{"id":785,"date":"2023-03-17T13:28:35","date_gmt":"2023-03-17T13:28:35","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&p=785"},"modified":"2025-08-23T00:52:41","modified_gmt":"2025-08-23T00:52:41","slug":"whole-numbers-learn-it-4","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/whole-numbers-learn-it-4\/","title":{"raw":"Whole Numbers: Learn It 4","rendered":"Whole Numbers: Learn It 4"},"content":{"raw":"

Adding Whole Numbers<\/h2>\r\n

A college student has a part-time job. Last week they worked [latex]3[\/latex] hours on Monday and [latex]4[\/latex] hours on Friday. To find the total number of hours they worked last week, they must add [latex]3[\/latex] and [latex]4[\/latex] together. The operation of addition <\/strong>combines numbers to get a sum<\/strong>. The notation we use to find the sum of [latex]3[\/latex] and [latex]4[\/latex] is:<\/p>\r\n

[latex]3+4[\/latex]<\/p>\r\n

We read this as three plus four<\/em> and the result is the sum of three and four. The numbers [latex]3[\/latex] and [latex]4[\/latex] are called the addends<\/strong>. A math statement that includes numbers and operations is called an expression<\/strong>.<\/p>\r\n

\r\n
\r\n

addition notation<\/h3>\r\n\r\nTo describe addition, we can use symbols and words.\r\n\r\n

 <\/p>\r\n

\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Operation<\/td>\r\nAddition<\/td>\r\n<\/tr>\r\n
Notation<\/td>\r\n[latex]+[\/latex]<\/td>\r\n<\/tr>\r\n
Expression<\/td>\r\n[latex]3+4[\/latex]<\/td>\r\n<\/tr>\r\n
Read as<\/td>\r\nthree plus four<\/td>\r\n<\/tr>\r\n
Result<\/td>\r\nthe sum of [latex]3[\/latex] and [latex]4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/center>\u00a0<\/div>\r\n<\/section>\r\n
You may see other words in problems besides \"plus\" that indicate the need for addition. Below are other addition words you might come across.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Operation<\/th>\r\nWords<\/th>\r\nExample<\/th>\r\nExpression<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
Addition<\/td>\r\n<\/tr>\r\n
plus<\/td>\r\n[latex]1[\/latex] plus [latex]2[\/latex]<\/td>\r\n[latex]1+2[\/latex]<\/td>\r\n<\/tr>\r\n
sum<\/td>\r\nthe sum of [latex]3[\/latex] and [latex]4[\/latex]<\/td>\r\n[latex]3+4[\/latex]<\/td>\r\n<\/tr>\r\n
increased by<\/td>\r\n[latex]5[\/latex] increased by [latex]6[\/latex]<\/td>\r\n[latex]5+6[\/latex]<\/td>\r\n<\/tr>\r\n
more than<\/td>\r\n[latex]8[\/latex] more than [latex]7[\/latex]<\/td>\r\n[latex]7+8[\/latex]<\/td>\r\n<\/tr>\r\n
total of<\/td>\r\nthe total of [latex]9[\/latex] and [latex]5[\/latex]<\/td>\r\n[latex]9+5[\/latex]<\/td>\r\n<\/tr>\r\n
added to<\/td>\r\n[latex]6[\/latex] added to [latex]4[\/latex]<\/td>\r\n[latex]4+6[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/section>\r\n
After talking to her counselor, Esmeralda needs to determine how many classes she has taken so far at Blue Sky College. Last year she took [latex]6[\/latex] classes, and this year will complete [latex]8[\/latex] classes. She needs to determine the sum of [latex]6[\/latex] and [latex]8[\/latex].
\r\n
\r\nFirst translate the sentence into math notation and then calculate the results.[reveal-answer q=\"771692\"]Show Solution[\/reveal-answer] [hidden-answer a=\"771692\"] Translate from words to math: [latex]6+8[\/latex]
\r\nWe read this as six plus eight<\/em>\u00a0and the result is the sum of six and eight.
\r\n
[latex]6+8=14[\/latex]<\/center>[\/hidden-answer]<\/section>\r\n
[ohm2_question hide_question_numbers=1]8853[\/ohm2_question]<\/section>\r\n

In the previous example, the sum of the ones was less than [latex]10[\/latex]. But what happens if the sum is [latex]10[\/latex] or more? Let\u2019s use our base - [latex]10[\/latex] model to find out. The graphic below\u00a0shows the addition of [latex]17[\/latex] and [latex]26[\/latex].<\/p>\r\n

\r\n[caption id=\"\" align=\"aligncenter\" width=\"619\"]\"An Figure 1. How to count and add blocks[\/caption]\r\n<\/center>\r\n

