MATH 009 JIM DAWSON. 1.1 WHOLE NUMBERS Memorize the place values from ones(units) through trillions...

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