Create a simpler related problem

This understanding involves constructing a simpler problem that preserves the essential quantities, relationships, and operations of a more complex one—for example, replacing large numbers with smaller ones, reducing the number of steps, or using friendlier fractions while maintaining the same ratio, pattern, or geometric structure. Reasoning through the simpler case can reveal a strategy or invariant that applies to the original problem; the focus is on familiar arithmetic, fractions, decimals, ratios, expressions, measurement, and geometry, not formal generalization or advanced abstract problem transformations.

Detailed Explanation: Create a simpler related problem

When a problem feels complicated, make a simpler related problem by changing the numbers or reducing the steps while keeping the important relationship the same.

A good simpler problem should:

use the same kind of quantities,
keep the same shape, ratio, or operation,
use smaller or friendlier numbers,
help you notice a strategy for the original problem.

Example

A rectangular garden is $(48)$ feet long and $(30)$ feet wide. How many feet of fencing are needed to go all the way around it?

Instead of working with $(48)$ and $(30)$ right away, create a smaller rectangle with the same proportions.

Both dimensions can be divided by $6$ :

48 \div 6=8

30 \div 6=5

So the simpler related problem is:

How much fencing is needed for a rectangle that is $8$ feet long and $5$ feet wide?

Find its perimeter:

8+5+8+5=26\text{ feet}

The original rectangle is $6$ times as large in each dimension, so its perimeter is also $6$ times as large:

26 \times 6=156

Therefore, the garden needs

\boxed{156\text{ feet of fencing}}

The simpler rectangle kept the same length-to-width relationship because both dimensions were divided by the same number. It helped us see the perimeter pattern before returning to the original problem.

Learn by doing: Create a simpler related problem

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Fraction Subtraction - Problem Simplification - Mixed - One Changed Denominator

Earned ?