10 ft to 20 yards write the ratio in the simplestt form
The Correct Answer and Explanation is :
To express the ratio of 10 feet to 20 yards in simplest form, we first need to ensure both measurements are in the same unit. We’ll convert the yards to feet.
Conversion Factors
1 yard = 3 feet
Step 1: Convert Yards to Feet
To convert 20 yards to feet:
[
20 \text{ yards} \times 3 \text{ feet/yard} = 60 \text{ feet}
]
Step 2: Set Up the Ratio
Now we have:
- 10 feet
- 60 feet (converted from 20 yards)
We can now express the ratio:
[
\text{Ratio} = \frac{10 \text{ feet}}{60 \text{ feet}}
]
Step 3: Simplify the Ratio
To simplify the ratio, we divide both numbers by their greatest common divisor (GCD). In this case, the GCD of 10 and 60 is 10.
[
\frac{10 \div 10}{60 \div 10} = \frac{1}{6}
]
Final Answer
Thus, the ratio of 10 feet to 20 yards in simplest form is:
[
\text{Ratio} = 1:6
]
Explanation
Ratios are a way to compare two quantities and can be expressed in various forms. In this case, we started with measurements in different units (feet and yards), which necessitated conversion to ensure a valid comparison. The conversion from yards to feet is straightforward, as each yard equals three feet.
Once both quantities were in the same unit, we set up the ratio by placing the two quantities as a fraction. The next step involved simplifying the fraction to its lowest terms, which is done by identifying the greatest common divisor (GCD) of the two numbers. In our example, dividing both the numerator and denominator by 10 allowed us to express the ratio in its simplest form.
Understanding ratios is essential in various fields, including mathematics, science, and daily life, as they help in comparing proportions and understanding relationships between different quantities. The final ratio of 1:6 indicates that for every one part of the first quantity (10 feet), there are six parts of the second quantity (20 yards when converted to feet).