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Word problems with ratio’s and proportions notes Absent Tues/Wed 4/30-5/1

Word problems with ratio’s and proportions notes Absent Tues/Wed 4/30-5/1.

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Word problems with ratio’s and proportions notes Absent Tues/Wed 4/30-5/1

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  1. Word problems with ratio’s and proportions notesAbsentTues/Wed 4/30-5/1

  2. Setting up ratio’s and proportions when solving word problems.When solving word problems using 1 ratio(fraction) it is important to get the right information in the numerator and denominator.Ex: when talking about a car do we say:miles per hour or hours per milesWhen solving word problems using proportions(2 ratio’s equal to each other) the numerators and denominators have to be talking about the same thing. There is usually an unknown.Ex: dogs5 = x dogs cats 10 6 cats

  3. Ratio Example • The table below shows the distance and times for 4 days of bicycling. Monday 30 miles 5 hrs. Tuesday 60 miles 12 hrs. Wed. 20 miles 2 hrs. Thurs. 35 miles 5 hrs On which day was the speed and miles the greatest? A) Monday B) Tuesday C) Wednesday D) Thursday • What can we make with these different miles and hours? • We can make ratio’s • What goes in the numerator? Miles or Hrs. • Can we divide these ratio’s? YES or NO • Which day had the greatest speed and miles? • 20 2 Wednesday at 10mph

  4. Ratio Example • Find the unit rate for a 3 lb. package of hamburger that costs $3.75. 3.75 = $1.25 a lb. 3 Solution • How do we set up this ratio? What goes in the numerator and denominator? • The price goes in the numerator and the weight goes in the denominator. • Do we multiply or divide to find the unit rate? • We divide to find the unit rate? Unit rate is $1.25 a lb.

  5. Proportion example • A van travels 600 miles in 15 hrs. How far will the van travel in 10 hrs. miles600 = xmiles hr 15 10 hr 10 · 600 = x · 15 6000 = 15x 15 15 x = 400 miles Solution • How do we set up a proportion? • We set up 2 ratio’s = to each other w/an unknown. • Does it matter what goes in the numerator and denominator of each fraction? • Yes it has to be the same topic in the numerator and denominator. • What is the unknown ? • The unknown is the amount of miles. • What do we do after we make the proportion? • We cross multiply. • What do we do after we cross multiply? We use inverse oper. and divide by 15 to both sides. X = 400 miles

  6. Proportion Example • Pete earns $70 for 5 hrs. of work. How much will he earn after 8 hrs. of work? money70 = xmoney hr 5 8 hr 8 · 70 = x · 5 560 = 5x 5 5 x = $112.00 Solution • How do we set up a proportion? • We set up 2 ratio’s = to each other w/an unknown. • Does it matter what goes in the numerator and denominator of each fraction? • Yes it has to be the same topic in the numerator and denominator. • What is the unknown? • The unknown is the amount of money. • What do we do after we make the proportion? • We cross multiply. • What do we do after we cross multiply? • We use inverse oper. and divide by 5 to both sides. X = $112.00

  7. Proportion Example • On the Padre field trip, there must be one adult for every 5 students. If 45 students go to the game, how many adults must attend? adults1 = x adults kids 5 45 kids 45 · 1 = x · 5 45 = 5x 5 5 x = 9 adults Solution • How do we set up a proportion? • We set up 2 ratio’s = to each other w/an unknown. • Does it matter what goes in the numerator and denominator of each fraction? • Yes it has to be the same topic in the numerator and denominator. • What is the unknown? • The unknown is the # of adults. • What do we do after we make the proportion? • We cross multiply. • What do we do after we cross multiply? • We use inverse oper. and divide by 5 to both sides. X = 9 adults

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