6 th Grade Unit 5 Lesson 1 Using Decimals in a Shopping Context Illustrative Mathematics

unit five lesson one using decimals in shopping context number one mai had fourteen dollars and fifty cents she spent four dollars and 35 cents at the snack bar and five dollars and 25 cents at the arcade what is the exact amount of money mai has left 14.50 minus four dollars and 35 cents equals ten dollars and fifteen cents then she spent five dollars and twenty five cents so ten dollars and fifteen cents minus five dollars and twenty five cents equals dollars and ninety cents number two large cheese pizza costs seven dollars and fifty cents diego has forty dollars to spend on pizzas how many large cheese pizzas can he afford explain or show your reasoning created chart with the number of pizzas on the right hand column and the cost of the pizzas in the left hand column one pizza cost seven dollars and fifty cents two pizzas cost fifteen dollars three pizzas cost seven dollars and fifty cents more than two pizzas so that would be twenty two dollars and fifty cents four pizzas that's easy you just double the price of two pizzas so double fifteen dollars to get thirty dollars five pizzas you're just adding seven dollars and fifty cents to thirty dollars which is thirty seven dollars and fifty cents and finally six pizzas is forty five dollars that's too expensive so diego can buy five whole pizzas with forty dollars number three tickets to show cost five dollars and fifty cents for adults and four dollars and twenty five cents for students family is purchasing two adult tickets and three student tickets estimate the cost five dollars and fifty cents can be estimated as six dollars and four dollars and twenty five cents can be estimated as four dollars so six plus six plus four plus four plus four or six plus four plus six plus four plus four that's the same as ten plus ten plus four or twenty four dollars the estimated total cost would be just about twenty four dollars what is the exact cost five dollars and fifty cents plus five dollars and fifty cents plus four dollars and twenty five cents plus four dollars and twenty five cents plus four dollars and twenty five cents is the same as eleven dollars plus twelve dollars and seventy five cents and that equals twenty three dollars and seventy five cents the exact cost for the tickets is twenty three dollars and seventy five cents if the family pays 25 what is the exact amount of change they should receive minus 23.75 equals and 1.25 cents the family should receive and change one dollar and 25 cents number four chicken costs three dollars and 20 cents per pound and beef costs 4.59 per pound answer each question and show your reasoning what is the exact cost of three pounds of chicken three dollars and 20 cents plus three dollars and twenty cents plus three dollars and twenty cents equals nine dollars and sixty cents three pounds of chicken at three dollars and twenty cents per pound comes to total of nine dollars and sixty cents what is the exact cost of three pounds of beef four dollars and fifty nine cents plus four dollars and fifty nine cents plus four dollars and fifty nine cents equals thirteen dollars and seventy seven cents so three pounds of beef at four dollars and fifty nine cents per pound comes to total of thirteen dollars and seventy seven cents how much more does three pounds of beef cost than three pounds of chicken since three pounds of beef cost thirteen dollars and seventy seven cents and three pounds of chicken cost nine dollars and sixty cents we'll have to subtract nine dollars and sixty cents from 13.77 and that comes to four dollars and 17 cents three pounds of beef costs four dollars and seventeen cents more than three pounds of chicken number five how many one-fifth leader glasses can lin fill with one and half liter bottle of water one and half divided by one-fifth equals three-halves divided by one-fifth and to figure this out we need to multiply three-halves times the reciprocal of one-fifth which is five over one so three-halves times five over one equals five-halves or seven and half lynn can fill seven and half one fifth liter glasses with one and half liter bottle how many one and half liter bottles of water does it take to fill 16 liter jug 16 divided by one and half equals 16 divided by three halves which is the same as 16 over one times the reciprocal of three halves which is two-thirds so 16 over one times two-thirds equals thirty-two thirds or ten and two-thirds it would take ten and two-thirds one-and-a-half liter bottles to fill 16 liter jug number six use the grid to complete this problem let the side length of each small square on the grid represent one half unit draw two different triangles each with base five and one-half units and area of 19 and 1 4 units squared why does each of your triangles have area 19 and 1 4 units squared explain your reasoning the area of triangle is half the base times the height they've given us the area that's 19 and 1 4 units squared they've given us the base that's five and half units we can figure out the missing area by seeing how many times five and half goes into nineteen and one fourth so 19 and one-fourth divided by five and half will equal half of the height 19 and 1 4 divided by five and one-half is the same as 77 fourths divided by 11 halves 77 4 times the reciprocal of 11 halves is 77 4 times 2 11 and that equals seven halves or three and half and remember that three and half is half of the height so if three and half is half of the height the full height would be seven so the height equals seven units here i've drawn two triangles both with base of five and half units and height of seven units both their areas are nineteen and one-fourth units squared number seven find each quotient five-sixths divided by one-sixths this one's easy because they have common denominators since the bottom number's the same we can just do 5 divided by 1 and that equals 5. or you can go ahead and treat it as if you didn't notice that it had common denominators and you could multiply 5 6 times the reciprocal of 1 6 so that would be five sixths times six over one which equals five over one or five one and one sixth divided by one twelfth one and one sixth can be rewritten as 7 so 7 6 divided by 1 12 is the same as 7 6 times the reciprocal of 1 over 12 which is 12 over 1. 7 6 times 12 over 1 equals 14 over 1 or 14. 10 6 divided by 1 24th that can be rewritten as 10 6 times the reciprocal of 1 24th which is 24 over 1. ten sixth times twenty four over one equals forty over one or forty congratulations you have completed unit five lesson one using decimals in shopping context you