Problem 78 - Elementary Algebra

Question

Find the number of 80,500 children and adolescents who are obese. Round to the nearest hundred. Approximately one in six children and adolescents are obese. (Source: www.cdc.gov, Nov. 2011)

Step-by-Step Solution

Answer

13,400 children and adolescents are obese.

Step 1: Understand the problem

We need to find out how many children and adolescents are obese out of a total of 80,500, given that approximately one in six are obese.

Step 2: Express the ratio as a fraction

Since one in six children and adolescents are obese, we can express this as the fraction \(\frac{1}{6}\).

Step 3: Multiply the total number by the fraction

Multiply the total number of children and adolescents (80,500) by the fraction \(\frac{1}{6}\): \[ 80,500 \times \frac{1}{6} \]

Step 4: Calculate the product

Perform the multiplication: \[ 80,500 \times \frac{1}{6} = 13,416.67 \]

Step 5: Round to the nearest hundred

To round 13,416.67 to the nearest hundred, look at the tens digit (1). Since it is less than 5, we round down to 13,400.

Key Concepts

Understanding Ratios

A ratio is a relationship between two numbers that expresses how much larger one is compared to the other. For example, if one in six children is obese, the ratio of obese children to the total number of children is 1:6. This ratio can also be expressed as the fraction \( \frac{1}{6} \).

Understanding and converting ratios is essential in various topics, including fractional multiplication. In our problem, we use this ratio to find out how many children out of 80,500 are obese.

• Step 1: Express the ratio as a fraction: \( \frac{1}{6} \)
• Step 2: Use the fraction to perform calculations.

Knowing how to work with ratios helps simplify many real-world problems by breaking them down into manageable parts. In this breakdown, each unit (1) obesity case is when compared to 6 total cases, helping simplify our multiplication step.

Rounding Numbers Made Simple

Rounding numbers is essential for simplifying complex calculations and making numbers easier to work with in everyday life. When rounding, always look at the digit immediately to the right of the place you're rounding to. Let's break this down:

• If the digit is less than 5, you round down.
• If the digit is 5 or greater, you round up.

In the exercise, we need to round 13,416.67 to the nearest hundred. Here's how:

• Identify the hundreds and tens place: 13,416.67 – the tens digit is 1.
• Since 1 is less than 5, we round down to 13,400.

Rounding helps simplify the numbers without significantly changing the value in practical terms, making them more manageable.

Multiplication of Numbers and Fractions

Multiplication is a fundamental arithmetic operation used to find the product of two numbers. When dealing with fractions, the process is slightly different but follows specific rules:

• To multiply a number by a fraction, multiply the number by the numerator (top part) of the fraction and then divide by the denominator (bottom part).
• For example, multiplying 80,500 by \( \frac{1}{6} \):

\[ 80,500 \times \frac{1}{6} = 13,416.67 \] This formula helps convert more complex problems into simpler multiplications. By breaking down the multiplication into manageable steps, you can avoid errors and make sure you arrive at the correct answer. This step is crucial in scenarios where accurate results are needed, such as our example where we need to identify the number of obese children accurately.