Multiplication as Scaling Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Multiplication as Scaling.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Understanding multiplication as stretching or shrinking a quantity by a factor—scaling up or down from the original.

Multiplying by 2 doubles something; by 0.5 cuts it in half; by 3 triples it.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Multiplication transforms size—it's not just repeated addition.

Common stuck point: Repeated addition works for whole numbers but not for 3 \times 0.5.

Sense of Study hint: Compare the result to the original: ask 'did it get bigger, smaller, or stay the same?' to check your scale factor.

Worked Examples

Example 1

easy
A recipe uses 3 cups of flour. If you make the recipe 4 times bigger, how many cups of flour do you need?

Solution

  1. 1
    Original amount: 3 cups.
  2. 2
    Scale factor: 4 (making it 4 times bigger).
  3. 3
    Multiply: \(3 \times 4 = 12\) cups.
  4. 4
    You need 12 cups of flour.

Answer

12 cups
Scaling by a factor means multiplying. Making something 4 times bigger means multiplying by 4.

Example 2

medium
A drawing of a cat is 5 cm tall. You scale it up to be 3 times taller. How tall is the scaled drawing?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A plant is 8 inches tall. After one month it is 2 times taller. How tall is it now?

Example 2

medium
A photo is 4 inches wide. A poster version is 6 times wider. How wide is the poster?

Background Knowledge

These ideas may be useful before you work through the harder examples.

multiplication