Problem 47 - Basic College Mathematics

Question

Worldwide, t-shirt exports had a total value of \(\$ 43,100,000,000\) in \(2016 .\) Of this amount, approximately \(\frac{2}{3}\) came from cotton t-shirts. Worldwide, what was the value of cotton t-shirts exported in \(2016 ?\)

Step-by-Step Solution

Answer

The value of cotton t-shirts exported in 2016 was \$28,733,333,333.33\.

Step 1 - Understand the problem

We need to determine the value of cotton t-shirts exported in 2016, given that they constitute \(\frac{2}{3}\) of the total t-shirt exports, which were valued at \$43,100,000,000\.

Step 2 - Calculate \(\frac{2}{3}\) of the total value

To find the value of cotton t-shirts, we multiply the total export value \$43,100,000,000\ by \(\frac{2}{3}\).

Step 3 - Perform the multiplication

Calculate \(\frac{2}{3} \times 43,100,000,000 \) which is \$28,733,333,333.33\.

Key Concepts

fractions in real-world problems

Fractions are everywhere in real life, even if you don’t notice them. In this exercise, understanding what \(\frac{2}{3}\) means is essential. When we say that \( \frac{2}{3} \) of the export value is from cotton t-shirts, we are looking at a part of the whole value.
Fractions help break down amounts into smaller, proportional pieces. Here, \( \frac{2}{3} \) tells us that out of every 3 parts of the total export value, 2 of those parts come from cotton t-shirts.
To solve the problem, you need to think of the total value as being split into 3 equal parts. Then, you find out how much value is in 2 of those parts. This is a practical application of fractions in real-world problems, like calculating portions, financial data, or even dividing pieces of pizza!
By multiplying the total value \(\text{\textdollar} 43,100,000,000\) by \( \frac{2}{3} \), you get the exact amount that pertains to cotton t-shirts. Grasping how to use fractions like this can help you understand and solve problems in various fields, from economics to everyday activities.

multiplication of large numbers

Multiplying large numbers might seem tricky, but breaking it down makes it easier. The exercise involves calculating \( \frac{2}{3} \times 43,100,000,000 \). Here's how to handle this:

• First, understand the fraction \( \frac{2}{3} \) as a division.
• To find \( \frac{2}{3} \) of \( 43,100,000,000 \), multiply 43,100,000,000 by 2. This step gives you 86,200,000,000.
• Next, divide 86,200,000,000 by 3.

Using a calculator, the result is the precise value, \( \text{\textdollar} 28,733,333,333.33 \). This step-by-step approach simplifies working with large numbers. Always remember:

• Break down the multiplication process.
• Take it one step at a time.
• Use tools like calculators to verify your results.
  

This method ensures accuracy and builds confidence in handling substantial figures.

understanding economic data

Economic data, like the value of t-shirt exports, provides insight into a country's or industry's performance. The total export value \( \text{\textdollar} 43,100,000,000 \) tells us how significant the t-shirt industry is globally.
Breaking that down to see \( \frac{2}{3} \) of it being from cotton t-shirts reveals valuable data. This means that a large portion of exports come from a single type of product, which can impact supply chains, pricing, and trade policies.
Understanding economic data helps in numerous ways:

• It informs businesses about market trends and consumer preferences.
• It aids governments in policy making and international trade relations.
• It affects economic strategies and decisions at both micro and macro levels.

Learning to interpret and use economic data empowers you to make informed decisions, whether in business, academics, or daily life. It’s a crucial skill in today’s data-driven world.