what are equivalent ratios to 48 to 18

2 min read 02-02-2025

Understanding equivalent ratios is a fundamental concept in mathematics with real-world applications in scaling recipes, map reading, and more. This article will explore how to find equivalent ratios to 48:18, explain the underlying principles, and provide examples to solidify your understanding.

Finding Equivalent Ratios: A Step-by-Step Guide

The ratio 48 to 18 can be written as 48:18 or 48/18. To find equivalent ratios, we need to multiply or divide both parts of the ratio by the same non-zero number. This maintains the proportional relationship between the two quantities.

Simplifying the Ratio

Before finding other equivalent ratios, let's simplify the given ratio 48:18. Both 48 and 18 are divisible by 6:

48 ÷ 6 = 8 18 ÷ 6 = 3

Therefore, the simplified ratio is 8:3. This is the simplest form of the ratio, meaning there's no common factor greater than 1 that divides both numbers. Any ratio equivalent to 48:18 will also simplify to 8:3.

Finding Equivalent Ratios by Multiplication

We can find equivalent ratios by multiplying both parts of the simplified ratio (8:3) by the same number:

Multiply by 2: 8 x 2 = 16, 3 x 2 = 6. This gives us the equivalent ratio 16:6.
Multiply by 3: 8 x 3 = 24, 3 x 3 = 9. This gives us the equivalent ratio 24:9.
Multiply by 4: 8 x 4 = 32, 3 x 4 = 12. This gives us the equivalent ratio 32:12.
Multiply by 5: 8 x 5 = 40, 3 x 5 = 15. This gives us the equivalent ratio 40:15.
Multiply by 6: 8 x 6 = 48, 3 x 6 = 18. This gives us the original ratio 48:18.

You can continue this process, multiplying by any whole number to generate an infinite number of equivalent ratios.

Finding Equivalent Ratios by Division (If Possible)

While we can't divide 8 and 3 by a common whole number to get a smaller, whole number ratio (because they are already in their simplest form), you could theoretically divide by a fraction. For example, dividing both by 1/2 would result in 16:6, which we've already found.

Real-World Applications

Equivalent ratios are useful in many everyday situations:

Scaling Recipes: If a recipe calls for a 2:1 ratio of flour to sugar, and you want to double the recipe, you'd use a 4:2 ratio (an equivalent ratio).
Map Scales: Maps use ratios to represent distances. A scale of 1:100,000 means that 1 cm on the map represents 100,000 cm in reality. Equivalent ratios help determine actual distances.
Unit Conversions: Converting units like kilometers to miles involves using equivalent ratios.

Equivalent Ratios Summary

The ratio 48:18 simplifies to 8:3. Infinitely many equivalent ratios exist, all of which can be obtained by multiplying both parts of the simplified ratio (8:3) by the same non-zero number. Remember that the fundamental principle is maintaining proportionality—whatever you do to one part of the ratio, you must do to the other. Understanding equivalent ratios is crucial for problem-solving in various mathematical contexts and real-world scenarios.