have the same number of decimal digits (use
extra 0s to the right of the decimal point if
necessary)
Compare corresponding digits starting at the left
until two of the digits are different. The number
with the larger digit is the larger of the decimals
Example
 9.234
> 9.210
Compare fractions to decimals
p.225
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Write both in the same form (decimals or
fractions)
Order of operations for decimals
p.227
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Again
 Please
 Excuse
 My
 Dear
 Aunt
 Sally
Ratio, Rate & Proportions
Ratio = a quotient of two numbers
 Rate = is a ratio used to compare two
different kinds of measures
 Proportions = a equation that states that
two ratios are equal.
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3 ways to write ratios
3 to 8
 3:8
⅜
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* ratios can be reduced, but should not be
written as mixed numbers!
Reducing ratios
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If ratio has decimals, move the decimal point to
make the numbers whole numbers. Remember
you have to move the decimal point the same
number of digits on the top and bottom.
 Example
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7.26 to 2.31
726 to 231
22 to 7
Using mixed numbers in Ratios
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Write 2⅓ days to 2 days as a ratio in lowest
terms.
2⅓
2
Change mixed number to an improper number
7/3
2
7X 1 =7
3 2 6
Solving for an unknown using
proportions.
5=x
8 12
 5(12) = 8(x)
 60 = 8x
 60 = 8x/8
 60/8 = x
 X = 7.5
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Solving for a unit rate
 Unit
rate = a rate in which the
denominator is 1 is called a unit
rate.
Solving for a unit rate
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If my car drove for 450 miles on one tank of gas
(15 gallons), what is the unit rate?
450 miles for 15 gallons
X miles for 1 gallon
450 = x
15 1
450 = 15(x)
450/15 = x
X = 30
Remember to ALWAYS write your units of
measurement
My car gets 30 miles per gallon!