Reteaching 5-1. Ratios
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1 Reteachig - Ratios A ratio is a compariso of two umbers by divisio. You ca write a ratio three ways. Compare the umber of red tulips to the umber of yellow tulips. red tulips yellow tulips to : or orage mums To fid equal ratios multiply or divide each part of the ratio by the same d Multiply by. ozero umber. The ratio is i simplest form. d Divide by. Use the drawigs at the top of the page. Write each ratio i three ways.. yellow tulips to red tulips. white mums to orage mums to ; : ; to ; : ;. red tulips to orage mums. yellow tulips to white mums to ; : ; to ; : ;. red tulips to all flowers. orage mums to all flowers to ; : ; to ; : ; 7. tulips to mums 8. white mums to tulips 8 to 8; 8 : 8; 8 8 to 8; : 8; 8 9. yellow tulips to all flowers 0. yellow tulips to orage mums to ; : ; to ; : ; Write two ratios equal to the give ratio. white mums. : Sample aswers: : 0; :. 8 to 0 Sample aswers: to ; to 0 Write each ratio i simplest form.. 0 : : : 8 8 : 9 Pearso Educatio Ic. publishig as Pearso Pretice Hall. All rights reserved. Reteachig Accelerated Grade 7 Lesso -
2 Reteachig - Uit Rates ad Proportioal Reasoig A rate is a ratio that compares two quatities measured i differet uits. The cost for 0 copies is $.0. The rate is $.0/0 copies ($.0 per 0 copies). A uit rate is a rate that has a deomiator of. You ca compare usig uit rates. To fid the uit rate for 0 copies: $.0 $.0/0 copies = 0 = $ = $. The uit rate is $0. per copy. This is also the uit price. Use the Copy Ceter chart. Fid the uit rate. COPY CENTER Color Copies copy $0. 0 copies $.0 copies $.0 0 copies $.0 copies $.00 For the better buy compare uit rates. The uit price for 0 copies is $0./copy. The uit price for copy is $0./copy. Sice $0. $0. the 0-copy price is the better buy.. copies. copies. 0 copies $.0 $.00 $.0 0 $.0 $.00 $.0 0 $0.0/copy $0.0/copy $0.09/copy Write the uit rate for each situatio.. drive 800 mi i 0 h. 90 mi o gal of gasolie 0 mi/hr mi/gal. jog 000 m i mi 7. $.0 for 7 tickets m/mi $.0/ticket Fid each uit price. The determie the better buy. 8. juice: 8 oz for $. 9. cloth: yd for $. 8 oz for $.70 yd for $7.78 $0.07/oz; $0.087/oz; 8 oz 0 0 $.8/yd; $.0/yd; yd Pearso Educatio Ic. publishig as Pearso Pretice Hall. All rights reserved. 0. socks: pairs for $.0. pecas: lb for $.80 pairs for $9.00 oz for $.00 $.7/pair; $.0/pair; pairs $0.0/oz; $0.0/oz; lb Reteachig Accelerated Grade 7 Lesso -
3 Reteachig - Proportios A proportio is a equatio statig that two ratios are equal. If two ratios form a proportio the cross products are equal. Cosider ad. 0 0 Both ratios are equal to the ratios are proportioal ? = 00? 00 = 00 Complete the cross products to determie which pairs of ratios could form a proportio. The write or o ? 0 = 0? = 8 8? 8 = 0? = 0? = 8? = 80 Determie if the ratios i each pair are proportioal o o 0 o Pearso Educatio Ic. publishig as Pearso Pretice Hall. All rights reserved. Reteachig Accelerated Grade 7 Lesso -
4 Reteachig - Solvig Proportios Solvig a proportio meas fidig a missig part of the proportio. You ca use uit rates to solve a proportio. First fid the uit rate. The multiply to solve the proportio. Shaw filled 8 bags of leaves i hours. At this rate how may bags would he fill i hours? Fid a uit rate for the umber of bags per hour. Divide by the deomiator. 8 bags 8 bags hours hours bags hour The uit rate is bags per hour. Multiply the uit rate by to fid the umber of bags he will fill i hours. Uit rate Number of hours Total T T T = At this rate Shaw ca fill bags i hours. If two ratios form a proportio the cross products are equal. Solve. Write the cross products.? =? Simplify. = Solve the equatio. = Solve.. The bookstore advertises otebooks for $7.7. At this rate how much will 7 otebooks cost?. Leroy ca lay bricks i hours. At this rate how may bricks ca he lay i 7 hours? Solve each proportio usig cross products... 0.? =? 0 = 0 = = = = 8 Solve each proportio. $ Pearso Educatio Ic. publishig as Pearso Pretice Hall. All rights reserved. Reteachig Accelerated Grade 7 Lesso -
