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Introduction to Addition
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Introduction

In this lesson, you will learn how to add like-terms and use 3 simple steps to add large numbers.


This video illustrates the lesson material below. Watching the video is optional.

Addition (04:53 mins) | Transcript


Addition

Addition is simply combining two groups of like things together. It has application in every part of life. Adding two small things can be done relatively easily and often without having to write anything down. However, adding large numbers takes more steps and usually requires writing things down in order to help us keep track of our addition.

Don’t be afraid to use your fingers while figuring out a math problem. Students that learn to count using their fingers actually do better in math. This kind of exercise gives the numbers a more visual representation and allows you to better learn the process of addition.

Adding Like-Things

When performing addition, you must add like-things or like-terms.

Imagine you have 4 apples and 7 oranges, and you want to add them together. 4 apples and 7 oranges will never become 11 apples. The same is true on the other side of the problem: 7 apples and 4 oranges will never be 11 oranges.

Two glass bowls on an extremely white background. The bowl on the left contains three apples, and the bowl on the right contains four oranges.

Figure 1

Thus, it is important to always add like-things: 3 apples and 4 apples will equal 7 apples.

Steps for Addition

There are a few steps for addition problems that are helpful, especially when adding larger numbers.

  1. Stack the numbers in columns according to their place values.
    • When adding, you can rearrange the numbers in whatever order you like. For example, if you are adding \(14+9\), you can rewrite the equation as \(9+14\).
    • The place value of a number is determined by its position in the number. Look at 14 as an example: the 4 is the first number on the right, so that means it is in the ones place. The second number, 1, is in the tens place.
    • Below is an example of what step 1 might look like:

      \begin{align*} 1&4\\ + & 9\\ \hline \end{align*}

  2. Add each column, starting on the right and moving to the left.
    • After lining up the equation, start by adding the numbers in the ones place column. When you add \(4+9\), you get 13. Put the 3 below the 9 in the ones place and carry the 1 to be added to the left column, as explained in step 3.
  3. Carry groups of 10 to the column to the left. Add the tens place column, including the number that was carried over from the ones place column: \(1 + 1 = 2\). So \(14 + 9 = 23\).
    \begin{align*}\color{orange}\small\text{1} \\1&4\\ + & 9\\ \hline 2&3\end{align*}

Visualizing Addition

In order to solve any addition equation, repeat the steps above as needed until you find the final answer.

Now look at this same problem visually. There are squares that represent \(14+9\). 14 is represented by one stick of 10 and four individual ones. 9 is represented by nine individual ones (see Figure 2).

The figure shows two columns of boxes on both sides. The first column on the left shows ten boxes that are connected to each other. The four boxes to its right have spaces between them. The column of boxes located on the far right shows five spaced out boxes and the column of four boxes on its left are also spaced out.

Figure 2

There are enough 1’s to create another stick of 10. You can take the four 1’s from the 14 and six 1’s from the 9 to create a stick of 10 (see Figure 3 and Figure 4).

The five boxes located at the far right of the image are all surrounded by an orange box, the first box on the inner column to the right is the only one surrounded by an orange box in that column. The column of boxes located in the inner left is also surrounded by an orange box.

Figure 3

The image shows a column of ten boxes on the left, another column of ten boxes in the middle, and only a column of three boxes on the right.

Figure 4

You can use these visual figures and say that 14 plus 9 is two sets of 10 and three 1’s, which equals 23.


Things to Remember


  • Steps for addition:
    1. Stack numbers in columns according to their place values.
    2. Add each column; start on the right and move to the left.
    3. Carry groups of 10 to the column to the left.
  • Addition is for combining like-things. You should not add things that are different.

Practice Problems

Evaluate the following expressions:
    1. \(4 + 3 =\) ? (
      Solution
      x
      Solution:
      7
      )
    2. \(2 + 7 =\) ? (
      Solution
      x
      Solution:
      9
      )
    3. \(7 + 9 =\) ? (
      Video Solution
      | Transcript)
    4. \(0 + 4 =\) ? (
      Solution
      x
      Solution: 4
      Details: In addition, a zero represents an empty or null value. If then, zero is an empty value, the four ones added to zero equals 4.
      )
    5. \(5 + 8 =\) ? (
      Solution
      x
      Solution: 13
      Details:
      This is a box that displays five blue circles on the left and eight blue circles on the right. Above those circles, five plus eight is listed.
      You can think of the 8 in this problem as five ones and three ones.

      This is a box that displays five pink circles on the left. On the right there are eight circles, but five out of these eight circles on the right are also pink. The expression five plus eight is written above these circles.
      You can think about this problem as having two fives and one three. Two fives give us 10. Plus three ones equals 13.

      This image is the same as the previous image but now there are arrows from the group of five pink circles on the left and five pink circles on the right to an equation: five plus five equals ten. There is another arrow from this equation and from the remaining three circles on the right pointing to another equation: ten plus three equals thirteen.

      Or
      \(5 + 8\)

      Rename 8 to \(5 + 3\)
      \(5 + 5 + 3\)

      Group the two 5's to make 10.
      \(10 + 3\)

      \(10 + 3 = 13\)
      )
    6. \(9 + 8 =\) ? (
      Video Solution
      | Transcript)

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