See also the
Dr. Math FAQ:
3D and higher
Browse Middle School Ratio/Proportion
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Unit conversions, unit cancellation.
What is a ratio?
- 100 Percent of Daily Allowance of Iron [09/30/2001]
A common foodstuff is found to contain .00125% iron. The serving size is
87.0 grams. If the recommended daily allowance is 18mg of iron, how many
servings would a person have to eat to get 100% of the daily allowance of
- Administering Insulin [07/09/2003]
If a doctor prescribes 30 units of insulin in 500 ml to be
administered over 2 hours, how many drops per minute should be
administered if the set is calibrated to deliver 20 drops per ml?
- Checking Proportions using Square Roots [04/11/2002]
Multiply two fractions, and then take their square root. If it equals
one of the fractions you began with, you have a true proportion. Does
this always work?
- Converting Ratios to Percentages [08/03/2003]
How do I convert 1:200 to a percentage?
- Cost of Cleaning a Building [07/03/2003]
If I clean a 3200 square foot building five nights per week for a sum
of $575.00 per month, what is the cost per square foot?
- Definition of Ratio [08/21/2003]
How is 'ratio' defined by mathematicians?
- Employee Pay Schedule [07/12/2003]
For a particular job, Moe should get 40% of the gross pay, Larry
should get 30%, and Curly should get 30%, assuming they all work the
same number of hours. But how should the money be divided if they
work different numbers of hours?
- Figuring Ratios [08/07/1997]
How do you figure the ratio of something?
- Finding and Working with Ratios [12/26/2001]
What is the ratio of the circumference of a circle to its radius? A snail
can move i inches in m minutes. How many feet can it move in h hours?
- Find the Ratio: 0.0625 : 0.09375 [05/15/2003]
Please help me find the ratio of 0.0625 : 0.09375 and tell me how to
- How Many Boxes? A Diagram [03/20/2003]
There were juice boxes in a cooler. Jared took 1/6 of them. Sara took
1/4 of what was left. Now there are 15 boxes. How many boxes were
there to start with?
- How Much Water Evaporated? [06/19/2003]
A substance is 99% water. Some water evaporates, leaving a substance
that is 98% water. How much of the water evaporated?
- Mean Proportionals and Geometric Means [01/06/1999]
How do you find the mean proportional of two numbers? What about two mean
proportionals? n mean proportionals?
- Mixing Alcohol, Cable TV Pricing [8/2/1996]
What amounts of 9 percent and 12 percent alcohol do you mix to get
300,000 gallons of 10 percent alcohol? For each 5-cent increase in the
monthly subscription price, 4 people will decide not to subscribe to
- Mixing Milk and Butterfat [09/04/2001]
Milk that has 5% butterfat is mixed with milk that has 2% butterfat. How
much of each is needed to obtain 60 gallons of milk that has 3%
- Percentage Increase in Cost of Eggs [8/4/1996]
When eggs went from 17 to 39 cents, by what percent did the price
- Rate vs. Ratio [10/23/2001]
What is a rate? What is a ratio? Are all rates ratios, and are all ratios rates?
- Ratios as Fractions [01/26/1997]
How do you put ratios into simplest form?
- Setting Up Proportions and Unit Conversions [7/25/1996]
If you can run 100 meters in 10 seconds, how long, in days, hours, and
minutes, does it take you to run 12,800,000 meters?
- Silver Alloy [07/12/2001]
Sterling Silver is 92.5% pure silver. How many grams of pure silver and
sterling silver must be mixed to obtain 100g of a 94% Silver alloy?
- Solving a Ratio with and without a Diagram [05/12/2003]
In an auditorium, the ratio of the number of girls to the number of
boys was 5:9. When 203 girls entered the auditorium, the new ratio of
the number of girls to the number of boys became 4:3. How many pupils
were in the auditorium at first?
- Time, Speed, Distance, and Unit Conversion [7/30/1996]
If a car moves at 44 mph for 50 minutes, how many kilometers does it
- What is a Ratio? [8/17/1996]
I need help understanding ratios.
- What Is a Ratio? [12/08/1996]
I need to know what a ratio is and how to do it.
- Abraham Lincoln and the Rule of Three [04/13/2003]
In the biography of Abraham Lincoln he states that he learned to
'read, write, and cipher to the rule of 3.' Can you please explain
the phrase 'cipher to the rule of 3'?
- Abraham Lincoln and the Rules of Three, Double and Single [06/08/2013]
Doctor Wallace extends the kind of proportional thinking suggested by a student
attempting a problem that Abraham Lincoln once solved.
Doctor Peterson follows up by looking back into the kind of ciphering textbooks the
Civil War President would have learned from, then solves the same interest rate problem with a
formula more familiar to modern students.
- Adding Tax and Tip [07/19/1998]
In pricing our hotel luncheons, we charge a base price plus a 6.8% tax
and a 20% service charge. How would I find the total in one step?
- Add Up Data First, Then Take the Average? Or Take the Averages First, Then Add? [01/20/2010]
Doctor Peterson explains weighted averages, using an extreme example to
illustrate how the order of operations that you choose will emphasize
different qualities of the same data set.
- Analyzing a Prescription for the Correct Dose [04/27/2005]
A 46 lb child is prescribed 1 Tsp of medicinal syrup three times a
day. There are 2 mg of medicine per 5 ml of syrup, and a safe dose is
0.1 mg per kg of body weight. Is the prescribed dose safe?
- Billions Taste the Rainbow Thousands of Billions of Billions of Times [03/06/2013]
A student who knows facts about populations and physical chemistry struggles to
determine how long would it take the world to consume a mole of Skittles. Doctor Ian
shows the power of algebra by introducing a key assumption that makes this Fermi
- Cake Recipe Ratio [03/05/2003]
A recipe for four-egg cake is supposed to be baked in three 9-inch-
diameter round cake pans. You have just three 10-inch-diameter cake
- Calculating Sales Tax [09/19/2001]
How do I calculate sales tax? Please describe the steps.
- Can Constant of Variation Be Negative? [01/22/2007]
Most books say that a is directly proportional to b if and only if a =
kb for some constant k. But I've never seen an example where k is
negative. Is that possible or does it have to be positive?
- Changing the Concentration of a Solution [05/30/2002]
A chemist has 6 liters of a 25% alcohol solution. How much alcohol
must he add so that the resulting solution contains 50% alcohol?
- Coffee or Tea? [07/09/2001]
Is there more coffee in the tea, or more tea in the coffee, or are they
- Combining Rates of Work: From Unit Rates to a General Model [12/23/2013]
A student solves a problem about combined rates of work, but struggles to
understand "units of work per man-hour" and the other ratios it entails. Doctor Ian
approaches the problem first by simplifying it into unit rates, then distinguishes the
direct proportions from the inverse ones en route to a general template that would
model the combination of any work rates.
- Combining Rates of Work, Revealing Constants of Word Problems [11/13/2011]
An adult wonders how to logically reason through problems that entail combining rates of work. Moved to re-examine the mechanics he learned in high school, Doctor Jerry introduces a
constant tacitly assumed in the wording of such problems.
- Comparing Prices [09/29/2003]
Which of these is the better buy: a 6-ounce can of tuna that sells for
$1.59, or a package of three 3-ounce cans for $2.19?
- Comparing Ratios and Fractions [01/06/2002]
What are the differences between ratios and fractions?
- Comparing Ratios to Form a Proportion [01/08/2004]
A discussion of how to determine if two ratios are equal and thus form
a proportion. Several techniques of comparing ratios are presented.