What are bench marks in estimating fractions and mixed.

In the context of estimating fractions and mixed numbers, benchmarks are reference points or commonly used fractions that help us make quick and approximate estimations. They serve as useful tools when trying to estimate the value of a fraction or mixed number without using precise calculations.

Typically, benchmarks are fractions with easily recognizable and round values, such as 0, 1/2, and 1. By comparing a given fraction or mixed number to these benchmarks, we can quickly determine its approximate value.

To estimate a fraction or mixed number using benchmarks, follow these general steps:

1. Identify a benchmark: Choose a benchmark that is close to the given fraction or mixed number. Common benchmarks include 0, 1/2, and 1, but you can use other fractions that you find convenient.

2. Determine if the fraction is closer to the benchmark below or above it: Compare the given fraction or mixed number to the benchmark. Decide if it is closer to the benchmark below it or the benchmark above it.

3. Make an approximation: Estimate the value of the fraction or mixed number based on its proximity to the benchmark. You can use the benchmark itself or a value slightly smaller or larger, depending on the situation.

Let's look at an example to better understand how to use benchmarks:

Example: Estimate the value of the fraction 4/7 using benchmarks.

1. Identify a benchmark: Let's choose 1/2 as our benchmark since it is close to 4/7.

2. Determine closer benchmark: Since 4/7 is closer to 1/2 than 1, we will use 1/2 as our benchmark.

3. Make an approximation: As 4/7 is slightly more than 1/2, we can estimate it as approximately 1/2 or slightly greater than 1/2.

By using benchmarks, we can quickly estimate the value of a fraction or mixed number without engaging in complex calculations. Keep in mind that these estimations may not be precise but are helpful for quick approximations.