5 Reteachig - Similar Figures Two polygos are similar if correspodig agles have the same measure ad the legths of correspodig sides are proportioal. You ca use proportios to fid missig legths i similar () figures. AB correspods to XY. Fid correspodig sides. AC correspods to XZ. BC correspods to YZ. Write ratios of their legths i a proportio. Substitute the iformatio you kow. Write cross products. Solve for. AB XY XZ AC 7. = 7. = The figures are similar. Fid the correspodig sides. The complete the proportio ad solve for.. AB correspods to QR.. BC correspods to RS. CA correspods to SQ. BC CA SQ RS 8 0 = The pairs of figures below are similar. Fid the value of each variable The legth of XZ is uits Pearso Educatio Ic. publishig as Pearso Pretice Hall. All rights reserved. Reteachig Accelerated Grade 7 Lesso -
6 Reteachig - A scale drawig is a elarged or reduced drawig of a object. A is a scale drawig. O this the pool is cm from the horse corral. What is the actual distace from the corral to the pool? Maps ad Scale Drawigs Silver Lake Camp Use the scale. Write a ratio of distace o the to actual distace. (cm) actual (m) Write a proportio usig the scale. (cm) actual (m) Use cross products. Solve for. = = 0 m The pool is 0 m from the corral. swimmig pool horse corral SCALE cm m lodge Use the iformatio o the. Write ad solve a proportio to fid the distace.. O the the mess hall is cm from the pool. What is the actual distace from the pool to the mess hall? =. The pool is actually m from the lodge. How far would the pool be from the lodge o the? = mess hall. The lodge is cm from the horse corral o the. What is the actual distace from the corral to the lodge? actual actual actual 00 m =. The mess hall is 0 m from the lodge. How far would the mess hall be from the lodge o the? actual 0. cm = cm. A volleyball court will be built 7 m from the lodge. How far would the volleyball court be from the lodge o the? m Pearso Educatio Ic. publishig as Pearso Pretice Hall. All rights reserved.. cm Reteachig Accelerated Grade 7 Lesso -
7 Reteachig -7 You ca use a table to determie if there is a proportioal relatioship. Compare the ratios to see if there is a proportioal relatioship. Proportioal Relatioships Hours Hours Pages 0 Pages 0 0 d There is a proportioal relatioship betwee pages ad hours. You ca use a graph to fid the uit rate. The lie passes through (0 0) ad ( ) therefore it passes through ( ). Sice r the the uit rate is pages/hour. 0 Z Z d There is ot a proportioal relatioship betwee pages ad hours. You ca use a ratio to fid the uit rate. The value of the ratio of quatities i a proportioal relatioship is called the costat of proportioality which is equivalet to the uit rate. pages hour Determie whether each table represets a proportioal relatioship. If so fid the costat of proportioality x 7 y $0.0 $.00 $7.0 y ( r) x 7. Z 7 ; there is ot a proportioal relatioship. x d Fid the pages per hour by dividig the umber of pages by the umber of hours. d Simplify. The costat of proportioality is. The uit rate is pages/hour. Pearso Educatio Ic. publishig as Pearso Pretice Hall. All rights reserved. y 7 7 ; the costat of proportioality is 7. Reteachig Accelerated Grade 7 Lesso -7
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