Problem 203 - Prealgebra

Question

In the following exercises, simplify. $$ 719+341 $$

Step-by-Step Solution

Answer

1060

Step 1: Understand the Problem

The problem asks to simplify the expression by adding the two numbers 719 and 341.

Step 2: Line up the Numbers

Write the numbers one below the other, aligning them by their place values (units, tens, and hundreds).

Step 3: Add the Units Column

Add the digits in the units column: 9 (from 719) + 1 (from 341) = 10. Write down 0 and carry over 1 to the tens column.

Step 4: Add the Tens Column

Add the digits in the tens column: 1 (from the carry-over) + 1 (from 719) + 4 (from 341) = 6. Write down 6.

Step 5: Add the Hundreds Column

Add the digits in the hundreds column: 7 (from 719) + 3 (from 341) = 10. Write down 10.

Step 6: Combine the Digits

Combine the digits of the final result from each column to form the simplified answer: 1060.

Key Concepts

Place Value

When performing addition, understanding **place value** is crucial. Place value refers to the position of a digit in a number. Each position represents a different power of 10. For instance, in the number 719:

• The digit '9' is in the units place, and it represents 9.
• The digit '1' is in the tens place, and it represents 10.
• The digit '7' is in the hundreds place, and it represents 700.

When we align the numbers 719 and 341 for addition, we must ensure each digit is in the correct column.
This alignment ensures we correctly add units to units, tens to tens, and hundreds to hundreds.

Carrying Over

One essential step in addition, especially with larger numbers, is **carrying over**. When the sum of digits in a column is 10 or more, you need to carry over the extra value to the next column.
Here’s what it looks like in our example:

• In the units column, 9 (from 719) + 1 (from 341) = 10. We write down 0 and carry over the 1 to the tens column.
• In the tens column, we add the carry-over 1 + original digits: 1 (from 719) + 4 (from 341) = 6. No carry-over is needed here.
• In the hundreds column, we add 7 (from 719) + 3 (from 341) = 10. We write down 10 as there are no more columns to carry over to.

Carrying over ensures that we distribute values correctly and get the accurate result after addition.

Simplifying Expressions

Simplifying expressions involves making a mathematical problem easier to solve. In our case, it means adding numbers together accurately to form a single, simpler number.
When given an expression like 719 + 341, we simplify it in several steps:

• Align the numbers by place value (units, tens, hundreds).
• Add each column starting from the units place.
• Write down the result and carry over where necessary.
• Finally, combine all digits from each column to form the simplified answer.

For our original problem:

• Units column: 9 + 1 = 10 (write down 0, carry over 1)
• Tens column: 1 (carry over) + 1 + 4 = 6
• Hundreds column: 7 + 3 = 10 (write down 10)

Combining these, the simplified expression is: 1060.