\.- of the origin are (0,0).!,i

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1 nt Name: Period Stards: Unit 3 Ratio Proportional Relationships Test Review/Studv Guide verbal descriptions of proportional relationships. situation. Vocabulary: Proportional relationship: a relationship between two equal ratios. Constant of proportionality: The constant value of the ratio of two proportional quantities x y; usually written ds y =.kx, where k is the constant of proportionality. ; Direct variation: a relationship between two variables in which they increase or decrease together at a constant rate. Origin: The point of intersection of the vertical horizontal axes of a plane. The coordinates \.- of the origin are (0,0).!,i Ratio: is a comparison of two quantities by division Equivalent ratios: ra{ios that make the same comparison. Proportional/in proportion: ratios that are equivalent. Rate: a comparison of two quantities that have different units. Unit rate: a rate in which the second quantity is 1. Unit price: a unit rate used to compare price per item. Scale drawing: a two dimensional drawing that accurately represents an object. Scale: gives the ratio of the dimensions in a drawing to the dimensions of the object. l;'i' 1,. i Ratios Proportions: 1. A ratio is formed when two quantities are compared. A ratio can be written in three ways: 1,to 2, L:2 or as a fraction 1. \--l Example: Compare 5 apples to 7 oranges as a ratio. This ratio can be written: 5 to 7 or 5 : 7 or I 7

2 2. Equivalent Ratios are ratios that are equal. To find an equivalent ratio you can simplify the original ratio, if possible, or you can multiply the numerator denominator of the ratio by the same number. Example: ; = ';(multiplied numerator denominator by 2) Example: 1 - ] = fltd'r,ded ratio multiplied them by 2 for the second one) the numerator denominator by 3 to find the first equivalent 3. Proportions: Ratios are proportional if they are equal. There are several ways to determine if ratios are proportional: (1)simplifylz) use cross product,(3)find the unit rate of eacfr ratio (a) find tl"re scale factor lf you can simplify ratios to the same value they are proportional. form are not equal; therefore, they are not proportional. ianai when in simplest You can use cross-products to determine if two ratios are proportion. Multiply the numerator of one ratio with the denominator of the second ratio, then multiply the denominator of the first ration bythe numeratorof the second ratio. lf the products are equalthe ratios are proportional A unit rate is the amount for one unit. The unit rate is shown in a ratio when the denominator is one. Finding the unit rate for two quantities will show if the ratios are proportional. Practice for ratios proportions Determine if the ratios are proportional L Z I I I 10 L6 : I t LL 21_ pge

3 Find the value'of the variable: 4s Sx lL -= x 3 L20 : x Find the unit rate: w Sag.gz for 3 cd's 153 cookies for 1.7 people L65 marbles for 1L bags Di rect Variation/Proportional Relationship The graph shows a direct variation: the line goes through the origin (0,0) the relationship is linear (it is a straight Iine). U pgs

4 The following table shows a relationship of x y. To determine if there is a constant of proportionality (direct variation) find the ratio of each relationship of x y: x I 12 v y_ x LLLLl By finding the simplesfform of each ratio you can determine that all ratios are.equivalent; By using x as the denominator you are finding the unit rate which is the constant of proportionality. For this set of data the constant of proportionality is 3. Practice for Direct Variation/Proportional relationship Does the following table represent a direct variation?, if so, what is the constant of proportionality? 1. x l 9 v L Given that y varies directly with x, find the equation of direct variation when x = L5 y Given that y varies directly with x, what is the equation of direct variation if y is 16 when x is 20? 4. lf y varies directlywith x y = t6 when x = 8, what is k? 5. lf y varies directlywith x y = L2 when x = 4, whot is k? \-/ UL\,{ *1

5 Percents, proportional relationships (markups, tax discounts) simple interest. To find the missing value in a when given a part the whole amount or when given the percent either the part or the whole amount use the following equation or proportion: % o whole - part or %o o of = is o/o = Part or 100 whole 100 of o/o [s To change a fractlgq!o a percent ysu dlvide the numerator by the dgnominalor. To change a percent to a decimalyou move the decimal two places to the left. To change a decimal to a percent you move the decimaltwo places to the right. To find the percent of change from one value to another use the following equation: annount of change ori.ginal amount Practice for finding missing values percent of change. L. 40% of what number is 18? 2.54isLsO% of what number? 3. What percent of LZA is 18? is what percent of 75? 5. 3Oo/o of what number is 96? 6. 75% of 40 is what number? 7. What is the percent increase or decrease from $320 to 5192? 8. lf you save 560 on a 5200 purchase, what is the percent of decrease in the cost? rys

6 The equation for finding simple interest is: I = prt ( lnterest = principal. rate r time) \r To find the total amount, p + J = t (principal + interest =total amount) Practice with principal, interest tax: at 6% for 3 years at 17% for 6 years at 4%for 12 years 4. Mrs. Johnson borrowed SSSOO to buy a used car. The bank charged simple interest of 8.25% per year. lf she had a 5 year loan, what was the total she paid for the car? 5,-Mr. Alexer had a loan of 5275,000 at an annual simple interest rate, After five years he had paid the bank 53SO,6Z5 which paid the loan in full. What as the interest rate on the loan? Proportional figures drawings: Proportional (scale) drawings make comparisons find dimensions between models/drawings actual objects. You solve for a missing value by using a proportion. You \-, can use proportions to determine if figures are similar to find an unknown scale. The measure of the model is always the numerator. Practice with proportional figures drawings: 1. A postcard is 4 in. wide by 6 in tall. lf the postcard is scaled to 6 in. wide how tall will it be? 2. A picture is 8 in. wide by 5 in. tall. lt will be turned into a 48 ft. wide billboard. How tall will the billboard be? 3. An isosceles triangle has a base of 20 cm legs measuring 36 cm. How long are the legs of a similar triangle with a base measuring 50 cm? 4. A basketball court is 84 ft long 50 ft wide. lf a model is drawn that is 21 in. long how wide willthe model be? \S/' Pgto