Ratio and Proportion Problems

Problem 1

A class of 22 students needed to collect information from four different places. In order to save time the class decided to divide into four teams and send a team to each place. Because each team had different amounts and kinds of information to collect they decided that a team of four should go to the library, a team of five to the museum, a team of five to the art gallery, and a team of eight to the zoo. When they left each team was given a sack for their lunch. When they returned they shared what each had for lunch and started to complain that the sandwiches in the lunches weren't divided in a fair manner. All teams got foot long sub sandwiches, but each group thought they weren't distributed fairly. The library team got three sandwiches, the museum team got four, the art gallery team got three, and the zoo team got seven. Decide if the distribution of sandwiches was fair and support your answer.

Problem 2Which can of cat food is a better deal? 20 cans for $23 or 12 cans for $15 and what would it cost if I bought 60 cans?

Ratio Table Created by students and teacher

First group |
Teacher added |
Second group |
Teacher added |
||

12 cans |
$15.00 |
15/12 |
20 cans |
$23.00 |
23/20 |

6 cans |
$7.50 |
7.5/6 |
10 cans |
$11.50 |
11.5/10 |

3 cans |
$3.75 |
3.75/3 |
5 cans |
$5.75 |
5.75/5 |

1 cans |
$1.25 |
1.25/1 |
1 cans |
$1.15 |
1.15/1 |

5/4 |
4.6/4 |
||||

60 cans |
$75.00 |
75/60 |
60 cans |
$69.00 |
69/60 |

Asks students if they could add more to ratio table? Student suggests divide 60 by 2 |
/30 |
/30 |
|||

Another student suggests 10 |
/10 |
/10 |
|||

…20,. |
/20 |
/20 |
|||

Also can check by adding some together to get others |

Problem 3I was in a grocery store looking for dog food for Buddy. I found a forty-pound sack for $23 and a twenty-five pound sack for $15. What would be the best deal?

Patchwork quilt square problem

Make a square with 16 congruent smaller squares (4x4). Color each of the16 squares. If six squares are red, then 6/16 was red. What percent is red?

6/16 = 3/8 = 1/4 + 1/8;

1/4 of a hundred is 25; & 1/8 would be 1/2 of 25 = 12 1/2 or 12.5

25 + 12.5 = 37.5; or .25 + .125 = .375

ProblemProve that 1/2 + 2/3 does not equal 2/5.

ProblemWhat is the difference between 3/10 and 2/5?

problemTwo stores are having a sale. Kmart is having 40% off and Walmart is having 25% off. Which is the better deal?

Purpose to see if students can tell that the whole is important. You can't tell which is because you don't know what the whole is. However, one could calculate the differences to find what the breakeven point is so that you could tell. The whole matters.

problemIf each student eats 3/4 of a pizza, then how many pizzas are needed for different amounts of people?

problemGoing to be cooking and need measuring cups. Let's make our own with these strips of paper and containers. Mark 1/2… on paper and glue to side. Paper strips six inches long. Mark 1/2, 1/4, 1/3, 2/3, 1/8, 1/6…

problemA group of six people

have five candy bars and want to share them equally. How much would each person get?

problemI used 2/3 of a can of paint to cover 1/2 of the porch floor. How much paint will be needed for the whole floor?

problemHow many bags of cookies can be make with 12 cookies and three bags?

problemJohn is baking a cake and only has a 1/2-cup measuring tool. The recipe calls for 2/3 of a cup of flour. How many times should he fill the 1/2-cup?

problemGoing to have a pizza party and the recipe is for 4. You will need to be increase it but you are not sure yet by how much. You decide to use a ratio table or a double number line to see how much would be needed for four to 40 people.

problemThe town is going to have a road rally. The course is going to be 24 miles long. The planners want to put signs along the way to let the participants know how far they have traveled. They would like to put signs that read 1/2 way 3/4, 1/8… Where are they going to put the signs? (Use a ratio table or a double number line.)

problemCalculate the percentage of electricity left in a battery (self-check). Convert the rectangle to percent and put time in hours to match on a double number line. Could do the same for light bulbs that are rated for so many hours of life.

problemA merchant wants to know how much money different percentages of $800 is so that s/he can decide if s/he wants to discount the object 10%, 20%, 30% 40%, 50% or more.

problemTime on a

clock. Mark a clock with fourths, thirds, fifths, sixths, and tenths. Try adding different fractions. 1/3 + 1/4 is how many minutes plus how many minutes? Or 1 1/4 - 2/3;

problemChris told Pat that s/he was .8 of the way to their goal of each saving a certain amount of money Pat said that s/he had only .5 of what Chris had. What part of their goal did Past have?

problemChris wanted to buy a leather coat for $350. Mom said she would help but Chris would have to pay 80%. How much would Chris have to pay?

ProblemMy son suggested that a good way to exercise is to jog for 1/3 of an hour and walk for 1/4 of an hour. How much time is that altogether? Or I could walk for 1/3, jog 1/2, and walk for 1/3. How much time? Or 1/4, 1/3, 1/4…

problemThree children buy two giant subs. How will they share it fairly? How much of each sub does each child get? If the subs cost $12, what should each child pay?

problem1/2 + 1/3 doesn't = 2/5. Why?

Put the following numbers in order.

75% |
16 2/3% |
.363636… |
66 2/3% |
1/5 |
1/10 |

.4545… |
2/5 |
.571328571428… |
1/6 |
.75 |
2/3 |

4/5 |
1/7 |
.112123123412345… |
.125 |
1/3 |
1/2 |

14 2/7% |
5% |
.090909… |
2/15 |
15% |
4/11 |

.1666… |
3/8 |
.08333… |
20% |
.66 |
1/5 |

5.05 |
5/8 |
.41666… |
33 1/3 |
4/7 |
1 1/4 |

5/9 |
44 4/9 |
1.333… |
.333… |
.8 |
.001 |

.999… |
5/11 |
.142857142857… |
1 |
75% |
.45 |

5 1/2 |
4/3 |

Discussion the different orders and try to resolve differences.