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MATH 009 JIM DAWSON

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.

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MATH 009 JIM DAWSON

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  1. MATH 009 JIM DAWSON

  2. 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

  3. Write five thousand forty-four in standard form. • 5,044 • Write 200,493 in expanded form. • 200,000+400+90+3

  4. 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).

  5. 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.

  6. 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.

  7. 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

  8. 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

  9. 1.7 PRIME FACTORING • Questions(steps) • Is the number prime? • Yes- prime • No – prime factor the number and move to question #2.

  10. #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

  11. 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).

  12. 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).

  13. LCM AND GCF • Multiply the numbers( the answer will be equal to or greater than the largest number given).

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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).

  20. 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.

  21. 2.5 SUBTRACTION OF FRACTIONS • Find the LCM(LCD) of the denominators. Use the LCM process, if needed. • Place the fractions in higher terms.

  22. SUBTRACTION • Subtract the numerators, borrow if needed. • Reduce , if needed. • Subtract the whole numbers.

  23. 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.

  24. 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.

  25. DIVISION • Early-reducing(cross-cancel) • Multiply numerators and denominators • Change an improper fraction to a mixed no. and reduce the proper fraction

  26. Order, Exponents, Order of Operations • Order using the inequality symbols. 1. Find the common denominators. 2. Place the fractions in higher terms.

  27. Order continued • 3. Compare the numerators and place the correct inequality symbol in the answer.

  28. Fractional Exponents • Write the original problem out and use the steps for multiplying fractions. Cross-cancel and multiply the numerators and the denominators.

  29. Order Relation To compare two fractions with different denominators; find the common denominator, place the fractions in higher terms, then compare the numerators and place the correct inequality symbol between the fractions.

  30. Order of Operations • Use PEMDAS the same way as Chapter 1.

  31. Combining Like Terms • Combine the terms that have the same variable part using the steps for addition and subtraction of fractions.

  32. Solving for the Unknown • If the variable and fraction are connected by addition use subtraction in both sides of the equation to solve the unknown. • If they are connected by subtraction use addition on both sides to solve. • If the variable and unknown are connected by multiplication use division on both sides.

  33. Decimal Notation • Standard Form: To write a decimal as a number( the place values tenths through hundred-billionths MUST be memorized). • Standard Form to Words: To write a decimal from a number to words. • Rounding: Find the place value being rounded and look ONE place to the right and use the same rules for rounding whole numbers.

  34. Addition and Subtraction of Decimals • Add and subtract decimals just the same as whole numbers and place the decimal point in the answer.

  35. Multiplying Decimals • Count the total number of place values in all of the numbers. • Set the problem up like whole numbers and multiply. • Move the decimal point from right to left in the answer.

  36. Division of Decimals • Make the divisor a whole number by moving the decimal point. • Move the decimal point the same number of places on the dividend. • Divide the same as whole numbers.

  37. Converting a Fraction to a Decimal • To change a fraction to a decimal: NUMERATOR divided by the DENOMINATOR. Round if asked to in the directions or the answer will terminate.

  38. Change a Decimal to a Fraction • Write the decimal as a fraction by using a multiple of 10 in the denominator and the number part in the numerator. • Reduce the answer if possible.

  39. Change a Decimal with a Fraction to a Fraction • Drop the decimal point and multiply the mixed number times 1 over 100.

  40. Ratios and Rates • Ratio- A comparison of two quantities with the same units( apples to apples…etc.) • Write the ratio as a fraction in simplest form(reduce) then with a colon (: ) and the word ( to ). • Rate- A comparison of two quantities that different units( apples to oranges…etc.) • Write as a fraction and reduce then STOP!

  41. Unit Rates • Unit Rate- A comparison of two quantities that have different units per 1. • Write the unit rate as a rate(fraction) then divide: NUMERATOR divided by the DENOMINATOR. This will make the answer per 1. • Label the answer.

  42. Proportions • Proving the proportion True or Not True. • Cross-multiply: If the answers are the same it is a True (T) proportion. If the answers are not the same it is a Not True (NT) proportion. • Solve for n: Cross-multiply the common numbers and divide the number across from n.

  43. More Proportions • Word problems: Write the two rates with like units in both numerators and like units in both denominators. • Cross-multiply and divide the number across from n.

  44. Converting Between Fractions, Decimals, and Percents • Change a percent to a decimal (then to a fraction). • Move the decimal point TWO places from left to right and drop the percent symbol. Multiply by 0.01. • Change the decimal to a fraction and reduce if needed.

  45. Change a Decimal to a Percent • To change a decimal: Move the decimal point TWO places from left to right or multiply by 100%. • If the decimal has a fraction move the decimal point TWO places from left to right and drop the decimal point.

  46. Change a Fraction to a Percent • Change the fraction to a decimal ( numerator divided by denominator) first. • Move the decimal point TWO places from left to right. • In the division, if the answer does not terminate by hundredths, write the remainder as a fraction in simplest form.

  47. Round to the nearest tenth ( of a percent ). • Change the fraction to a decimal to the ten-thousandths place value. • Move the decimal point TWO places from left to right and round the percent to the nearest tenth of a percent.

  48. Change a Percent with a Fraction to a Fraction • If the percent has a fraction in it: Drop the % symbol and multiply by 1 OVER 100 to convert to a fraction.

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