lesson
Updated 6 days ago · 2 views
If you are building a skateboard ramp that is 54 inches long, but your blueprint only uses feet, do you multiply by 12 or divide by 12?
Guessing whether to multiply or divide leads to easy mistakes, but setting up a simple proportion guarantees the right answer every single time.
The Proportion Setup
A proportion is an equation showing that two ratios (fractions comparing two quantities) are completely equal.
To convert any measurement, we write a known conversion fact as our first ratio and our problem's values as our second ratio.
📊A clean visual diagram explaining how to set up a conversion proportion. Show two equal fraction bars: on the left, a card labeled 'Known Fact' showing (1 foot) / (12 inches); on the right, a card labeled 'Your Problem' showing (x feet) / (54 inches). Highlight the top row with a light blue banner labeled 'Units must match: Feet' and the bottom row with a light orange banner labeled 'Units must match: Inches'. Include an equals sign between them. Light theme (#f8f9fa), rounded corners, dark text (#1e2945).
The golden rule is unit alignment: if feet are on top on the left, feet must be on top on the right.
Solving with Cross-Products
When two fractions are equal, their diagonal products (called cross-products) are also equal.
This works because multiplying both sides of the equation by both denominators eliminates the fractions without changing the balance.
📊A step-by-step animated card demonstrating cross-multiplication for 1/12 = x/54. Step 1: Show the proportion with diagonal criss-cross arrows linking 1 to 54 (blue) and 12 to x (orange). Step 2: Show the equation 1 * 54 = 12 * x, simplifying to 54 = 12x. Step 3: Show dividing both sides by 12: x = 54 / 12 = 4.5 feet. Clean layout with step badges (1, 2, 3), dark text (#1e2945), responsive to 350px width.
Dividing 54 by 12 gives x=4.5, which means 54 inches is exactly 4.5 feet.
A common mistake is writing units in mismatched spots, like placing inches on the bottom on one side and on the top on the other side. If your units don't align straight across, your answer will be upside down!