Transcript 009

MATH 009 JIM DAWSON
1.1 WHOLE NUMBERS
• Memorize the place values from
ones(units) through trillions to
see the pattern.
• Write 26,709 in standard form:
• Twenty-six thousand seven
hundred nine
• Write five thousand forty-four
in standard form.
• 5,044
• Write 200,493 in expanded
form.
• 200,000+400+90+3
1.4 MULYIPLYING WHOLE
NUMBERS
• Memorize the multiplication
table up to 12 x 12.
• Factors- numbers that are
multiplied together to equal a
PRODUCT( the answer to a
multiplication problem).
1.5 DIVISION OF WHOLE
NUMBERS
• Division is used to separate
objects into equal groups.
• Quotient- the answer to a
division problem.
• Most mistakes in division are
made in the subtraction portion.
1.6 EXPONENTS
• Base- the number being
multiplied.
• Exponent- the number to the
top right of the base telling you
how many times the number by
itself.
ORDER OF OPERATIONS
AGREEMENT
• Do all operations inside
parentheses( other grouping
symbols as well)
• Solve exponents
• Multiply and divide as they
occur from left to right
PEMDAS
• Add and subtract as they occur
from left to right
• 5 x (8-4)-2; 8-4=4
• 5 x 4 – 2; 5 x 4=20
• 20-2=18
1.7 PRIME FACTORING
• Questions(steps)
• Is the number prime?
• Yes- prime
• No – prime factor the number
and move to question #2.
• #2- is the number an even
number? Yes- start with 2
•
N0- go to question #3
• Add the digits of the number
together, if the answer is
divisible by 3-Yes- start with 3
• No- go to question #4
• Does the number end with a 5?
•
Yes- start with 5
•
N0- start with 7 and
continue until a prime number
works ( hit or miss).
2.1 FINDING THE LCM AND
GCF
• LCM- Least Common Multiple
• Factor the numbers and place
them in a chart.
• Circle the largest product of
each set of numbers( prime
numbers).
LCM AND GCF
• Multiply the numbers( the
answer will be equal to or
greater than the largest number
given).
GCF
• GCF- Greatest Common Factor
• Factor the numbers and place
the answer in a chart
• Circle the smallest product in
each set of numbers that are in
common.
2.2 CONVERTING
FRACTIONS
• Conversion #1- to change an
improper fraction to a mixed
number or whole number.
• Numerator divided by the
denominator and write the
remainder as a fraction.
CONVERTING FRACTIONS
• Conversion #2- convert a mixed
number or whole number to an
improper fraction.
• Multiply the whole number times
the denominator and add the
numerator. The denominator stays
the same.
CONVERTING FRACTIONS
• Conversion #3- Building
equivalent fractions.
• Divide the new denominator by the
original denominator and multiply
the answer by the original
numerator to place the fraction in
higher terms.
CONVERTING FRACTIONS
• Conversion #4- Simplest form or
Reducing fractions.
• Prime factor the numerator and
denominator then cancel the
common numbers. Multiply the top
and bottom to finish reducing.
2.4 ADDITION OF
FRACTIONS
• Find the LCM(LCD) of the
denominators. Use the LCM
process, if needed.
• Place the fractions in higher
terms (conv. # 3).
ADDITION
• Add the numerators ONLY.
• Place the answer in simplest
form by using conversions # 1
and/or #4. You may use one ,
both, or neither.
• Add the whole numbers.
2.5 SUBTRACTION OF
FRACTIONS
• Find the LCM(LCD) of the
denominators. Use the LCM
process, if needed.
• Place the fractions in higher
terms.
SUBTRACTION
• Subtract the numerators, borrow
if needed.
• Reduce , if needed.
• Subtract the whole numbers.
2.6 MULTIPLYING
FRACTIONS
• Change the mixed nos. or whole
nos. to improper fractions.
• Early reducing ( cross-cancel)
• Multiply numerators and
denominators.
• Change improper to mixed nos.
2.7 DIVISION OF FRACTIONS
• Change mixed nos. or whole
nos. to improper fractions.
• Change division to
multiplication and invert the
fraction after the divided by
symbol.
DIVISION
• Early-reducing(cross-cancel)
• Multiply numerators and
denominators
• Change an improper fraction to
a mixed no. and reduce the
proper fraction