Problem 33 - Fundamentals of Mathematics

Question

\(\frac{3}{8}\) of what number is \(0 ?\)

Step-by-Step Solution

Answer

The unknown number is 0.

Step 1: Understand the Problem

We are given a fraction of a number which results in zero. Specifically, \( \frac{3}{8} \) of an unknown number equals \(0\). Our task is to find this unknown number.

Step 2: Set Up the Equation

Let \( x \) represent the unknown number. According to the problem, \( \frac{3}{8} \cdot x = 0 \).

Step 3: Solve the Equation

To solve for \( x \), we can isolate \( x \) by dividing both sides of the equation by \( \frac{3}{8} \). Dividing both sides by \( \frac{3}{8} \), we get: \[ x = \frac{0}{\frac{3}{8}} \].

Step 4: Simplify the Equation

Since any number divided by a nonzero number is zero, \( \frac{0}{\frac{3}{8}} = 0 \). Therefore, \( x = 0 \).

Key Concepts

Understanding the Unknown Number

An unknown number is something we do not know yet. In problems, it is often represented by a letter like \( x \). This way, we have a placeholder for the number we need to find. In this exercise, the unknown number is a part of an equation. Using a letter helps us to find out what the number should be, given that some part of it is zero. Let's think about this: when we use a letter for something unknown, it organizes our thought process. It becomes this mystery that we need to solve by using math. Here, our letter, \( x \), represents the number that, when multiplied by \( \frac{3}{8} \), gives us zero. That's our starting point. We use equations to find out what this \( x \) has to be.

Equation Solving Basics

Solving an equation means finding out what our unknown number is. We do this by using different math operations to "untangle" the equation. When we start with the equation \( \frac{3}{8} \cdot x = 0 \), our goal is to find out what \( x \) must be. Here's how equations help us figure things out:

• We can use operations like addition, subtraction, multiplication, and division to simplify and solve the equation.
• We should perform the same operation on both sides to keep the equation balanced.

In our problem, we solve the equation by dividing both sides by the fraction \( \frac{3}{8} \). This allows us to isolate \( x \) on one side and figure out what its value is.

Dividing by Fractions

Dividing by fractions can be tricky, but remember, it is the same as multiplying by the reciprocal of the fraction. The reciprocal of a fraction is what you get when you flip the numerator and the denominator. So, for \( \frac{3}{8} \), its reciprocal would be \( \frac{8}{3} \). When you divide by a fraction, for example, \( x = \frac{0}{\frac{3}{8}} \), you actually multiply by the reciprocal:

• Multiply \( 0 \) by \( \frac{8}{3} \).
• This means \( 0 \times \frac{8}{3} = 0 \) because any number multiplied by zero is always zero.

This operation allowed us to simplify the equation and show that \( x = 0 \). It's a neat trick with fractions that helps solve equations! Always remember: dividing by a fraction is just like flipping and multiplying.