Question

Find the percent. Round to the nearest whole percent. \(-292\) people in favor out of 450 people surveyed

Short answer

There was a mistake in the problem, the number of people in favor must be a positive number. The answer could not be calculated.

Step-by-step solution

Identify the numbers

The problem gives us two numbers: -292 and 450. The number -292 represents those in favor and 450 represents the total persons who were surveyed.

Calculate the ratio

Set up a ratio of favorable to total. This would be \(-292/450\). This ratio tells us the fraction of people who are in favor out of the total surveyed.

Convert fraction to percent

To convert the fraction to a percent, multiply the fraction by 100. This would be \((\-292/450) \times 100\).

Round to nearest whole percent

Once you get your answer, round it to the nearest whole number.

Key concepts

Ratio and Proportion

Grasping the concept of a ratio helps to understand relationships between two quantities. It compares parts to each other or to a whole. On the other hand, proportion indicates that two ratios are equal. When given two quantities, like the number of people in favor versus the total number surveyed, we can set up a ratio to express the fraction of the favorable responses.

For instance, if out of 450 people surveyed, 292 are in favor, we express this as a ratio like so: \(\frac{292}{450}\). This communicates that for every 450 people considered, 292 are in favor. Important to note is that in the exercise given, the number of people in favor is negative, which is an abnormal situation. Normally, a count of people is a positive number, indicating a possible error in the supplied data.

To examine if ratios form a proportion, one could set this ratio equal to another ratio and solve to check if the two are equivalent. If they are, then it can be said that they are proportional to each other.

Fraction to Percent Conversion

Transitioning from fractions to percentages is a fundamental skill in mathematics, serving practical purposes in everyday life, such as understanding survey results or calculating discounts. A percentage is merely a fraction with a denominator of 100, which represents a part of a whole per hundred.

Converting a fraction like \(\frac{-292}{450}\) to a percentage involves multiplying the fraction by 100. This operation effectively tells us how many times the numerator of the fraction fits into 100. The calculation \(\frac{-292}{450} \times 100\) helps us see what percentage of surveyed people are in favor. However, if you encounter a negative number in a real situation, such as -292, it's crucial to revisit the data since percentages tend to represent non-negative quantities like rates or shares.

Rounding Numbers

Arriving at a practical, understandable figure often requires rounding numbers. In daily life, and not just academic exercises, approximate values are frequently more useful than exact ones for ease of communication and decision-making. Rounding involves modifying a number to the nearest whole number, tenth, hundredth, etc., based on a set level of precision.

Rounding to the nearest whole percent means looking at the digit in the tenths place (or the first digit after the decimal point when expressed as a decimal) and deciding whether to round up or down. If that digit is 5 or greater, we round up, and if it's less than 5, we round down. This way, the percentage \(\frac{-292}{450} \times 100\), once calculated, will be rounded to the nearest whole number, yielding a more condensed and comprehensible figure for reporting or comparison purposes. Remember, a negative percent doesn't normally make sense in contexts like survey results, so a negative outcome would indicate a need to double-check the figures or the context wherein the data is being applied.