Question

If Mozart composed his first music at the age of 4 and continued composing and performing until he died at the age of \(35,\) what percent of his life was spent composing music?

Short answer

Answer: Mozart spent approximately 88.57% of his life composing music.

Step-by-step solution

Calculate the years Mozart composed music

Subtract the age when Mozart started composing music (4 years) from his total age when he died (35 years) to find the total number of years he was composing music: \(35 - 4 = 31\) years Mozart spent 31 years of his life composing music.

Calculate the percentage of his life spent composing music

Now, we need to calculate the percentage of Mozart's life spent composing music. We do this by dividing the number of years he composed music (31 years) by his total age at the time of his death (35 years), then multiply the result by 100: \(\frac{31}{35} \times 100\%\)

Simplify the fraction and calculate the percentage

Now, we'll simplify the fraction \(\frac{31}{35}\) and calculate the percentage: \(\frac{31}{35} \approx 0.8857\) Then multiply by 100 to get the percentage: \(0.8857 \times 100\% \approx 88.57\%\) So, Mozart spent approximately \(88.57\%\) of his life composing music.

Key concepts

Basic Arithmetic Operations

Basic arithmetic operations are the foundation of many mathematical tasks. These include addition, subtraction, multiplication, and division. Understanding how to perform and apply these operations can help solve various real-world problems, such as calculating expenses, measuring distances, or even figuring out how much of something you consume over time.

Let's look at how these operations were used in Mozart's life example. When we wanted to find out the number of years Mozart spent composing music, we used subtraction. By subtracting the year he started (4 years old) from the year he unfortunately passed away (35 years old), we found that he spent 31 years composing. This simple step of subtraction, represented by the equation:

• \(35 - 4 = 31\)

helped give a clearer picture of his achievements over his lifetime.

After determining the years spent composing, to find the percentage of his life he dedicated to music, we used division and multiplication. Dividing the 31 years of composing by his total life span of 35 years gives us the fraction of his life he devoted to music. Then, we multiply the fraction by 100 to convert it to a percentage, facilitating a clearer understanding and communication of this portion as:

• \(\frac{31}{35} \times 100\% \approx 88.57\%\)

Understanding these basic operations allows for successful navigation and solution of similar fraction-to-percentage problems!

Life-span Age Calculation

Life-span age calculation helps us understand how long someone lived and how to distribute this time into different activities or milestones. It's a simple yet insightful exercise used in a variety of personal and professional analyses.

Consider Mozart, who started composing at 4 and continued until he died at 35. His entire lifespan for composing can be calculated by simply subtracting the starting age (4 years) from his total life age (35 years). This gives us:

• \(35 - 4 = 31\)

This result shows that 31 years of Mozart's life were dedicated to music, a significant chunk considering his total age of 35 years. This calculation forms the basis for deeper analysis, like discovering what percentages of his life were dedicated to different activities.

Being able to convert these age calculations into useful insights is crucial. It allows one to apply these calculations to other life scenarios, such as determining life stages in people or animals, understanding career durations, or planning life goals and achievements. Such analysis often leads to more profound reflections and planning for the future.

Composing Music Duration

Understanding the duration of time dedicated to activities like composing music can provide fascinating insights into someone's life. For Mozart, whose life was heavily devoted to creating music, this becomes a remarkable aspect of his biography.

To calculate the duration of his composing career, we focused on the years between age 4 and 35, arriving at a total of 31 years. But what does this mean in percentage terms? By converting these years into a percentage of his life, it becomes clear how central music was to Mozart.

• The fraction of his life's duration spent composing was calculated as \(\frac{31}{35}\).
• Converting this fraction to a percentage involves multiplying by 100, which results in approximately \(88.57\%\).

This high percentage illustrates that almost the entirety of Mozart's life was consumed by music. Understanding this percentage conversion is not only useful for historical context, but it can also help you in various other fields. It might be analyzing dedication to a hobby or converting similar fractions of time in day-to-day life.

By grasping these calculations, you can better appreciate the scope and depth of someone's commitment, be it in arts, sports, sciences, or other pursuits.