Problem 13 - Prealgebra

Question

Multiply. $$25 \cdot \frac{1}{1,000}$$

Step-by-Step Solution

Answer

Multiply 25 by \( \frac{1}{1,000} \) to get 0.025.

Step 1: Understand the Operation

We need to multiply the whole number 25 by the fraction \( \frac{1}{1,000} \). This is equivalent to finding the fraction of 25 that is \( \frac{1}{1,000} \).

Step 2: Apply Fraction Multiplication

To multiply a whole number by a fraction, treat the whole number as a fraction with a denominator of 1. Thus, rewrite 25 as \( \frac{25}{1} \). Then multiply across the numerators and denominators: \( \frac{25}{1} \cdot \frac{1}{1,000} = \frac{25 \cdot 1}{1 \cdot 1,000} = \frac{25}{1,000} \).

Step 3: Convert Fraction to Decimal

To express \( \frac{25}{1,000} \) as a decimal, divide 25 by 1,000: \( 25 \div 1,000 = 0.025 \).

Step 4: Conclusion

The result of multiplying 25 by \( \frac{1}{1,000} \) is 0.025.

Key Concepts

Fraction Multiplication

When you multiply a whole number by a fraction, you're essentially taking a fraction of that number. Let's break this down with an example. When you have the number 25 and you need to multiply it by \( \frac{1}{1,000} \), you're finding out what 1/1000th of 25 is. To make the multiplication straightforward, first convert the whole number into a fraction. This is simply done by giving it a denominator of 1. Thus, 25 becomes \( \frac{25}{1} \).

• To multiply fractions, multiply the numerators (top numbers) with each other.
• Multiply the denominators (bottom numbers) with each other as well.
• This means \( \frac{25}{1} \times \frac{1}{1,000} = \frac{25 \times 1}{1 \times 1,000} \).

This results in \( \frac{25}{1,000} \), which is the fraction representation of the product.

Converting Fractions to Decimals

Fraction to decimal conversion is a useful skill, especially in cases where decimals are easier to understand or to use in further calculations. To convert a fraction like \( \frac{25}{1,000} \) into a decimal, you divide the numerator by the denominator. Here’s how it works in this example:

• The numerator is 25, and the denominator is 1,000.
• Perform the division: 25 divided by 1,000 equals 0.025.
• Thus, \( \frac{25}{1,000} \) is the same as 0.025 in decimal form.

Converting fractions to decimals can simplify the number and make it easier to use in real-world situations, like measuring or tracking data.

Basic Arithmetic Operations

Understanding the basic arithmetic operations is crucial in mathematics as they form the foundation for all calculations. These operations include addition, subtraction, multiplication, and division.
When it comes to multiplying a whole number by a fraction, you’re essentially performing two main operations:

• First, rewriting the whole number as a fraction by putting it over 1.
• Second, executing multiplication across both numerators and denominators as explained before.

Remember that multiplication is repeated addition, but when a fraction is involved, it changes your perspective – it's like adding a smaller piece each time, hence the result will often be smaller than the whole number you're starting with.