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Chapter 1: Problem 6

$$ \begin{array}{r} 23 \\ 45 \\ +30 \\ \hline \end{array} $$

Short Answer

Expert verified
The sum is 98.

Step by step solution

01

Arrange the numbers

Start by arranging all the numbers in a column format for easy addition:\[ \begin{array}{c} 23 \ 45 \ +30 \ \hline \end{array}\]
02

Add the ones column

Look at the rightmost column (ones place). Add the digits 3, 5, and 0 together:\[ 3 + 5 + 0 = 8 \]
03

Add the tens column

Now, move to the next column on the left (tens place). Add the digits 2, 4, and 3 together:\[ 2 + 4 + 3 = 9 \]
04

Write the sum

Combine the results of the addition from the ones and tens columns to get the final answer:\[ \begin{array}{c} 23 \ 45 \ +30 \ \hline 98 \ \end{array}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Place Value
Understanding place value is essential to mastering addition, especially with two-digit numbers. It tells us the value of the digit based on its position in the number. Each digit in a number represents a different power of ten, depending on its place. For instance, in the number 23:
  • The '2' is in the tens place and represents 20 (2 x 10).
  • The '3' is in the ones place and represents 3.
Recognizing which digit sits in which place helps in breaking down numbers easily and ensures correct addition. By focusing on one place value at a time, calculations become more manageable and less prone to errors. When we add, we typically start with the ones place and then move left to the tens place, which aligns with the method of dealing with smaller values first before handling larger values.
Column Addition
Column addition is a useful method for adding multi-digit numbers, maximizing accuracy and minimizing mistakes by focusing on one column at a time. Imagine stacking your numbers on top of one another like in a vertical list. Here's how column addition works:
  • First, arrange the numbers so each place value aligns vertically, with ones under ones, tens under tens, and so forth.
  • Start adding from the rightmost column, which is the ones, moving leftwards.
  • Carry over any value above 9 to the next column, adjusting your addition accordingly.
This step-by-step approach ensures each place value is individually accounted for and allows easier handling of potential carryover numbers. It benefits greatly from a clear understanding of place values which dictates how digits interact when added together.
Two-Digit Numbers
Adding two-digit numbers may seem complex at first, but with a bit of practice, it becomes straightforward. Two-digit numbers have both tens and ones places, and understanding how these work together is crucial to success in addition tasks.
  • When you add two-digit numbers, you start by adding the digits in the ones place.
  • If the result is 10 or more, write down the ones digit and carry over the tens digit to the next column.
  • Next, add up the digits in the tens column, also taking into account any number you carried over.
Let's take as an example the numbers 23, 45, and 30. First, you sum up the ones place: 3 + 5 + 0 = 8. Then, move to the tens place: 2 + 4 + 3 = 9. There are no carryovers needed here, making it a perfect example of how addition of two-digit numbers can be smooth and simple.

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