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On each page, manipulatives graphics are placed in stacks in the visible display area and also to the right, off-screen, in storage. There is also one more copy on the storage page.V As noted above, colored cells are hot, formula cells, and compute the labeled items.$ To create your own pages of notes:H1st: Save this spreadsheet in a location you can find on your computer.X2nd: Insert a new worksheet in the spreadsheet -- Insert, Worksheet, or Alt + I, then W.C3rd: Name the page -- right-click the tab at the bottom, then name.?4th: Copy and paste material from other worksheets as desired.#Signed Number Board for Subtraction b1208.xls+Reduce A Fraction in Tilted Array Display. 1st: /Make IDENTICAL rows (or columns), if possible. 2nd: :Remove ALL BUT ONE row (or column) from the display area. 3rd: IRepeat steps 1 and 2 to see if the reduced fraction may also be reduced.  3Fraction Bars are stored above. Work area is below.reducebarsReduce the fraction 12/15*Reduce A Fraction in Tilted Tile Display. 0Reduce Fractions in Numerator / Denominator Form1st:BSimplify the tiles in the numerator and denominator display areas.2nd:"Factor the numerator, if possible.3rd:$Factor the denominator, if possible.4th:WUse the factors they DON'T have in common as the new numerator and the new denominator.GWhenever possible, remove a top factor with an identical bottom factor.TO REDUCE, USE THE!FACTORS THEY DON'T HAVE IN COMMON-AS THE NEW NUMERATOR AND THE NEW DENOMINATOR.5th:4Repeat steps 1 and 2 and 3 and 4 as often as needed.(2x -2x -12)/(4x+8)Reduce (2x -2x -12)/(4x+8). Reduce 12/15.ex. I. Reduce. 2x -2x -12 = x -x -6 (x+2)(x-3)x - 34x+82x+4(x+2)(2)`Multiply 2/3 by 4/5mult (x+y) cubedRepresent and Analyze (-4) / (4)(x - 2) / ( 2 - x)  (x+4)(x-2)/(x+4)(2-x)analyzeFractions -4/4 etc.binomialDIVISIONUse a blank rectangular sheet of paper to separate the storage region from the display area and to create a border for the rectangular area. RRepresent the divisor vertically in storage on the left edge of the display area. eRepresent the dividend in the display area in descending order beginning with the upper left corner. Arrange, if possible, the dividend in IDENTICAL rows in the display area. Matching one row per vertical divisor tile leaves remainders extra in the storage area. Once a single rectangular arrangement of tiles (extra remainder tiles excluded) is created, represent the appropriate quotient horizontally in the storage area as dictated by the dividend. 6th:mIf a single rectangular arrangement of tiles is not possible, add zeros as needed to fill the required area. 7th:%Read the quotient and the remainder. x3 - y3(x - y)(x2 + xy + y2)  Dividex3 - y3byx-yExpandx-y to the 2nd and 3rd powers"Divide a cubic. Expand a binomial. Multiply in Tilted Tile Display.5Reduce by Tilted Tile and by Numerator / Denominator.b ߼k]~seSE)|~ TF  cc.  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