Notes: The Number System (6.NS. 8) Adding Fractions ) Find a common denominator. (LCM) ) Convert the fractions.(equivalent Denominators) ) Add the numerators and keep the denominator. ) Simplify. 6 8 9 7 6 6 7 7 6 7 7 Subtracting Fractions : ) Find a common denominator. (LCM) ) Convert the fractions. (Equivalent Denominators) )Subtract the numerators and keep the denominator. Borrow if necessary. ) Subtract the whole numbers. ) Simplify. 8 8 8 0 8 (Borrow) 9 8 6 9 8 7 7 Adding Fraction Subtracting Fraction : Multiplying Fractions ) Convert any mied numbers to improper fractions. ) Cross reduce if possible. ) Multiply straight across. ) Simplify if possible. Eamples of Multiplying Fractions 6 9 9 0 6 0 6 9 9 9 0 9 0 9 Multiplying Fraction Multiplying Fractions Eample : Dividing Fractions ) Convert any mied numbers to improper fractions. ) Keep, Change, Flip (KCF) Keep the first fraction. Change the operation to multiplication. Flip the second fraction to its reciprocal. ) Follow multiplication rules. 6 K C F 6 X Dividing Fractions Eample: 0 70 0 70 60 0 K C F 70 0 6 0 0 6 Dividing Fraction Dividing Fractions Eample
Notes: The Number System (6.NS. 8) Simplifying Fractions ) Find the GCF of the numerator & denominator. ) Divide each number by the GCF. OR Use the upside down cake method 6 Factors 6:,,, 8, 6 :,,,, 0, N D Eample 6 (N) (D) 6 8 0 / Converting Mied Numbers to Improper Fractions ) Multiply the denominator and the whole number. ) Use that answer and add it to the numerator. ) Keep your original denominator. () (8) Eamples 6 Simplifying Fractions Converting Mied Numbers to Improper Fractions Converting Improper Fractions to Mied Numbers ) Divide the numerator by the denominator. (That's your whole number) ) The remainder is your numerator. ) Keep your original denominator. ) Simplify final answer. Eamples 8 r 8 8 0 8 Equivalent Fractions Multiply or divide the numerator and denominator by the same number to get an equivalent fraction. 8 Equivalent 7 6 7 9 Eample??? () Converting Improper Fractions to Mied Numbers Equivalent Fractions Vocabulary Dividend the amount you want to divide up, the total amount you have Divisor the number you divide by, how big you want each group to be Quotient the answer to a division problem, how many groups you end up with (fraction bar) divisor *Hint* The r in divisor makes the house *Hint* quotient Long Division dividend *Hint* The dividend is the number in the house dividend divisor quotient When you're racing to the house, the first number gets in and closes the down on the second number. Long Division Long Division
Notes: The Number System (6.NS. 8) Parts of a Decimal Division Problem Quotient (Answer). 6.. 6. Divisor (Dividing by) Dividend (Start with) Adding Decimals Review. Line up your decimal points.. Add in 0's as placeholders.. Drop your decimal point straight down.. Add each number. Eamples:.67.90 0.68.70 0 08.9 8.7 6.8.9 Parts of a Decimal Divison Problem Adding Decimals Subtracting Decimals Review. Line up your decimal points.. Add in 0's as placeholders. Subtract each number.. Drop your decimal point straight down. Eamples:.67.9 0.68.7 8.9 6 0.67 0.68.70.0 08.9 0.98 06..90 0.77 9 6 0 0 Multiplying Decimals Review. Line up your numbers to the right.. Multiply without looking at the decimal points.. Count how many digits are to the right of each decimal point.. Move you decimal to the left that many times. 6 Eample:.7.8.7.8 0 0 0 7 0 0 0 0 0 () () () Total Digits to right of decimal 0. Subtracting Decimals Multiplying Decimals Dividing Decimals Review. Format your numbers. Eample:..6. Move decimal point in.6. the divisor and dividend to the right until the 00. 6.. divisor is a whole number. 8. Divide the numbers. 8 8 0. Answer:. Place Value Chart Dividing Decimals Place Value Chart
