Problem 90 - Prealgebra

Question

In the following exercises, add. $$92 + 39$$

Step-by-Step Solution

Answer

131

Step 1: Align the Numbers

Write the numbers vertically and align them by their rightmost digits. This makes it easier to add each column of digits.

Step 2: Add the Units Place

Start by adding the digits in the units (ones) place: \(2 + 9 = 11\). Write down the 1 in the units place and carry over the 1 to the tens place.

Step 3: Add the Tens Place

Next, add the digits in the tens place along with the carried over 1: \(9 + 3 + 1 = 13\). Write the digit 3 in the tens place and carry over the 1 to the hundreds place.

Step 4: Combine the Results

There is no more digit to add in the hundreds place, but we have the carried over 1. So, we write down the 1 in front of the 3. The final result of the addition is 131.

Key Concepts

Vertical Alignment in Math

When adding numbers, aligning them vertically is essential for accuracy. The concept involves writing numbers so that their digits align in columns based on place value, which makes it easier to add and keep track of carrying over any extra values.

• Align numbers by their rightmost digits.
• The units (ones), tens, hundreds, and so on should be in their respective columns.

Consider our exercise:

    92
 + 39
 ---- 

This method helps you avoid mistakes when adding each place value individually and ensures that you handle carrying over correctly.

Carrying Over in Addition

When the sum of a column exceeds 9, you 'carry over' the extra value to the next column on the left. This ensures the correct addition for our example exercise:

    92
 + 39
 ----
    11

Here, adding the units place resulted in 11 (with 2 + 9), where 1 is written down, and 1 is carried over to the tens place. Now, add the tens place along with the carried 1:

 (1) 92
  + 39
  -----
    13
 

The carried over 1 added to the tens place results in 13, where you write 3 and carry over another 1 to the next place value.

Place Value Addition

Understanding place value is crucial in addition. Place value refers to the position of a digit in a number, which determines its value. Let's break down our example:

• Units (ones) place: Deals with the rightmost digit.
• Tens place: Left of the units place.

In the exercise, we have:

    92
 + 39
 -----
 

Breaking it down, we start by adding the units (ones) place: ewline

 2 + 9 = 11 
 Write down '1', carry '1' over to the tens place.

Next, add the digits in the tens place plus the carried over 1:

 9 + 3 + 1 = 13 
 Write down '3', and because there is no hundreds place digit, write the carried '1' in front of '3'.

This place value addition ensures each digit is correctly added based on its positional context, leading to the final result of 131.