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> 1) or smaller (factor <1< 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 44 servings uses 2.52.5 cups of oats, 1.51.5 cups of milk, and 14\frac{1}{4} cup of honey. Scale the recipe up to 1010 servings.

Example 2

hard
A model of a building is built at scale 1:2001:200. The model has volume 0.50.5 L. What is the volume of the actual building in m3^3?

Example 3

easy
Scale the ratio 4:54:5 by a factor of 33.

Example 4

medium
A square has side 66 cm. By what scale factor must its side be enlarged so that the new area is 144144 cm2^2?

Example 5

medium
A rectangle with width 33 cm and height 55 cm is scaled by a factor of 44. Find the new perimeter.

Example 6

hard
A photo is enlarged so its width grows from 44 in to 1010 in. By what factor does its area increase?

Example 7

medium
A cube has side length 22 cm. The cube is scaled by a factor of 33. Find the new volume.

Example 8

medium
A drawing is scaled by 23\frac{2}{3}. A line that was 99 cm becomes how long?

Example 9

easy
A map has a scale of 1:25,0001:25{,}000. Two cities are 88 cm apart on the map. What is the actual distance in kilometres?

Example 10

easy
A model car is built at a scale of 1:181:18. The model is 2424 cm long. How long is the actual car in metres?

Example 11

medium
A model airplane has wingspan 3030 cm. The real airplane has wingspan 3636 m. Find the scale of the model.

Example 12

challenge
If scaling a quantity by aa then by bb gives the same result as scaling by 1212, and a=3a=3, find bb.

Example 13

medium
A bag of dog food lasts 1212 days for 11 dog. Scaled for 44 dogs eating the same amount each, how many days does it last?

Example 14

easy
Scale the ratio 2:32:3 up by a factor of 55.

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 1:201:20. It uses 0.50.5 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 88 people and uses 200200 g of butter. A similar cake (geometrically scaled by a factor of 32\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 22 m holds 500500 L. A similar tank, scaled by a linear factor of 1.51.5, holds how many litres?

Example 19

challenge
A statue is built at 18\tfrac{1}{8} scale of a real human (every linear dimension is one-eighth). The model weighs 0.40.4 kg (assume same material density as a real human, whose mass is about 8080 kg). Verify whether the 18\tfrac{1}{8} linear scale is consistent with these masses.

Example 20

easy
A model is 110\frac{1}{10} the size of the real car. The real car is 55 m. Model length?
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