Scale


Basics

Scale refers to the ratio of image size to actual size.

To answer questions regarding scale, you will often need to work with
ratio, proportion, and cross-multiplication.

In order to cross-multiply, it is helpful to understand algebraic equations.
It is also helpful to know your multiplication and division tables.


Question
In the map above, the ratio of distance = 1 inch to 300 miles = 1:300 = \bf\displaystyle\frac{1}{300} .
How many miles do 4 inches on the map represent?

Answer
1200 miles

Answer Process
To solve for an unknown variable in proportionate ratios, cross-multiply.

For ratios \bf\displaystyle\frac{1}{300} and \bf\displaystyle\frac{4}{d} 
ad = bc
ad = 1 × d
bc = 300 × 4
1 × d = 300 × 4
1d = 1200
d = 1200


Question

In the map above, the ratio of distance = 1 inch to 300 miles = 1:300 = \bf\displaystyle\frac{1}{300} .
Also in the map, Jackson, Mississippi and Columbia, South Carolina are approximately 2 inches apart.  In the real world, approximately how many miles are Jackson and Columbia apart?

Answer
600 miles

Answer Process
To solve for an unknown variable in proportionate ratios, cross-multiply.

For ratios \bf\displaystyle\frac{1}{300} and \bf\displaystyle\frac{2}{d} 
ad = bc
ad = 1 × d
bc = 300 × 2
1 × d = 300 × 2
1d = 600
d = 600


Practice – Questions
1.  In the map above, the ratio of distance = 1 inch to 300 miles = 1:300 = \bf\displaystyle\frac{1}{300} .
How many miles do 6 inches on the map represent?

2.  In the map above, the ratio of distance = 1 inch to 300 miles = 1:300 = \bf\displaystyle\frac{1}{300} .
Also in the map, Columbus, Ohio and Tallahassee, Florida are approximately 3 inches apart.  In the real world, approximately how many miles are Columbus and Tallahassee apart?

3.  In the map above, the ratio of distance = 1 inch to 300 miles = 1:300 = \bf\displaystyle\frac{1}{300} .
Also in the map, Montgomery, Alabama and Montpelier, Vermont are approximately 5 inches apart.  In the real world, approximately how many miles are Montgomery and Montpelier apart?

4.  In the image below, a cow is 1 inch long.  In the real world, a cow is 60 inches long.
Using a colon, write a scale representing this cow.

5.  In the image below, a cow is 1 inch long.  In the real world, a cow is 60 inches long.
Using a fraction, write a scale representing this cow.


Practice – Answers

1.  1800

2.  900

3.  1500

4.  1:60

5.  \bf\displaystyle\frac{1}{60}

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