Problem 16 - Prealgebra

Question

Multiply. $$36.5 \cdot \frac{1}{1,000} \cdot 100$$

Step-by-Step Solution

Answer

3.65

Step 1: Simplify the Fraction

First, solve the fraction \( \frac{1}{1,000} \). This fraction represents 0.001 in decimal form. So, \( \frac{1}{1,000} = 0.001 \).

Step 2: Multiply with the Decimal

Next, multiply 36.5 by the decimal equivalent of the fraction obtained in Step 1.\[ 36.5 imes 0.001 = 0.0365 \]

Step 3: Multiply by 100

Finally, use the result from Step 2 and multiply it by 100.\[ 0.0365 imes 100 = 3.65 \]

Key Concepts

Fractions and Decimals

In mathematics, fractions and decimals are just two ways of representing the same kinds of numbers - those that aren't whole.

• A fraction like \( \frac{1}{1,000} \), tells us directly how many parts, out of a whole, we have.
• This fraction, for example, means one part of a thousand, and it is the same as writing 0.001 in decimal form.
• Decimals make it easy to perform calculations especially when dealing with powers of ten like 10, 100, 1,000, and so on.

Converting fractions to decimals makes multiplication straightforward as decimals align with our base-ten number system. So, next time you see a fraction like \( \frac{1}{1,000} \), think of how it translates to a neat little decimal point - 0.001.

Basic Arithmetic Operations

Arithmetic operations such as addition, subtraction, multiplication, and division are the building blocks of mathematics. Here, we'll focus on multiplication, a fundamental operation.

• Multiplication is repeated addition. For instance, multiplying 36.5 by 0.001 means we are adding 36.5, a very tiny amount of 0.001 times.
• To make it easy, align the decimal points when multiplying by small decimal or fractional values as it helps maintain precision.

Understanding the underlying arithmetic operation helps with conceptual clarity. By grasping these operations deeply, you will become more equipped to tackle more complex computations with ease.

Mathematical Problem-Solving

Mathematical problem-solving is about figuring out the best path to arrive at a solution.

• Start by identifying what the problem demands: here, it's multiplying a decimal by a fraction, and then by 100.
• Breaking down the problem into simple, manageable steps like converting fractions to decimals can significantly simplify the process.
• Each multiplication step builds on the previous result, illustrating the power of orderly computation.

Strong problem-solving skills arise from practice and familiarity with different types of numbers and operations. The goal is to approach each problem methodically and with confidence, ensuring accuracy and efficiency in calculations.