Notes: The Number System (6.NS. 8) Vocabulary Least Common Multiple The smallest number other than 0, that is a multiple of two or more given numbers. Greatest Common Factor The largest common factor of two or more given numbers/ (How most people learn it) Find the of and. LCM (Least Common Multiple) :, 8, 7, 96,,, 68, 9, 6 :, 6, 96, 8, 60, 9,, 6 LCM: 96 GCF (Greatest Common Factor) :,, 8, 6 :, 6, 8 GCF: 8 Vocabulary Find the of and.. What number goes into both numbers?. Factor out that number.. Repeat as many times as possible. GCF Multiple the left side. LCM Multiple the L shape. (Using Upside Down Cake Method) Find the of and. 6 6 8 GCF: 8 LCM: 96 GCF LCM (multiply side) (multiply L shape) 6 6 8 6 6 8 Gina purchases materials to make watches for a jewelry show. There are 6 watch faces in a pack and 9 watch bands in a pack. What is the least number of watches Gina can make without having any supplies left over. What are you solving for? LCM How do you know? Building up until equal (Multiples) Answer: 8 watches 9 6 8 Madison has 6 roses and daisies to use in floral centerpieces for a party. Each centerpiece will have the same number of flowers and will contain only roses or only daisies. What is the greatest number of flowers that Madison can use in each centerpiece? 7 6 8 6 7 What are you solving for? GCF How do you know? Breaking apart (Separating) Answer: Flowers Word Problems Word Problems
Notes: The Number System (6.NS. 8) Plotting Points on a Number Line Plot each point on the number line. Point B: Point A:. Point X: / 8 7 6 0 6 7 8 Identify each point on the number line. k c m a 8 7 6 0 6 7 8 a: 8 k: 7. c: m:. Opposites( ) on a Number Line Opposite Number Two numbers that are an equal distance from zero on a number line. 8 7 6 0 6 7 8 What is the opposite of: : : : : 7: 7 ( 6): 6 Reminder: The opposite sign is a negative sign. Plotting Points on a Number Line Opposites Absolute Value Absolute Value The distance of a number from zero on a number line. 8 7 6 0 6 7 8 Solve: I I II I I I 7I 7 I6I 6 I I Reminder: Distance is always positive. Comparing and Ordering Numbers smaller larger 8 7 6 0 6 7 8 > greater than 6 > < less than < equal I I Order from least to greatest. 6,.,., I I, 0, 6.,, 0, I I. Absolute Value Comparing and Ordering Positive and Negative Numbers Determining if it's Positive or Negative Positive Numbers Increase Plus Ecess of Credit Above Gain Received Profit Negative Numbers Decrease Minus Below Owes Subtraction Debt Loss Determining if it's Positive or Negative ft below sea level $8 in my account 8 Debt of $.8.8 Increase of 8 minutes 8 Owes $ to cafe 7 o below zero 7 Loss of yards / feet above sea level / Determining if it's Positice or Negative Determining if it's Positice or Negative
Notes: The Number System (6.NS. 8) X Ais The Coordinate Plane Y Ais Quadrant II Quadrant I (,) (,) Origin (0,0) (, ) (, ) Quadrant III Quadrant IV Parts of a Coordinate Plane The coordinate plane is divided into four regions. Each region is called a quadrant. ais: the horizontal number line. y ais: the vertical number line. Origin: the center of the coordinate plane. It has coordinates (0, 0). It is the point where we always start when we are graphing. Ordered pair: a pair of numbers that represents a unique point in the coordinate plane. The first value is the coordinate and the second value is the y coordinate. E. : (, ) is the coordinate is the y coordinate Coordinate Plane Important Parts. F Identify the Correct Quadrant. A II. H. A. B. D. E. G. C B I C IV D III E IV F ais G y ais H I. E. B. F. G. H. D Plotting Points. A. C A (,6) B (,) C (8, ) D (, ) E (0,7) F (, ) G (,0) H (0,0) Identifying the Quadrant Plotting Points Writing Coordinates. H A (7, 6). D. B. G. E. F. C. A B (,) C (0, ) D (6,7) E (6,0) F ( 6, ) G (0,0) H ( 9,9) Mied Review Write the coordinate and the Quadrant. A (6, 6) IV. F. B. E. H. C. G. D. A B (0,7) y ais C (0,0) origin D (, 7) III E (8,) I F ( 8,7) II G (6, ) IV H ( 7,0) ais Writing Coordinates Mied Review 6