Problem 15 - Fundamentals of Mathematics

Question

\(\frac{1}{3}\) of 2 is what number

Step-by-Step Solution

Answer

\(\frac{2}{3}\)

Step 1: Understanding the Problem

The problem asks us to find a number that is \( \frac{1}{3} \) of 2. This means we need to take the fraction \( \frac{1}{3} \) and multiply it by 2.

Step 2: Set Up the Equation

In mathematical terms, finding \( \frac{1}{3} \) of 2 can be translated into the equation: \(\frac{1}{3} \times 2\).

Step 3: Solve the Equation

Multiply the fraction \(\frac{1}{3}\) by 2: \(\frac{1}{3} \times 2 = \frac{2}{3}\). This is because multiplying a fraction by a whole number means multiplying the numerator (the 1 in \( \frac{1}{3} \)) by the whole number (2), resulting in \( \frac{2}{3} \).

Step 4: Final Answer

The number that is \(\frac{1}{3}\) of 2 is \(\frac{2}{3}\). This is our solution.

Key Concepts

Multiplying Fractions

When you multiply fractions, you work with the numerators and denominators to find the product. To multiply a fraction by a whole number, you simply multiply the numerator of the fraction by the whole number, while the denominator remains unchanged. In this way, multiplying fractions is about:

• Multiplying the numerators together.
• Keeping the denominator the same (except when multiplying two fractions together).

Example:

• If you have the fraction \( \frac{1}{3} \) and want to multiply it by 2, you will multiply 1 by 2, resulting in 2. Thus, \( \frac{1}{3} \times 2 = \frac{2}{3} \).

This simplicity helps to ensure you don't get confused with different denominators or mixed numbers. Just focus on the top numbers, and you're set!
Practice makes perfect. Try multiplying different fractions by whole numbers to get used to the process.

Basic Arithmetic

Basic arithmetic is the heart of all mathematics. It involves simple operations like addition, subtraction, multiplication, and division.
When dealing with fractions, understanding multiplication becomes essential. Arithmetic operations with fractions require a few more steps than operations with whole numbers, but they follow a consistent structure:

• Multiplication involves dealing only with the numerators and multiplying them, keeping denominators consistent if necessary.
• Even more straightforward is dealing with whole numbers. For example, multiplying any number by 1 leaves it unchanged, while multiplying by 0 results in 0.

Becoming familiar with these basics provides a strong foundation for dealing with more complex math problems. Remember to keep practicing, and these skills will start to feel more comfortable over time.

Fraction of a Number

Fraction of a number is all about understanding how to find a part of any given number using fractions. Say you have a whole number like 2, and you want to find out \( \frac{1}{3} \) of 2.
This involves multiplying the fraction by the whole number, as covered in our primary example: \( \frac{1}{3} \times 2 = \frac{2}{3} \).
In practical terms, finding a fraction of a number helps us in daily tasks, like:

• Dividing food into equal portions.
• Calculating discounts and percentages.
• Understanding time segments of an hour or day.

Whenever you see a phrase like 'fraction of a number', think of it as slicing a whole into smaller, equal parts. Always aim to multiply directly to get the correct part or portion you're calculating.