Problem 67 - Prealgebra

Question

What is \(\frac{1}{3}\) of the sum of 8 and \(4 ?\)

Step-by-Step Solution

Answer

The result is 4.

Step 1: Understand the Problem

We need to find one-third of the sum of two numbers, which are 8 and 4.

Step 2: Calculate the Sum

Add the two numbers together: \[ 8 + 4 = 12 \]

Step 3: Calculate One-Third

Divide the sum (which is 12) by 3 to find one-third of it:\[ \frac{12}{3} = 4 \]

Key Concepts

Addition

Addition is an essential mathematical operation that combines two or more numbers into a single value, known as the sum. Whenever you add two numbers, you're basically "counting together." In the example exercise, we needed to add 8 and 4 to get their total value.
Here's how it works:

• Start by aligning the numbers, which can be helpful if you're working with larger numbers.
• Add the digits starting from the rightmost position (the units), then move to the left (tens, hundreds, etc.).
• In our specific example, you simply add 8 and 4. This gives us the sum, 12.

Understanding addition is foundational as it applies to various scenarios in math, from calculating totals to understanding more complex equations.

Division

Division is like sharing. It involves splitting a number into equal parts or groups. In the exercise, we needed to find one-third of the sum, so we divided the total by 3.
Here's a breakdown of division:

• You have a total amount, or dividend, which you want to divide.
• You divide this amount by the number of parts, or divisor, you need. This tells you how many items fit into each part.
• In our case, with a sum of 12 as the dividend and 3 as the divisor, dividing 12 by 3 gave us the answer, which is 4.

Remember, division helps to find out how many times one number is contained within another, or to distribute an amount among a set number of pieces.

Basic Arithmetic

Basic arithmetic covers the fundamental operations, which are addition, subtraction, multiplication, and division. These operations form the building blocks for more advanced math topics.
Here's what makes them essential:

• **Addition** combines numbers to form a larger sum.
• **Subtraction** is the inverse of addition. It removes one number from another.
• **Multiplication** is repeated addition. If you're familiar with any times tables, you've mastered this operation.
• **Division** breaks a number into smaller parts, as we explained earlier.

By getting comfortable with these basics, anyone can solve everyday problems, from calculating a grocery bill to determining how much fabric you need for a project. Practicing these skills increases your speed and confidence in handling math tasks.