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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