An 8-inch By 10-inch Photograph Is Being Reduced By A Scale Factor Of 2 4 \frac{2}{4} 4 2 ​ . What Are The New Dimensions?

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Introduction

When it comes to reducing the size of an image, a scale factor is often used to determine the new dimensions. In this article, we will explore how to calculate the new dimensions of an 8-inch by 10-inch photograph when it is reduced by a scale factor of 24\frac{2}{4}.

Understanding Scale Factors

A scale factor is a ratio that represents the amount of change in the size of an object. In this case, the scale factor is 24\frac{2}{4}, which can be simplified to 12\frac{1}{2}. This means that the new dimensions of the photograph will be half the size of the original dimensions.

Calculating the New Dimensions

To calculate the new dimensions of the photograph, we need to multiply the original dimensions by the scale factor. The original dimensions are 8 inches by 10 inches, and the scale factor is 12\frac{1}{2}.

Length

The length of the photograph is 10 inches. To calculate the new length, we multiply 10 inches by the scale factor of 12\frac{1}{2}.

New Length=10×12=5 inches\text{New Length} = 10 \times \frac{1}{2} = 5 \text{ inches}

Width

The width of the photograph is 8 inches. To calculate the new width, we multiply 8 inches by the scale factor of 12\frac{1}{2}.

New Width=8×12=4 inches\text{New Width} = 8 \times \frac{1}{2} = 4 \text{ inches}

Conclusion

In conclusion, when an 8-inch by 10-inch photograph is reduced by a scale factor of 24\frac{2}{4}, the new dimensions are 5 inches by 4 inches.

Example Use Case

Reducing the size of an image is a common task in graphic design and photography. For example, a photographer may want to reduce the size of a large image to fit it on a smaller canvas or to make it easier to print.

Tips and Tricks

When working with scale factors, it's essential to remember that the scale factor is a ratio, not a percentage. This means that a scale factor of 12\frac{1}{2} is not the same as a 50% reduction.

Frequently Asked Questions

Q: What is a scale factor?

A: A scale factor is a ratio that represents the amount of change in the size of an object.

Q: How do I calculate the new dimensions of an image when it is reduced by a scale factor?

A: To calculate the new dimensions, multiply the original dimensions by the scale factor.

Q: What is the difference between a scale factor and a percentage?

A: A scale factor is a ratio, while a percentage is a fraction of 100. For example, a scale factor of 12\frac{1}{2} is not the same as a 50% reduction.

Further Reading

If you want to learn more about scale factors and how to use them in real-world applications, check out the following resources:

References

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Introduction

Scale factors are an essential concept in mathematics, particularly in geometry and measurement. However, they can be confusing, especially when it comes to applying them in real-world situations. In this article, we will answer some of the most frequently asked questions about scale factors, providing you with a better understanding of this concept.

Q&A

Q: What is a scale factor?

A: A scale factor is a ratio that represents the amount of change in the size of an object. It is used to determine the new dimensions of an object when it is enlarged or reduced.

Q: How do I calculate the new dimensions of an image when it is reduced by a scale factor?

A: To calculate the new dimensions, multiply the original dimensions by the scale factor. For example, if the original dimensions are 10 inches by 8 inches and the scale factor is 12\frac{1}{2}, the new dimensions would be 5 inches by 4 inches.

Q: What is the difference between a scale factor and a percentage?

A: A scale factor is a ratio, while a percentage is a fraction of 100. For example, a scale factor of 12\frac{1}{2} is not the same as a 50% reduction. To convert a scale factor to a percentage, multiply the scale factor by 100.

Q: Can I use a scale factor to enlarge an object?

A: Yes, you can use a scale factor to enlarge an object. To do this, multiply the original dimensions by the scale factor. For example, if the original dimensions are 5 inches by 4 inches and the scale factor is 2, the new dimensions would be 10 inches by 8 inches.

Q: How do I determine the scale factor of an object?

A: To determine the scale factor of an object, you need to know the original and new dimensions of the object. You can then divide the new dimensions by the original dimensions to get the scale factor. For example, if the original dimensions are 10 inches by 8 inches and the new dimensions are 20 inches by 16 inches, the scale factor would be 2.

Q: Can I use a scale factor to compare the sizes of two objects?

A: Yes, you can use a scale factor to compare the sizes of two objects. To do this, divide the dimensions of one object by the dimensions of the other object. For example, if one object has dimensions of 10 inches by 8 inches and the other object has dimensions of 20 inches by 16 inches, the scale factor would be 2, indicating that the second object is twice the size of the first object.

Q: How do I apply scale factors in real-world situations?

A: Scale factors are used in a variety of real-world situations, including architecture, engineering, and graphic design. For example, architects use scale factors to design buildings and bridges, while engineers use them to design machines and mechanisms. Graphic designers use scale factors to create images and graphics that are proportional to the original image.

Conclusion

Scale factors are an essential concept in mathematics, particularly in geometry and measurement. By understanding how to calculate and apply scale factors, you can solve a variety of problems in real-world situations. Whether you are an architect, engineer, or graphic designer, scale factors are an essential tool to have in your toolkit.

Example Use Case

Reducing the size of an image is a common task in graphic design and photography. For example, a photographer may want to reduce the size of a large image to fit it on a smaller canvas or to make it easier to print.

Tips and Tricks

When working with scale factors, it's essential to remember that the scale factor is a ratio, not a percentage. This means that a scale factor of 12\frac{1}{2} is not the same as a 50% reduction.

Further Reading

If you want to learn more about scale factors and how to use them in real-world applications, check out the following resources:

References