 <\/p>\r\n

When we add the ones, [latex]7+6[\/latex], we get [latex]13[\/latex] ones. Because we have more than [latex]10[\/latex] ones, we can exchange [latex]10[\/latex] of the ones for [latex]1[\/latex] ten. Now we have [latex]4[\/latex] tens and [latex]3[\/latex] ones. Without using the model, we show this as a small red [latex]1[\/latex] above the digits in the tens place. When the sum in a place value column is greater than [latex]9[\/latex], we carry over to the next column to the left. Carrying is the same as regrouping by exchanging. For example, [latex]10[\/latex] ones for [latex]1[\/latex] ten or [latex]10[\/latex] tens for [latex]1[\/latex] hundred.<\/p>\r\n

Adding numbers together may seem confusing, but it can be easy and fun with the right problem-solving strategies! When adding two numbers together, try the following steps.\r\n\r\n
    \r\n\t
  1. Write the numbers so each place value lines up vertically.<\/li>\r\n\t
  2. Add the digits in each place value. Work from right to left starting with the ones place. If a sum in a place value is more than [latex]9[\/latex], carry to the next place value.<\/li>\r\n\t
  3. Continue adding each place value from right to left, adding each place value and carrying if needed.<\/li>\r\n<\/ol>\r\n<\/section>\r\n
    Add: [latex]43+69[\/latex]. [reveal-answer q=\"61333\"]Show Solution[\/reveal-answer] [hidden-answer a=\"61333\"]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Write the numbers so the digits line up vertically.<\/td>\r\n[latex]\\begin{array}{c}\\hfill 43\\\\ \\\\ \\hfill \\underset{\\text{____}}{+69}\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n
    Add the digits in each place. Add the ones: [latex]3+9=12[\/latex]<\/td>\r\n <\/td>\r\n<\/tr>\r\n
    Write the [latex]2[\/latex] in the ones place in the sum. Add the [latex]1[\/latex] ten to the tens place.<\/td>\r\n[latex]\\begin{array}{c}\\hfill \\stackrel{1}{4}3\\\\ \\hfill \\underset{\\text{____}}{+69}\\\\ \\hfill 2\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n
    Now add the tens: [latex]1+4+6=11[\/latex] Write the [latex]11 [\/latex] in the sum.<\/td>\r\n[latex]\\begin{array}{c}\\hfill \\stackrel{1}{4}3\\\\ \\hfill \\underset{\\text{____}}{+69}\\\\ \\hfill 112\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n[\/hidden-answer]<\/section>\r\n
    [ohm2_question hide_question_numbers=1]3257[\/ohm2_question]<\/section>\r\n

    When adding whole numbers together we have to keep a couple of properties in mind.<\/p>\r\n

    \r\n
    \r\n

    properties of addition<\/h3>\r\nIdentity Property of Addition<\/strong>\r\n

    The sum of any number [latex]a[\/latex] and [latex]0[\/latex] is the number.<\/p>\r\n

    [latex]\\begin{array}{}\\\\ a+0=a\\\\ 0+a=a\\end{array}[\/latex]<\/center>\r\n

     <\/p>\r\nCommutative Property of Addition<\/strong>\r\n

    Changing the order of the addends [latex]a[\/latex] and [latex]b[\/latex] does not change their sum.<\/p>\r\n

     <\/p>\r\n

    [latex]a+b=b+a[\/latex]<\/center>\r\n

     <\/p>\r\n<\/div>\r\n<\/section>\r\n

    [ohm2_question hide_question_numbers=1]3255[\/ohm2_question]<\/section>\r\n
    [ohm2_question hide_question_numbers=1]3256[\/ohm2_question]<\/section>\r\n

    Add Whole Numbers in Applications<\/h3>\r\n

    Now that we have practiced adding whole numbers, let\u2019s use what we\u2019ve learned to solve real-world problems. We\u2019ll start by outlining a plan. First, we need to read the problem to determine what we are looking for. Then we write a word phrase that gives the information to find it. Next we translate the word phrase into math notation and then simplify. Finally, we write a sentence to answer the question.<\/p>\r\n

    Hao earned grades of [latex]87,93,68,95,\\text{and }89[\/latex] on the five tests of the semester. What is the total number of points he earned on the five tests? [reveal-answer q=\"430478\"]Show Solution[\/reveal-answer] [hidden-answer a=\"430478\"] We are asked to find the total number of points on the tests.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Write a phrase.<\/td>\r\nthe sum of points on the tests<\/td>\r\n<\/tr>\r\n
    Translate to math notation.<\/td>\r\n[latex]87+93+68+95+89[\/latex]<\/td>\r\n<\/tr>\r\n
    Then we simplify by adding.<\/td>\r\n <\/td>\r\n<\/tr>\r\n
    Since there are several numbers, we will write them vertically.<\/td>\r\n[latex]\\begin{array}{}\\\\ \\\\ \\\\ \\stackrel{3}{8}7\\hfill \\\\ 93\\hfill \\\\ 68\\hfill \\\\ 95\\hfill \\\\ \\underset{\\text{+____}}{89}\\hfill \\\\ 432\\hfill \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n
    Write a sentence to answer the question.<\/td>\r\nHao earned a total of\u00a0[latex]432[\/latex] points.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

