Scale Factor

Let's learn about SCALE and SCALE FACTORS!

What is it?????

What is SCALE FACTOR?

• ​A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. It is most commonly written with a colon :

Scale factors are proportional. So you need to set up a proportion to solve!

Remember - proportions are just equivalent ratios.

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​TYPES OF SCALE DRAWINGS

• If the scale drawing is LARGER than the original, then it is an enlargement. The scale factor is GREATER than 1.

• ​

• If the scale drawing is SMALLER than the original, then it is a reduction. The scale factor is LESS than 1.

Example:

​Remember to cross multiply then divide to solve for x!

Finding the Scale Factor

Finding the Scale Factor

In order to use a scale factor, multiply each side length by the scale factor to find the new side length for the scaled copy.

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If the scale factor is 3, then each side will be exactly ​three times as big as in the original image.​ (This means the longest side in your SCALED COPY in this case will be 27 in.)

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Using the Scale Factor

Using the Scale Factor

​A photo is being resized.  The original photo is 4 inches by 6 inches.  Given the dimensions of the resized photo, find the scale factor.

1. 2.5 in. by 3.75 in.

​A photo is being resized.  The original photo is 4 inches by 6 inches.  Given the dimensions of the resized photo, find the scale factor.

1. 12 in. by 18 in.

Multiple Choice

A scale drawing has a scale of 1cm: 2ft. What is the actual width of a pool if it is 6cm on the drawing? Remember to set up the proportion - 1/2 = 6/x. Cross multiply then divide!

• 3ft

• 6ft

• 12ft

How do we find the scale ratio?

• write the ratio of the model to the actual size

• simplify!

Example:

Multiple Choice

A model ship is 30cm long and the actual ship is 150m long. What is the scale?

Set it up as a ratio in a fraction then simplify - 30/150.

• 1cm:5m

• 1cm:3m

• 1cm:50m

• 1cm:150m

Multiple Choice

If the scale factor is less than one, the new figure will be...

• an enlargement

• bigger

• a reduction

• a scale factor

Multiple Choice

If the scale factor is greater than one, the new figure will be...

• an enlargement

• a reduction

• a scale

• not proportional

Multiple Choice

Scale factor of 1/4 is a ...

• enlargement

• reduction

Multiple Choice

Scale factor of 4 is a ...

• enlargement

• reduction

Multiple Choice

If you want to find the scale factor from one figure to another, which formula should you use?

• old/ new

• model / actual

• actual / model

Multiple Choice

What is the scale factor from the large triangle to the small triangle?

• 1/2

• 2/3

• 3/4

• 2

Multiple Choice

What is the value of the missing side length?

• 10

• 6

• 9

• 12

How to solve?

• Second number

• divide by

• first number

Multiple Choice

An area rug is 9 feet wide. In a photograph, the image of the rug is 3 inches wide. What is the scale of the model? Remember to set up your proportion - 3/9 = 1/x

• one inch = 3 feet

• one inch = .33 feet

• one inch = 36 inches

Multiple Choice

A model airplane is built with a wing span of 23 inches. The actual wing span is 92 ft. What is the scale of the model?

• one inch = 48 inches

• one inch = .25 feet

• one inch = 4 feet

Multiple Choice

Edgar drew a scale drawing of the town library. The scale of the drawing was 5 centimeters : 2 meters. The parking lot is 34 meters wide in real life. How wide is the parking lot in the drawing? Set up a proportion to solve.

• 85 cm

• 68 cm

Multiple Choice

The two rectangles are scale drawings. What is the measurement of x?

• 21

• 1.25

• 20

• 4

Multiple Choice

What is the scale factor from the small fry to the large fry?

• 1/3

• 48

• 4

• 3