Question

Write the ratio 2 yards to 2 feet in simplest form.

Short answer

The simplest form of the ratio is 3:1.

Step-by-step solution

Convert Yards to Feet

We start by converting yards to feet. We know that 1 yard equals 3 feet. Therefore, 2 yards is equal to \(2 \times 3 = 6\) feet.

Write the Ratio

Now, we express the given problem as a ratio, with the consistent units in feet. We have 6 feet from the conversion and 2 feet as given, so the ratio is \(\frac{6 \text{ feet}}{2 \text{ feet}}\).

Simplify the Ratio

To simplify the fraction \(\frac{6}{2}\), we divide both the numerator and the denominator by their greatest common divisor, which is 2. Thus, \(\frac{6 \div 2}{2 \div 2} = \frac{3}{1}\).

Key concepts

Unit Conversion

Unit conversion is the process of changing one unit of measurement to another, ensuring consistency and comparability in calculations.
This is especially important when working with ratios, as both quantities in a ratio must be expressed in the same units. In our exercise, the initial quantities were given in yards and feet.
To solve the problem, we needed to convert yards into feet, because these are the units more frequently used together in a mathematical context.
Here's how you do it:

• Recall basic conversion values, such as 1 yard = 3 feet.
• Multiply the quantity in yards by 3 to convert to feet.

This basic principle applies to any kind of unit conversion you encounter.
For example, with time, volume, or mass, knowing key conversion factors helps you translate quantities quickly and accurately. Remember, practicing these conversions will make them second nature.

Simplifying Fractions

Simplifying fractions is the method of reducing a fraction to its simplest form. This means making the numerator and the denominator as small as possible while still maintaining their ratio.
In mathematics, this process is not only useful for ease of computation but also essential for clarity and presentation of results.
In the exercise, we took the ratio \(\frac{6}{2}\) and simplified it by:

• Finding the greatest common divisor (GCD) of 6 and 2, which is 2.
• Dividing both the numerator and denominator by their GCD.

This resulted in the simplified fraction \(\frac{3}{1}\).
Finding the GCD helps ensure you simplify properly, and it works with any fraction, no matter how large or complex. Remember, simplifying fractions helps in comparing ratios and understanding relationships between numbers.

Mathematics Education

Mathematics education is crucial for developing analytical and problem-solving skills. Understanding core mathematical concepts, such as unit conversion and simplifying fractions, are foundational skills in this field.
These skills enable students to handle complex problems more effectively by breaking them into manageable parts.
Teaching these concepts involves demonstrating practical applications across various scenarios, which helps students see the relevance of math in everyday life.

• Use real-world examples to illustrate concepts.
• Encourage students to practice through numerous exercises.
• Provide visual aids and step-by-step tutorials.

By mastering basic skills, students gain confidence in their mathematical abilities, laying the groundwork for more advanced topics.
Remember, the aim is to build understanding and fluency, not just memorization. Seeing mathematics as a tool for inquiry and exploration opens up new pathways for learning and innovation.