Problem 86 - Prealgebra

Question

The National Safe Kids Campaign and Bell Sports sponsored a study that surveyed 8,159 children ages 5 to 14 who were riding bicycles. Approximately \(\frac{2}{5}\) of the children were wearing helmets, and of those, only \(\frac{13}{20}\) were wearing the helmets correctly. About how many of the children were wearing helmets correctly?

Step-by-Step Solution

Answer

Approximately 2,121 children were wearing helmets correctly.

Step 1: Determine Total Helmet Wearers

Find the fraction of children wearing helmets. Since \(\frac{2}{5}\) of the children surveyed were wearing helmets, calculate the total number of children wearing helmets as follows:\[\text{Total helmet wearers} = \frac{2}{5} \times 8,159\]

Step 2: Calculate Number Wearing Helmets

Now, compute the product from step 1 to determine the total number of children wearing helmets:\[\text{Total helmet wearers} = \frac{2}{5} \times 8,159 = 3,263.6\]Since the number of children must be a whole number, round it to 3,264.

Step 3: Find Correct Helmet Users

Calculate how many of the helmet wearers were wearing the helmet correctly. Since \(\frac{13}{20}\) of the helmet wearers were doing so correctly, multiply the total number of helmets wearers by this fraction:\[\text{Correct helmet wearers} = \frac{13}{20} \times 3,264\]

Step 4: Compute Correct Helmet Wearers

Now, compute the result from step 3:\[\text{Correct helmet wearers} = \frac{13}{20} \times 3,264 = 2,121.2\]Round the result to the nearest whole number: 2,121.

Key Concepts

Understanding Multiplying Fractions

Multiplying fractions is a straightforward process once you get the hang of it. Imagine you have two numbers, both less than one, and you multiply them. The result will be a number smaller than the smallest of the two. This happens because you're effectively taking a portion of a portion, naturally making the result smaller. When we multiply fractions, we follow these simple steps:

• Multiply the numerators (the top numbers) of the fractions to get the numerator of the product.
• Multiply the denominators (the bottom numbers) of the fractions to get the denominator of the product.
• Simplify the resulting fraction if necessary to get the final answer.

Here's how it works in our bicycle helmet example: We started by determining the fraction of total children wearing helmets and then multiplying this by the fraction wearing them correctly. So, \(\frac{2}{5} \times 8,159 = 3,263.6\).The next step was to determine how many children wore helmets correctly with \(\frac{13}{20} \times 3,264\). Remember, fractions help us find parts of whole things, and multiplying them is just as easy as multiplying numbers!

Principles of Rounding Numbers

Numbers don't always make perfect sense in fractions or decimals, especially when counting things like people, where you can't have a fraction of a person! Rounding is our helpful friend here. It allows us to turn those untidy numbers into something easier to work with. Here's how you do it:

• First, identify the decimal place you're rounding to—often, it's the nearest whole number.
• Look at the first digit to the right of your rounding place. If it's 5 or more, round up. If it's less than 5, round down.
• Adjust the last digit of your number according to your findings.

In the helmet problem, when we calculated \(3,263.6\) people wearing helmets, we couldn't have a fraction of a child. We rounded \(3,263.6\) to \(3,264\), giving us a sensible whole number. This method ensures that the numbers we work with are practical and realistic, especially in counting cases.

Ensuring Children's Safety with Helmets

Children's safety is paramount, especially when they're engaging in activities like cycling where falls can lead to serious injuries. Wearing a helmet significantly reduces this risk, but it is crucial that the helmet is worn correctly to provide maximum protection. Here are some safety tips:

• Ensure that the helmet fits snugly and comfortably. It shouldn't wobble much on the head.
• The helmet should sit level on the child’s head and not tilt backward or forward.
• The chin strap should be securely fastened and tight enough that only two fingers can fit between the strap and the chin.

In our study scenario, only \(\frac{13}{20}\) of the children wearing helmets had them on correctly, indicating room for safety improvement. Parents and guardians can play a key role by reinforcing good helmet-wearing habits. By educating children on how to wear helmets correctly, we can ensure their adventurous spirit is backed by top-notch safety.