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
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 1:15
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 Matt 4 minutes to mix some paint for his science
project. It takes him 3 hours to complete painting his science project. What is
the ratio of the time it takes Matt to mix the paint to the time it takes Matt
to paint his project?
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.
Dani’s dad’s car 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
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