Practice Scaling in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Changing the size of a quantity by multiplying by a factor, making it proportionally larger (factor $> 1$ ) or smaller (factor $< 1$ ).

Zooming in or out—everything gets bigger or smaller by the same factor.

Showing a random 20 of 50 problems.

Example 1

medium

A recipe for

4

servings uses

2.5

cups of oats,

1.5

cups of milk, and

\frac{1}{4}

cup of honey. Scale the recipe up to

10

servings.

Example 2

hard

A model of a building is built at scale

1:200

. The model has volume

0.5

L. What is the volume of the actual building in m

^3

Example 3

easy

Scale the ratio

4:5

by a factor of

3

Example 4

medium

A square has side

6

cm. By what scale factor must its side be enlarged so that the new area is

144

^2

Example 5

medium

A rectangle with width

3

cm and height

5

cm is scaled by a factor of

4

. Find the new perimeter.

Example 6

hard

A photo is enlarged so its width grows from

4

in to

10

in. By what factor does its area increase?

Example 7

medium

A cube has side length

2

cm. The cube is scaled by a factor of

3

. Find the new volume.

Example 8

medium

A drawing is scaled by

\frac{2}{3}

. A line that was

9

cm becomes how long?

Example 9

easy

A map has a scale of

1:25{,}000

. Two cities are

8

cm apart on the map. What is the actual distance in kilometres?

Example 10

easy

A model car is built at a scale of

1:18

. The model is

24

cm long. How long is the actual car in metres?

Example 11

medium

A model airplane has wingspan

30

cm. The real airplane has wingspan

36

m. Find the scale of the model.

Example 12

challenge

If scaling a quantity by

a

then by

b

gives the same result as scaling by

12

, and

a=3

, find

b

Example 13

medium

A bag of dog food lasts

12

days for

1

dog. Scaled for

4

dogs eating the same amount each, how many days does it last?

Example 14

easy

Scale the ratio

2:3

up by a factor of

5

Example 15

easy

If every ingredient is tripled, by what factor is a recipe scaled?

Example 16

challenge

A model car is built at scale

1:20

. It uses

0.5

kg of material. Assuming the same density and shape, how much material would the full-size car need?

Example 17

hard

A small cake serves

8

people and uses

200

g of butter. A similar cake (geometrically scaled by a factor of

\tfrac{3}{2}

in every linear dimension) is baked. How many grams of butter does it use?

Example 18

hard

A cylindrical tank of height

2

m holds

500

L. A similar tank, scaled by a linear factor of

1.5

, holds how many litres?

Example 19

challenge

A statue is built at

\tfrac{1}{8}

scale of a real human (every linear dimension is one-eighth). The model weighs

0.4

kg (assume same material density as a real human, whose mass is about

80

kg). Verify whether the

\tfrac{1}{8}

linear scale is consistent with these masses.

Example 20

easy

A model is

\frac{1}{10}

the size of the real car. The real car is

5

m. Model length?

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Related Concepts

Multiplication Ratios Similarity Proportional Relationships