Express each ratio as a fraction in simplest form . 18 pounds to 22 pounds
The Correct Answer and Explanation is:
To express the ratio of 18 pounds to 22 pounds as a fraction in simplest form, we can follow these steps:
- Write the Ratio as a Fraction: The ratio of 18 pounds to 22 pounds can be written as the fraction ( \frac{18}{22} ).
- Identify the Greatest Common Factor (GCF): To simplify this fraction, we need to find the greatest common factor of the numerator (18) and the denominator (22). The factors of 18 are:
- 1, 2, 3, 6, 9, 18
The factors of 22 are: - 1, 2, 11, 22 The largest common factor between these two sets is 2.
- Divide by the GCF: To simplify the fraction, divide both the numerator and the denominator by their GCF.
- For the numerator: ( 18 \div 2 = 9 )
- For the denominator: ( 22 \div 2 = 11 ) So, we have: [
\frac{18}{22} = \frac{9}{11}
]
- Final Answer: Thus, the simplified form of the ratio of 18 pounds to 22 pounds is ( \frac{9}{11} ).
Explanation
Ratios are used to compare two quantities and can be expressed in different forms, including fractions. When expressing a ratio as a fraction, the objective is to simplify it to its lowest terms to facilitate understanding and comparison.
In our example, the ratio of 18 to 22 was straightforward to convert to a fraction. The process of simplifying involves identifying the greatest common factor (GCF), which allows us to reduce the fraction. This is crucial because working with simplified fractions makes calculations easier and allows for clearer communication of numerical relationships.
Furthermore, recognizing the GCF not only helps in simplification but also enhances our understanding of the relationship between the two quantities being compared. The simplified fraction ( \frac{9}{11} ) now provides a clear picture of the proportional relationship between the two weights.
In everyday applications, such as cooking, shopping, or even in scientific measurements, understanding how to express and simplify ratios is vital. It aids in accurate measurement and comparison, which are essential skills in various practical situations.