Arithmetic with Whole Numbers

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  • 0:05 Four Operations
  • 0:19 Addition
  • 2:12 Subtraction
  • 4:10 Multiplication
  • 6:21 Division
  • 8:54 Lesson Summary
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Lesson Transcript
Instructor: Chad Sorrells

Chad has taught Math for the last 9 years in Middle School. He has a M.S. in Instructional Technology and Elementary Education.

There are four basic mathematical operations: addition, subtraction, multiplication, and division. These four operations are used in a wide range of everyday skills and are the fundamental blocks of arithmetic.

Four Operations

There are four operations that can be performed when working with whole numbers. These four operations are addition, subtraction, multiplication, and division. We use the operations in everyday life for a multitude of tasks.

Addition

The most basic of these four operations is addition. Addition is the operation that involves calculating the total amount of a represented group. To add a set of numbers together, we first need to line them up vertically by place value. Then, add each column of numbers from right to left. If a column has a sum greater than 9, we will carry the tens place to the next column.

Let's take a visit to the local mall to visit my good friends Val and Keri. They own a local cookie shop where they are busy getting ready for their customers.

Val and Keri have several orders placed for today and need to know how many cookies they should bake. They have orders of 116 chocolate chip cookies, 524 sugar cookies, and 75 snicker doodle cookies. Val asks Keri to calculate how many cookies they must bake today.

Keri knows that to start adding these numbers together, she must line them up vertically by place value. So, Keri writes down 524, 116, and 75 lined up on the order form.

Keri begins by adding the column on the right. 4 + 6 + 5 equals 15. She knows that since her value is greater than 9, she must carry the tens place to the next column. So, she writes down the 5 and carries the 1 to the next column.

To add the next column, Keri will need to add 7 + 1 + 2 + the 1 that we carried. The sum of these numbers is 11. Again, Keri must carry the tens value since the total is greater than 9.

Next, she needs to add the last column 5 + 1 + the carried 1 equals 7. Keri now knows that they need to bake 715 cookies to fill all of their customer orders.

Subtraction

The next operation is subtraction. Subtraction is the operation that involves taking away value from the total amount. To subtract whole numbers, we will need to line the numbers up by place value from right to left. Next, we will subtract each place value. Occasionally, the value that we are subtracting is not large enough to take away the value. When this happens, we must borrow value from the next place value. When you borrow from the next place value, you are borrowing a set of ten. This set of ten is added to the existing value, and subtraction is continued.

Let's check back in on Val and Keri to see how they are doing on the cookie order. Val and Keri have cooked all of the chocolate chip and snicker doodle cookies but still need to cook the sugar cookies. As they are preparing to start the sugar cookies, the phone rings. Val answers, and it's their customer. She tells Val that she needs to reduce her order for sugar cookies. She had originally ordered 524 sugar cookies but needs to subtract 134 of them.

Val now needs to subtract the customer's original order of 524 sugar cookies by 134. To do this, he must first line up the number from right to left by place value.

To begin, Val starts with the values on the right. 4 minus 4 is 0.

Next, Val needs to subtract 2 minus 3. However, he knows that you cannot take 3 from 2, so he must borrow. So, he borrows a set of ten from the next place value. As he borrows a set from the 5, its value becomes a 4. The set of ten also increases the value of the 2 to 12.

Val can now subtract, 12 minus 3 is 9, and 4 minus 1 is 3. Val now knows that he only needs to cook 390 sugar cookies to fill the customer's order.

Multiplication

Multiplication is another one of the four operations. Multiplication is the process of adding multiple sets of the same number. To multiply, we will take each place value and multiply it to every value in the other number. If the number being multiplied has more than one value, you must add a zero as a place holder each time you move to the next place value. This process continues until all of the places have been multiplied.

Back in the cookie shop, Val and Keri have finished their daily order. As they talk, Keri wonders if they cooked this many cookies daily, how many cookies would they cook in 126 days. To do this, she will need to multiply the daily cookie order of 715 by 126 days.

To start this problem, Keri needs to multiply the 6 by each of the values on top from right to left. If a value is greater than 9, the tens place will be carried to the next place and added to the multiplied value.

Six times 5 is 30, so we keep the zero and carry the 3.

Next, we multiply 6 times 1, which is 6, and then add the carried three to equal 9. The value 9 is written below.

Then, we multiply the 6 times the 7, which is 42. Since there are no additional places on top to be multiplied, we write the 42 below.

Next, we must multiply each place on top by the 2. Since we moved one place on the bottom, we will need to add a zero to the next line below. As we multiply the 2 to each value on top, we get 14300.

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