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This Concept Map has information related to: Ratio and Proportion, Ratio and Proportion resource Flash Ratio and Proportion Problem Walk throughs on the web (has audio), 3 unknowns spoken these read like reds varied directly as blues aquared and inversely as greens. When there are 80 reds there were 4 blues and 2 greens. How many reds were there when there were 8 blues and ten greens., Ratio Method ???? <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mfrac> <mmultiscripts> <mtext> R </mtext> <mtext> 1 </mtext> <none/> </mmultiscripts> <mmultiscripts> <mtext> R </mtext> <mtext> 2 </mtext> <none/> </mmultiscripts> </mfrac> <mtext> = </mtext> <mfrac> <mmultiscripts> <mmultiscripts> <mtext> B </mtext> <mtext> 2 </mtext> <none/> </mmultiscripts> <none/> <mtext> 2 </mtext> </mmultiscripts> <mmultiscripts> <mmultiscripts> <mtext> B </mtext> <mtext> 2 </mtext> <none/> </mmultiscripts> <none/> <mtext> 2 </mtext> </mmultiscripts> </mfrac> <mtext> ∗ </mtext> <mfrac> <mmultiscripts> <mtext> G </mtext> <mtext> 2 </mtext> <none/> </mmultiscripts> <mmultiscripts> <mtext> G </mtext> <mtext> 1 </mtext> <none/> </mmultiscripts> </mfrac> </mrow> </math>, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> transformations to solve for </mtext> <mmultiscripts> <mtext> R </mtext> <mtext> 2 </mtext> <none/> </mmultiscripts> </mrow> </math> answer <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mmultiscripts> <mtext> R </mtext> <mtext> 2 </mtext> <none/> </mmultiscripts> <mtext> = 64 </mtext> </mrow> </math>, simplify solve by cross-multiplying <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> transformations to solve for </mtext> <mmultiscripts> <mtext> R </mtext> <mtext> 2 </mtext> <none/> </mmultiscripts> </mrow> </math>, Same problem. . . two methods called Variation Methods, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mfrac> <mtext> 1 </mtext> <mtext> 2 </mtext> </mfrac> <mtext> = </mtext> <mfrac> <mtext> x </mtext> <mtext> 10 </mtext> </mfrac> <mtext> : a proportion: equal ratios </mtext> </mrow> </math> EQ Why are equivalent fractions proportional?, simplify solve by cross-multiplying <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> 80∗128 = </mtext> <mmultiscripts> <mtext> R </mtext> <mtext> 2 </mtext> <none/> </mmultiscripts> <mtext> ∗160 </mtext> </mrow> </math>, Proportional Reasoning applications Scale Drawings, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mfrac> <mmultiscripts> <mtext> R </mtext> <mtext> 1 </mtext> <none/> </mmultiscripts> <mmultiscripts> <mtext> R </mtext> <mtext> 2 </mtext> <none/> </mmultiscripts> </mfrac> <mtext> = </mtext> <mfrac> <mmultiscripts> <mmultiscripts> <mtext> B </mtext> <mtext> 2 </mtext> <none/> </mmultiscripts> <none/> <mtext> 2 </mtext> </mmultiscripts> <mmultiscripts> <mmultiscripts> <mtext> B </mtext> <mtext> 2 </mtext> <none/> </mmultiscripts> <none/> <mtext> 2 </mtext> </mmultiscripts> </mfrac> <mtext> ∗ </mtext> <mfrac> <mmultiscripts> <mtext> G </mtext> <mtext> 2 </mtext> <none/> </mmultiscripts> <mmultiscripts> <mtext> G </mtext> <mtext> 1 </mtext> <none/> </mmultiscripts> </mfrac> </mrow> </math> In this method you plug in numbers from both 1st and 2nd scenarios - indicated by the subscripts simplify