Problem 31 - Elementary Algebra

Question

Find the percent of adults who wear a seatbelt on every trip. Round to the nearest percent. One in 7 adults did wear a seat belt on every trip. (Source: www.cdc.gov, Jan. 4, 2011)

Step-by-Step Solution

Answer

14 percent of adults wear a seatbelt on every trip.

Step 1 - Understand the Problem

The problem states that one in 7 adults wears a seat belt on every trip. The goal is to find the percentage of such adults and round it to the nearest whole number.

Step 2 - Convert Fraction to Percentage

Since one in seven adults wears a seat belt on every trip, this can be expressed as the fraction \( \frac{1}{7} \). To convert this fraction to a percentage, multiply by 100: \[ \frac{1}{7} \times 100 = 14.2857 \text{ percent} \].

Step 3 - Round to the Nearest Percent

To round 14.2857 percent to the nearest whole number, look at the digit in the tenths place (2). Since it is less than 5, round down to 14 percent.

Key Concepts

fractions to percentages

Understanding how to convert fractions into percentages is a fundamental skill in math. To convert a fraction to a percentage, you simply multiply the fraction by 100. This works because a percentage is just a fraction out of 100. For example, in the given exercise, one in seven adults wearing a seatbelt is represented as the fraction \(\frac{1}{7}\).
To find what fraction \(\frac{1}{7}\) equates to in percentage terms, we multiply by 100:
\[\frac{1}{7} \times 100 \]. This equals approximately 14.2857. Therefore, 14.2857 percent of adults wear a seatbelt on every trip.

rounding numbers

Rounding numbers makes them simpler to use and understand by reducing the number of digits while keeping the value close to what it was. When rounding a number, you need to decide which decimal place you are rounding to. In this example, we are rounding to the nearest whole number.
For 14.2857, we look at the digit in the tenths place, which is 2. If this digit is less than 5, we round down. If it is 5 or more, we round up. Here, since 2 is less than 5, we round down:
14.2857 becomes 14 when rounded to the nearest whole number. This means approximately 14 percent of adults wear a seatbelt on every trip.

basic arithmetic

Basic arithmetic is the foundation of all higher-level math. In our exercise, we used simple multiplication and division, which are core operations in arithmetic. Here's a quick breakdown:

• **Multiplication**: We multiplied the fraction \(\frac{1}{7}\) by 100 to convert it into a percentage. This step is crucial as it helps in understanding how fractions relate to percentages.
• **Division**: Understanding that one in seven can be written as the fraction \(\frac{1}{7}\) involves dividing one by seven. This helps in converting ratios and real-world scenarios into fractions easily.
• Making sense of such basic math operations ensures you can tackle more complex math problems efficiently in the future.