Ratios and Proportions
Definitions:
  • ratio - A ratio is a comparison, by division, between two like or unlike quantities.
  •           A ratio is written either as a fraction, like a/b, or as a:b, and read as "a to b".
  •           A ratio may compare a (1) part to a whole, (2) part to another part, 
  •           (3) or whole to a part of the whole.
  •           A ratio may represent a rate, unit price, percentage, or an average.
  • proportion - A proportion is the equality of two ratios.
A certain mix of grass seed calls for five parts blue grass and three parts clover seed.  Make a table showing this ratio for 8, 16, 24, and 40 pounds of grass seed.

Alisha uses 12 gallons of gasoline for every 250 miles that she drives.  Her friend Nicole uses about 15 gallons of gasoline for every 300 miles that she drives.  Who gets the better gasoline mileage and why?

If 6 bars of soap cost $2.35, how much would 10 bars of soap cost?

A nickel contains 3 ounces of copper for every ounce of nickel.   How much nickel is required for 14 pounds of copper?

If a person spends $32 to drive 1000 miles, how much would she spend at the same rate to drive 15,000 miles?

Suppose Barry Bonds has 148 hits in 500 at bats.  How many hits does he need in his next 10 at bats to raise his batting average to .300?

Marge say that if Terry has 7 hits in her next 20 at bats, she will increase her batting average, which is currently .305.  Vickie says that Marge is wrong.  Who is right and why?

The ratio of girls to boys in Mr. Maddox’s class of 30 students is 3:2.  The ratio of girls to boys in Ms. Wood’s class of 27 students is 2:1.  Which teacher has more girls?  How many more girls?

 A basketball player has made 135 free throws in 180 attempts.  Of the next 50 free throws attempted, how many would she have to make to raise her percent of free throws made by 5%?

Amanda and Jeremy are debating about who is the better saver.  Amanda earned $30,000 and saved $1200.  Jeremy earned $20,000 and saved $900.  who is the better saver?  Justify your decision.

Karla is planning a trip to Paris.  She notes that $1 buys 5.5 French francs.  If she doesn't want to pay more than $100 be night for a hotel room, what is the maximum number of francs she should pay for the room?

Mike needs 4 acres of pasture to sustain 10 horses.  How many acres would he need to sustain 15 horses?

A candle is 30 in. long.  After burning for 12 min., the candle is 25 in. long.  At this rate, how long will it take for the whole candle to burn?

A grasshopper can jump 20 times its length.  If jumping abilities in humans were proportional to grasshoppers, how far could a 6-ft-tall person jump?

Shauna and Tracy worked 3½ hr and 4½ hr respectively, on a display.  If they were paid $176 for the completed display, how much did each earn?

 

 
The electrical resistance of a wire is measured in ohms.  If the electrical resistance of a 5-ft wire is 4.2 ohms, what is the resistance of 18 ft of the same wire?

At any given time on a sunny day, the ratio of the height of an object that is perpendicular to the ground to the length of its shadow is the same for all objects.  If a 30-ft flagpole casts a shadow of 12 ft, how tall is a tree that casts a 14 ft shadow?

A Boeing 747 jet is approximately 230 ft long and has a wingspan of 195 ft.  What would be the wingspan of a scale model of this plane whose length is 40 cm?

Five-eighths of the students at a college live in dormitories.  If 7500 students at this college live in dormitories, how many students attend the college?

Jayme has finished reading two-thirds of a book and has 76 pages left to read.  How many pages has she read?