8 feet to 6 yards as a ratio
The correct answer and explanation is:
Correct Answer:
8 feet : 6 yards = 8 : 18 = 4 : 9
Explanation (300 words):
To compare 8 feet to 6 yards as a ratio, we must first express both quantities in the same unit. You can either convert feet to yards or convert yards to feet. Let’s choose to convert yards to feet, since 1 yard = 3 feet.
So:
- 6 yards × 3 feet/yard = 18 feet
Now we are comparing:
- 8 feet : 18 feet
This simplifies to a ratio of:
- 8 : 18
To reduce this to its simplest form, divide both terms by their greatest common divisor (GCD). The GCD of 8 and 18 is 2.
So:
- 8 ÷ 2 = 4
- 18 ÷ 2 = 9
Thus, the simplest form of the ratio is:
- 4 : 9
Why This Matters:
Ratios are used to compare two quantities that are related. They help express how much of one thing there is compared to another. However, a meaningful ratio requires comparable units, just like comparing apples to apples. That’s why converting all units to the same base (feet in this case) is essential before simplifying.
This ratio (4:9) tells us that for every 4 feet, there are 9 feet when measured equivalently to 6 yards. You can think of it as a proportion that keeps their relationship consistent, even if scaled.
Understanding unit conversions and simplifying ratios is foundational in subjects like mathematics, science, construction, and finance where clear, proportional relationships must be communicated efficiently and accurately.