Problem 70 - Prealgebra

Question

In the following exercises, model the addition. $$15 + 63$$

Step-by-Step Solution

Answer

The answer is 78.

Step 1: Write Down the Addition Problem

Start by writing down the addition problem given in the exercise: \(15 + 63\)

Step 2: Align the Numbers

Align the numbers vertically so that the ones place of each number is in the same column: \[\begin{array}{r} 15 \ +63 \end{array}\]

Step 3: Add the Ones Place

Add the digits in the ones place: \(5 + 3 = 8\)Write 8 in the ones place of the answer.

Step 4: Add the Tens Place

Add the digits in the tens place: \(1 + 6 = 7\)Write 7 in the tens place of the answer.

Step 5: Write the Final Answer

Combine the digits from the previous steps to write the final answer: \(78\)

Key Concepts

arithmetic

Arithmetic is one of the foundational skills in mathematics. It involves the basic operations such as addition, subtraction, multiplication, and division. In this exercise, we focus on addition, which combines two or more numbers to get a total sum.

Understanding arithmetic is crucial because it is used in everyday life, from shopping and cooking to budgeting and construction. Learning how to add numbers correctly sets the stage for more advanced math topics.

To add numbers, you line them up by their place values (units, tens, hundreds, etc.) and add each column starting from the rightmost column (units). This way, you ensure that each digit is correctly aligned with its place value counterpart.

place value

Place value is a fundamental concept in arithmetic that helps us understand the value of each digit in a number. Each digit's value depends on its position within the number. For example, in the number 63, '6' is in the tens place, meaning it represents 60 (6 tens), and '3' is in the ones place, meaning it represents 3 (3 ones).

Let's break down the addition of 15 and 63 using place value:

• First, align both numbers by their place values:
  - Ones place aligns with ones place
  - Tens place aligns with tens place
  
• Add the digits starting from the ones place moving to the tens place.

This ensures that the calculations are accurate, and every digit is appropriately accounted for.

Understanding place value is essential because it helps simplify arithmetic operations and provides a clearer understanding of how numbers work. It also lays the groundwork for more complex operations like multiplication and division.

step-by-step solution

The step-by-step solution method helps break down complicated problems into smaller, manageable parts. This makes it easier to understand and solve math problems without getting overwhelmed. Here’s how we can solve the addition problem using a step-by-step approach:

• Step 1: Write Down the Addition Problem
  Start by writing down the addition problem given in the exercise: \(15 + 63\)
  
• Step 2: Align the Numbers
  Align the numbers vertically so that the ones place of each number is in the same column. It should look like this:
  \[ \begin{array}{r} 15 \ +63 \end{array} \]
  
• Step 3: Add the Ones Place
  Add the digits in the ones place: \(5 + 3 = 8\)
  Write 8 in the ones place of the answer.
  
• Step 4: Add the Tens Place
  Add the digits in the tens place: \(1 + 6 = 7\)
  Write 7 in the tens place of the answer.
  
• Step 5: Write the Final Answer
  Combine the digits from the previous steps to write the final answer: 78

By following this method, you can easily add any two-digit numbers and get the accurate result.