Math 6 Honors ( Periods 1, 2, & 3)

Ratios 7-6

In our textbook, the example given involves the number of students --at what I called a mythical middle school --as well as the number of teachers. There are 35 teachers and 525 students. We can compare the number of teachers to the number of students by writing a quotient


number of teachers
number of students

35
525

1/15

The quotient of one number divided by a second number is called the ratio of the first number to the second number.

We can write a ratio in the following ways:

1/15 OR 1:15 OR 1 to 15

All of these expressions are read one to fifteen.

If the colon notation is used the first number is divided by the second. A ratio is said to be lowest terms if the two numbers are “relatively prime.”
You do not change an improper fraction to a mixed number if the improper fraction represents a ratio


There are 9 players on a baseball team. Four of these are infielders and 3 are outfielders. Find each ratio in lowest terms.

a. infielders to outfielders

b. outfields to total players

# of infielders
# of outfielders
= 4/3 or 4:3 or 4 to 3



# of outfielders
# total of players
= 3/9 = 1/3 or 1:3 or 1 to 3

Some ratios compare measurements. In these cases we must be sure the measurements are expressed in the same units

It takes Kiana (or Helen or Emme) 4 minutes to mix some paint. It takes her 3 hours to complete painting her room. What is the ratio of the time it takes Kiana (or Helen or Emme) to mix the paint to the time it takes her to paint her room?
Use minutes as a common unit for measuring time. You must convert the hours to minutes first

3h = 3 • 60min = 180 min

The ratio is :
min. to mix
min. to paint

= 4/180 = 1/45 or 1:45

Some ratios are in the form

40 miles per hour or 5 pencils for a dollar
“ I want my… I want my…. I want my … MPG!!”

These ratios involve quantities of different kinds and are called rates. Rates may be expressed as decimals or mixed numbers. Rates should be simplified to a per unit form. When a rate is expressed in a per unit form, such a rate is often called a unit rate.

I know you will be driving in a blick of an eye... so Justin, in his Lamborghini(and Shane in his Corvette and Nick in his yellow Lamborghini) went 258 miles on 12 gallons of gas. Express the rate of fuel consumption in miles per gallon.

The rate of fuel consumption is

258 miles
12 gallons

= 21 1/2 miles per gallon

Some of the most common units in which rates are given are the following:
mi/gal or mpg miles per gallon
mi/h or mph miles per hour
km/L kilometers per liter
km/h kilometers per hour

Page 229
1 What is the cost of grapes in dollars per kilogram if 4.5 kg of grapes costs $7.56?
$7.56/4.5 kg divide carefully and you discover it is $1.68/kg
2. THe index of refraction of a transparent substance is the ratio of the speed of light in space to the speed of light in the substance.
Using the table from the textbook (look at page 229) Find the index of refraction of
a) glass
300,000/200,000 straight from the chart, which can simplify to 3/2
b) water
300,000/225,000 again from the chart, which can simplify to 4/3

3. The mechanical advantage of a simple machine is the ratio of the weight lifted by the machine to the forse necessary to lift it.
What is the mechanical advantage of a jack that lifts a 3200 pound car with a force of 120 pounds?
3200/120 = 80/3

4. The C string of a cello vibrates 654 times in 5 seconds. How many vibrations per second is this?
654 vibrations/5seconds... divide carefully and you find... 130 4/5 vibrations per second

5. A four-cubic-foot volume of water at sea level weights 250 pounds. What is the density of water in pound per cubic foot?
250 pounds/4 cubic ft ... divide carefully and you find 62 1/2 lb/ft³

6. A share of stock that costs $88 earned $16 last year. What was the price to earnings ratio?
88/16 = 11/2

7. we did in our spiral notebooks this year... please check