Problem 428 - Prealgebra

Question

Simplify. $$647+528$$

Step-by-Step Solution

Answer

1175

Step 1: Add the Units Place

Add the digits in the units place: 7 (from 647) and 8 (from 528). \(7 + 8 = 15\). Write down 5 and carry over 1 to the tens place.

Step 2: Add the Tens Place

Add the digits in the tens place along with the carry-over: 4 (from 647), 2 (from 528), and the carry-over 1. \(4 + 2 + 1 = 7\). Write down 7.

Step 3: Add the Hundreds Place

Add the digits in the hundreds place: 6 (from 647) and 5 (from 528). \(6 + 5 = 11\). Write down 11 next to the previously obtained result.

Key Concepts

Important Steps in Carrying out Addition

Addition is one of the first arithmetic operations you learn, and understanding each step is crucial. The concept of 'step-by-step math' means breaking down the problem into smaller, manageable parts. This way, you can follow the logical progression of the problem and avoid mistakes. For instance, in the exercise provided, we start by adding the smallest units first, like this:

• First, add the units or ones place.
• Next, add the tens place.
• Lastly, add the hundreds place.

These steps ensure accuracy and make it easier to handle more complex problems as you progress in your math journey.

How Addition with Carry Works

When adding larger numbers, sometimes the sum of the digits in one place value (like the ones or tens place) exceeds 9. This is where 'addition with carry' comes into play. Carrying means moving the extra value to the next higher place value. Let's break it down with our example:
1. In the units place, we add 7 and 8 to get 15. We write down 5 and 'carry' over the 1 to the tens place.
2. In the tens place, we then add 4, 2, and the carried-over 1 to get 7. We write down 7.
3. In the hundreds place, we just add 6 and 5 to get 11 and write it down.
This carrying process ensures every digit adds up correctly even when the sums exceed their place value.

The Building Blocks of Basic Arithmetic

Basic arithmetic is a critical foundation in mathematics, consisting mainly of addition, subtraction, multiplication, and division. Addition is often the first operation taught because it is straightforward and intuitive. Here's why mastering basic arithmetic is important:

• It helps you solve everyday problems like calculating expenses.
• It forms the foundation for advanced math topics, including algebra and calculus.
• It improves your logical thinking and problem-solving skills.

So by simplifying sums like 647 + 528, you not only practice arithmetic but also prepare yourself for more complex mathematical challenges. This involves recognizing place values, understanding carrying technique, and following step-by-step procedures for accurate results.