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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?
- Ratio and Proportion: Beaches and Hawks [10/26/1998]
On a map, the scale states that 3 inches represent 125 miles. Two beaches
are 5.2 inches apart. How far apart are they in miles?
- Ratio and Proportion: Jobs [7/7/1996]
30 men can complete a job in 12 days at 8 hours/day. How many hours/ day
will it take to complete the job in 10 days with 24 men?
- Ratio of Anti-Freeze to Water [7/28/1996]
How much water should I add to a gallon of anti-freeze to make a 60/40
- Ratio of Apples to Pears to Oranges [09/13/2002]
If the ratio of apples to pears to oranges is 7:8:10, how many pears
are there if the total number of fruits is 500?
- Ratio of Greek to Latin Exams [06/10/2003]
Susanna's average score on all exams was 88. On Greek exams it was 80,
and on Latin exams 92. What is the ratio of the number of Greek exams
to the number of Latin exams?
- Ratio of Ore to Copper [9/4/1996]
Ore contains 2 percent copper. How much ore is needed to obtain 24 tons
- Ratio of Rates and Work [06/06/1998]
Given the rates of 5 semi-skilled and 4 skilled workers, can you find how
long it takes 1 semi-skilled and 2 skilled workers to do a job?
- Ratio of Ratios [06/05/2002]
In a community, 3/5 of the men are married to 2/3 of the women. What
fraction of the residents are married?
- Ratio of Sides and Ratio of Areas [02/11/1999]
If the sides of a triangle are in the ratio of 1:7, what is the ratio of
their areas? What about for other shapes?
- Ratio of Volume to Surface Area in Humans [12/09/1999]
What is the healthy ratio of volume to surface area for humans?
- The Ratio of Water to Wine [10/22/1995]
A cask is filled with 45 gallons of wine. Nine gallons are removed and
the cask is refilled with water. The nine gallons of the mixture are
removed and the cask is again refilled with water. What is the ratio of
water to wine in the final mixture?
- Ratios and Fractions: A Reconciliation [04/02/2013]
Teachers have a disagreement about whether a fraction can compare part to part.
Doctor Peterson first distinguishes between ratios and fractions before reconciling them
and warning against inflexible thinking.
- Ratios and Geometry [10/29/1998]
An airplane flying at 33,000 feet has a visibility of 100 miles. What
percent of the total land area to the horizon is visible?
- Ratios and Mixtures [05/10/2001]
Sue needs to mix up a potion for her client... in what ratio must Sue mix
the honey and turpentine?
- Ratios and Proportions in Everyday Life [05/13/2002]
How are ratios and proportions used in everyday life?
- Ratios Between Keys on a Piano [11/05/1997]
I know that there is a formula to describe a ratio from one key to
another but I can't find it...
- Ratios Containing a Zero [07/03/2005]
What does the ratio 1:0 mean? What does the ratio 0:1 mean? Are they
- Ratio Set-Up Problem [09/02/2003]
Concrete can be made by mixing cement, sand, and gravel in the ratio
3:6:8. How much gravel is needed to make 850 m^3 of cement?
- Ratios: Second Number [01/04/1998]
What does the second number in a ratio stand for?
- Recipes and Adjusting Ingredient Amounts [04/20/2005]
In a recipe, 5 1/2 cups of coconut uses 14 ounces of milk, but I only
have 4 cups of coconut, so how many ounces of milk do I use?
- Rule of Three [06/15/2002]
Please explain to me briefly (and with an example) the concept of the
rule of three.
- Scale Factor of Similar Shapes [05/12/2000]
Find the scale factor, the ratio of the perimeters, and the ratio of the
areas of two regular octagons that have sides of lengths 21 and 28,
- Scaling up from a Numerator and Denominator to a Triple Ratio [07/08/2011]
A student familiar with fractions struggles to put more than two unknowns into one
proportional relationship. Doctor Jerry sets up equations to represent the scale factors.
- Setting up Proportions [03/11/2010]
Doctor Peterson explains how a proportion resembles a table of
data, and shows a seventh grader how to spot mistakes when
setting up relationships between ratios.
- Sides of Similar Triangles [06/11/1998]
The sides of a triangle are 24, 16, and 12. The shortest side of a
similar triangle is 6. Find the longest side of this triangle.
- Similar Rectangles [05/03/1997]
The outside boundary of an unfolded card is similar to its boundary when
it is folded. Find the width of the card if the open length is 8 and the
folded length is 4.
- Single Variable Algebraic Mixture Problem [05/03/2005]
Brittany needs a mixture of 76% oats and 24% corn. She currently has
25 pounds of a mixture that is 28% oats. How many pounds of oats
should be added to the mixture?
- Skilled and Semi-Skilled Workers [09/04/2002]
Four skilled workers do a job in 5 days, and five semi-skilled workers
do the same job in 6 days. How many days will it take for two skilled
and one semi-skilled worker to do that job?
- Solving a Ratio Problem [02/06/2006]
There are 33 red and yellow counters in a container. The ratio of red
to yellow is 3 to 8. How many of each color are in the container?
- Tea and Cakes [11/13/2002]
A cafe sold tea at 30 cents a cup and cakes at 50 cents each. Everyone
in a group had the same number of cups of tea and the same number of
cakes. The bill came to $13.30. How many cups of tea did each person
- Triangle and Trapezium Ratio [10/26/1998]
ABCD is a square with sides of length 4 cm. Find M on BC so that the
ratio of triangle ABM and trapezium ADCM is equal to 1/3.
- Turning a Perimeter into a Scale Factor [02/17/2003]
Perimeter and area ratios of similar figures are given. Find each
- Two Numbers in 5:3 Ratio [12/07/2002]
Two numbers have a ratio of 5:3. The larger number is 36 more than
half the difference of the two numbers. What are the two numbers?
There are two pairs of numbers that will make this a true statement.
You need to find both of them.
- Using a Diagram to Find a Formula [11/13/2002]
A bag contains green, yellow and orange marbles. The ratio of green
to yellow marbles is 2:5. The ratio of yellow to orange marbles is
3:4. What is the ratio of green marbles to orange marbles?
- Using Estimation to Check Your Answer [03/28/2008]
I had to find the percent increase in population from 38,000,000 to
515,000,000 and I got 1,255%. But that seems way too big. Where am I
- Using Scale Drawings [05/24/2002]
Use a scale drawing to determine the actual size of an object.
- Variation on Combined Work [06/13/2002]
If you run a large pipe for 4 hours, and run a small pipe for 9 hours,
you can fill 1/2 a pool. If you run both pipes together for 12 hours,
you can fill the whole pool. How long would it take to fill the pool
using each pipe by itself?
- Visualizing Ratios to Scale Least Common Multiples [10/02/2010]
The ratio of Cotsworld sheep to Swaledales is 3:5, and the
ratio of Swaledales to Longwools is 7:4. What is the ratio
of Cotsworlds to Longwools?
- Weighted Averages [11/30/2001]
An advertisement for an orange drink claims that the drink contains 10%
orange juice. How much pure orange juice would have to be added to 5
quarts of the drink to obtain a mixture containing 40% orange juice?
- Which is More? [05/21/2002]
Given a choice between nickels stacked to your height, or quarters
placed end to end to your height, which should you choose?