Problem 17 - Prealgebra

Question

In an illustration of a honeybee, the length of the bee is 4.8 centimeters. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

Step-by-Step Solution

Answer

The scale of the drawing is 4:1.

Step 1: Understanding the Problem

We need to find the scale of the illustration of a honeybee compared to its actual size. The picture is 4.8 centimeters long, while the real bee is only 1.2 centimeters long.

Step 2: Writing the Scale Ratio

To find the scale, we write a ratio of the illustration length to the actual length. This is done by dividing the illustration length by the actual length. The scale ratio is given by \( \frac{4.8 \, \text{cm}}{1.2 \, \text{cm}} \).

Step 3: Calculating the Ratio

Calculate \( \frac{4.8}{1.2} \). Divide 4.8 by 1.2 to get the scale ratio. Performing the division, we get 4.

Step 4: Interpreting the Scale

The scale 4 means the illustration is four times larger than the actual honeybee. This ratio is written as 4:1.

Key Concepts

Measurement Conversion

Measurement conversion is an important skill, helping us understand the relationships between different units or quantities. Here, we're looking at the illustration and real size of a honeybee. To comprehend the scale, we need to convert or relate one measurement to another.
- The length of the illustration is 4.8 centimeters. - The actual length of the honeybee is 1.2 centimeters.
The key here is seeing how the larger measurement in the illustration converts to its counterpart in reality through division. When converting, you're often tasked with finding what one unit in a drawing represents in actual size. Being able to switch between these measurements helps in various fields such as architecture, engineering, and even in our exercise of scale drawings.

Ratios in Mathematics

Ratios are fundamental in understanding relationships in mathematics, showing how two quantities compare. In this exercise, the ratio reveals how many times larger the illustration is compared to the actual size of the honeybee.
When dealing with ratios:

• Place the larger number first when indicating something larger or more expansive.
• In this problem, the ratio is calculated by dividing the length of the drawing by the real length: \( \frac{4.8}{1.2} \).
• This division results in \(4\), meaning each 1 cm on the illustration equates to 4 cm in reality.

Ratios like this are not just simple numbers but represent a multiplicative relationship. The ratio \(4:1\) is interpreted such that every unit on the small side needs to be multiplied by 4, emphasizing the enlarged dimensions of the illustration.

Interpretation of Scale in Drawings

Scale in drawings helps in creating representations of objects that are either much larger or smaller than what can be easily visible. In the context of our exercise, the scale helps illustrate a honeybee larger than life for easier observation of details.

• A scale of \(4:1\) suggests that every unit measure in real life is expanded to four units in the drawing.
• Interpretation of scale is straightforward, yet crucial: it indicates the level of enlargement or reduction.
• For this honeybee depiction, scale allows us to see minute details more clearly.

Understanding this concept aids in fields like map-making or model building, where creating a practical, understandable version of something large or distant is necessary. It allows us to make calculations, predictions, and analyses as if handling the object directly.