     <\/p>\r\n

    Notice that we added points<\/em>, so the sum is [latex]432[\/latex] points<\/em>. It is important to include the appropriate units in all answers to applications problems.<\/p>\r\n\r\n[\/hidden-answer]<\/section>\r\n

    [ohm2_question hide_question_numbers=1]8871[\/ohm2_question]<\/section>\r\n

    Some application problems involve shapes. For example, a person might need to know the distance around a garden to put up a fence or around a picture to frame it. The perimeter is the distance around a geometric figure. The perimeter of a figure is the sum of the lengths of its sides.<\/p>\r\n

    \r\n

    Find the perimeter of the patio shown.<\/p>\r\n

    \"This<\/center>[reveal-answer q=\"126824\"]Show Solution[\/reveal-answer] [hidden-answer a=\"126824\"]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    We are asked to find the perimeter.<\/td>\r\n <\/td>\r\n<\/tr>\r\n
    Write a phrase.<\/td>\r\nthe sum of the sides<\/td>\r\n<\/tr>\r\n
    Translate to math notation.<\/td>\r\n[latex]4+6+2+3+2+9[\/latex]<\/td>\r\n<\/tr>\r\n
    Simplify by adding.<\/td>\r\n[latex]26[\/latex]<\/td>\r\n<\/tr>\r\n
    Write a sentence to answer the question.<\/td>\r\n <\/td>\r\n<\/tr>\r\n
    We added feet, so the sum is [latex]26[\/latex] feet.<\/td>\r\nThe perimeter of the patio is [latex]26[\/latex] feet.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n[\/hidden-answer]<\/section>","rendered":"

    Adding Whole Numbers<\/h2>\n

    A college student has a part-time job. Last week they worked [latex]3[\/latex] hours on Monday and [latex]4[\/latex] hours on Friday. To find the total number of hours they worked last week, they must add [latex]3[\/latex] and [latex]4[\/latex] together. The operation of addition <\/strong>combines numbers to get a sum<\/strong>. The notation we use to find the sum of [latex]3[\/latex] and [latex]4[\/latex] is:<\/p>\n

    [latex]3+4[\/latex]<\/p>\n

    We read this as three plus four<\/em> and the result is the sum of three and four. The numbers [latex]3[\/latex] and [latex]4[\/latex] are called the addends<\/strong>. A math statement that includes numbers and operations is called an expression<\/strong>.<\/p>\n

    \n
    \n

    addition notation<\/h3>\n

    To describe addition, we can use symbols and words.<\/p>\n

     <\/p>\n

    \n\n\n\n\n\n\n\n
    Operation<\/td>\nAddition<\/td>\n<\/tr>\n
    Notation<\/td>\n[latex]+[\/latex]<\/td>\n<\/tr>\n
    Expression<\/td>\n[latex]3+4[\/latex]<\/td>\n<\/tr>\n
    Read as<\/td>\nthree plus four<\/td>\n<\/tr>\n
    Result<\/td>\nthe sum of [latex]3[\/latex] and [latex]4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

    \u00a0<\/p><\/div>\n<\/section>\n

    You may see other words in problems besides “plus” that indicate the need for addition. Below are other addition words you might come across.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n
    Operation<\/th>\nWords<\/th>\nExample<\/th>\nExpression<\/th>\n<\/tr>\n<\/thead>\n
    Addition<\/td>\n<\/tr>\n
    plus<\/td>\n[latex]1[\/latex] plus [latex]2[\/latex]<\/td>\n[latex]1+2[\/latex]<\/td>\n<\/tr>\n
    sum<\/td>\nthe sum of [latex]3[\/latex] and [latex]4[\/latex]<\/td>\n[latex]3+4[\/latex]<\/td>\n<\/tr>\n
    increased by<\/td>\n[latex]5[\/latex] increased by [latex]6[\/latex]<\/td>\n[latex]5+6[\/latex]<\/td>\n<\/tr>\n
    more than<\/td>\n[latex]8[\/latex] more than [latex]7[\/latex]<\/td>\n[latex]7+8[\/latex]<\/td>\n<\/tr>\n
    total of<\/td>\nthe total of [latex]9[\/latex] and [latex]5[\/latex]<\/td>\n[latex]9+5[\/latex]<\/td>\n<\/tr>\n
    added to<\/td>\n[latex]6[\/latex] added to [latex]4[\/latex]<\/td>\n[latex]4+6[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n
    After talking to her counselor, Esmeralda needs to determine how many classes she has taken so far at Blue Sky College. Last year she took [latex]6[\/latex] classes, and this year will complete [latex]8[\/latex] classes. She needs to determine the sum of [latex]6[\/latex] and [latex]8[\/latex]. <\/p>\n

    First translate the sentence into math notation and then calculate the results.<\/p>\n