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Journal Chapter 7 and 8

Journal Chapter 7 and 8. Ratios and Proportions. A ratio compares two or more numbers using a division . It can be written as: A to B or A:B or A/B. A proportion is an equation that shows that two ratios are equal . It is written as: A/B = C/D.

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Journal Chapter 7 and 8

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  1. Journal Chapter 7 and 8

  2. Ratios andProportions A ratio compares twoor more numbersusing a division. It can be written as: A to B orA:Bor A/B. A proportionisanequationthat shows thattwo ratios are equal. Itiswritten as: A/B = C/D. Boththeproportionsandthe ratios involve ratios. SolvingProportions: Multiply A times D and B times C. Simplifytofindthevalueofthe variable. a/6 = 5/2 Cross Mutliply 2a = 30 Simplify a = 15

  3. More examples: 5/c = 9/6 30 = 9c 3.3 = c 4/5 = x/9 36 = 5x 7.2 = x 8/9 = 2/a 8a = 18 a = 2.25

  4. Ifyouwantto check ifyourisequal, youneedtosolvetheproportionandthenplug in thevaluethatyoufoudforthe variable. Ifthe ratios are equalthentheproportionisequal. x/2 = 40/16 16x = 80 X = 5 Plug in thevalueofthe variable 5/2 = 40/16 Yes, theproportionisequal. a/3 = 27/a a (squared) = 81 Squaredrootof a (squared) = a andSquaredrootof 81 = 9 So then, a = 9 9/3 = 27/9 Yes, theproportionisequal 5/6 = b/7 35 = 6b 5.8 = b 5/6 = 5.8/7 No, theproportionisnotequal

  5. Similar Polygons Whentwopolygons are similar, theyhavethesameshapebuttheydon’thavethesamesize. A and B are similar. a b

  6. A and B are similar b a A A and B are similar B

  7. Thescale factor describes how muchthesizeof a shapeisenlargedorredudced. Example: A square’ssizeneedsto be increasedwithoutchangingitsshape. Tellthecoordinatesoftheshapeafterbeingincreasedifthescale factor is 2. Coordinatesofthesquare: a(0, 0) b(0, 4) c(4, 4) d(4, 0) 2 x 0 = 0 A = (0, 0) 2 x 0 = 0, 2 x 4 = 8, B = (0, 8) 2 x 4 = 8, 2 x 4 = 8, C = (8, 8) 2 x 4 = 8, 2 x 0 = 0, D = (8, 0)

  8. A picture’ssizeneedsto be increased. Thescale factor is 3. Thecoordinates are

  9. Similar RightTriangles Thealtitudetothehypotenuseof a righttrianglecreatestwotrianglesthat are similar tothe original righttriangle. x/10 = 10/20 20x = 100 X = 5 y/20 = 25/y Y(squared) = 12500 Y = 111.8 z/5 = 25/z Z(squared) = 125 Z = 11.18 y 10 z 20 x

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