Problem 33 - Prealgebra

Question

In a recent year, the number of \(\$ 1\) bills in circulation in the United States was about 7 billion. Suppose the number of \(\$ 5\) bills in circulation was \(25 \%\) of the number of \$1 bills. About how many \(\$ 5\) bills were in circulation?

Step-by-Step Solution

Answer

There were about 1.75 billion \(\$5\) bills in circulation.

Step 1: Understand the Given Information

We are given that there are approximately 7 billion \(\\(1\) bills in circulation in the United States. Additionally, the number of \(\\)5\) bills is \(25\%\) of that total.

Step 2: Convert the Percentage to a Decimal

The percentage given is \(25\%\). To use it in calculations, convert it to a decimal by dividing by 100: \(25\% = 0.25\).

Step 3: Calculate the Number of $5 Bills

Multiply the total number of \(\\(1\) bills by the decimal to find the number of \(\\)5\) bills: \(7\text{ billion} \times 0.25 = 1.75\text{ billion}\).

Key Concepts

Understanding Basic Arithmetic

Basic arithmetic refers to the fundamental operations that we use in mathematics to solve various problems. These operations are addition, subtraction, multiplication, and division. In everyday life, basic arithmetic helps us count money, measure ingredients, and calculate distances. In the current problem, our use of arithmetic comes into play when we multiply and divide numbers.
Specifically, when determining how many $5 bills are in circulation based on the given percentage, we multiply. This direct application of multiplication is straightforward. We take the total number of $1 bills available ( 7 billion) and simply multiply this number by the given percentage in its decimal form. This process shows how basic arithmetic allows us to move smoothly through the steps of solving real-world problems.

The Art of Problem Solving

Problem-solving is an essential skill in mathematics and daily life. It involves understanding what is asked and then finding the steps needed to reach a solution. Breaking down a problem into steps can make complex issues feel more manageable. In this exercise, the problem was broken down into understanding the given information, converting percentages, and then calculating using math.
By starting with what we know and what is given, we can focus on finding a thoughtful and numerical solution. This process often involves:

• Identifying the exact question being asked
• Understanding what information is needed to solve it
• Performing calculations precisely

This structured approach boosts our confidence when tackling math challenges. Thus, problem-solving in mathematics teaches us a systematic way of thinking, which is applicable to many areas of life.

Converting Percentages to Decimals

The conversion of percentages to decimals is a simple yet crucial step in performing mathematical calculations. Percentages are used to express ratios and proportions as parts of 100. For example, 25% means 25 parts out of 100. To ease our calculations, we often convert percentages to decimals.
This is done by dividing the percentage value by 100. Therefore, 25% becomes 0.25 when converted into a decimal. This decimal form makes it easier to multiply and find totals, like calculating parts of a whole.
With this problem, converting the percentage of $5 bills from 25% to 0.25 allows us to calculate the exact number of bills by simple multiplication. Here's how it looks:

• 25% divided by 100 = 0.25
• Take the decimal (0.25) and multiply it by the total
• 7 billion multiplied by 0.25 equals 1.75 billion

This strategy not only streamlines our math but also ensures accuracy when dealing with larger numbers and complex scenarios.