Introduction
Ratios in real life
Ratios are first introduced in grade 6 and explored further in grade 7. But they’re not just for math class — they’re everywhere in real life! For example, ratios help us understand statistics, measure distances on maps, and even bake the perfect cake by measuring ingredients. One of the most interesting uses of ratios is in creating eco-friendly and sustainable products. In this article, we’ll explore how ratios play a key role in sustainability.
What is a sustainable or eco-friendly product?
Designing an eco-friendly product means using less energy, reducing waste, and choosing materials that don’t harm the environment. It also includes creating sustainable packaging. But “sustainable” doesn’t just mean using recycled materials — it also means making packaging as efficient as possible. This is where ratios come in! The same ratios you learn in school help measure how effectively a product is packaged. Let’s take a closer look.
Using ratios to measure packaging efficiency
What is packaging efficiency?
How can we tell if a product’s packaging is efficient? One way is to measure the volume of the product itself and compare it to the volume of its packaging using ratios.
For example, the pizza (the product) has one volume, while the box (the package) has a larger volume. Comparing these volumes helps determine how efficiently the pizza is packaged.
Let’s break this down with a detailed example: soap.
Example: Soap packaging
Calculating Volumes
Using ratios to compare volumes
In the picture, you can see a bar of soap packed in a paperboard box, along with their dimensions.
Dimensions in centimeters:
• Soap: 9.7 cm × 5.9 cm × 3.1 cm
• Box: 10.2 cm × 6.4 cm × 3.6 cm
First, let’s calculate the volume of the soap:
First, let’s calculate the volume of the soap:
- In inches: \(3.8 \times 2.3 \times 1.2 \approx 10.5 \, \text{in}^3\)
- In centimeters: \(9.7 \times 5.9 \times 3.1 \approx 177.4 \, \text{cm}^3\)
Next, let’s calculate the volume of the soap’s box:
- In inches: \(4 \times 2.5 \times 1.4 = 14 \, \text{in}^3\)
- In centimeters: \(10.2 \times 6.4 \times 3.6 \approx 235 \, \text{cm}^3\)
Now, let’s find the ratio of the soap’s volume to its package’s volume:
\(\frac{10.5}{14} = 0.75 \, (75\%)\)
\(\frac{177.4}{235} = 0.75 \, (75\%)\)
This ratio can also be simplified to \(\frac{3}{4}\) or 3:4, meaning that for every 3 units of soap volume, there are 4 units of packaging volume. In other words, about 75% of the total volume is taken up by the soap, while the remaining 25% is empty space in the packaging.
What is the product-to-package ratio?
The measure we just calculated is called the product-to-package ratio. This metric shows how efficiently a product is packaged. A higher ratio means the packaging is efficient, with minimal wasted space or material. A lower ratio indicates excess packaging, which can increase costs and create more waste. Sustainability experts often use this metric to evaluate packaging efficiency.
How good is the 3:4 ratio?
Is a 3:4 (or 75%) ratio good or bad? To find out, we need to compare it to another product, like toothpaste. We explore this in detail in our video (preview below), available to our subscribers. Consider subscribing to our collection of real-world math educational videos for full access to a variety of scenarios showing how math is applied in everyday life!
Conclusion
This example shows how ratios, the same ones you learn in 7th-grade math, can help measure and compare the eco-friendliness of product packaging. While the product-to-package ratio isn’t the only way to evaluate sustainability, it’s an important tool. Sustainability specialists use ratios like this every day to make products more efficient and environmentally friendly.
If a career in sustainability interests you, mastering math and science is a great first step. Who knew that something as simple as ratios could have such a big impact on the planet?
References:
This publication was prepared using both scientific and trade-related sources, which you can verify and explore further.