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SAT Mathematics Level 2: Help and Review22 chapters | 225 lessons

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Lesson Transcript

Instructor:
*Cory Haley*

Understanding what turnaround facts are can help you more easily learn addition and multiplication facts. In this lesson, we'll look at turnaround facts and the commutative property of addition and multiplication.

A **turnaround** fact is a multiplication or an addition fact in math which you're able to 'turn around' or reverse the addends or factors and still get the same answer. **Addends** are numbers that are added together to get a sum. **Factors** are numbers that are multiplied together to get a product.

Take a look at the number sentence:

3 + 2 = 5

Based on our knowledge of turnaround facts, we also know that if we reverse the 3 and the 2, it will not change our answer. See: 2 + 3 = 5.

Now let's look at a multiplication problem with the factors of 3 and 4. We know that 3 * 4 = 12, so it must be true that if we reverse the 3 and the 4, that 4 * 3 = 12. Does this turnaround process look familiar? Well, if you have worked with the commutative property, it should be familiar. Let's talk a little more about the commutative property.

Have you ever heard of the word 'commutative'? 'Commutative' comes from the word 'commute'. So what does 'commute' mean?

Think for a second about driving a car or riding a bike. As you can see, these vehicles are used to move around, and no matter where they move to, they are still the same. That is what the commutative property is all about - the ability to move around multiplication factors and addition addends with the answer remaining the same.

In math, we have several basic number properties. They are the associative property, distributive property, and the commutative property. We are going to discuss the **commutative property**, or the moving around of multiplication and addition facts to gain a better understanding of turnaround facts.

With addition problems, the commutative property states that if a + b = c, then b + a = c. For multiplication, it states that if a * b = c, then b * a = c. We use the commutative property and turnaround facts only in addition and multiplication. They do not work with other operations such as division and subtraction.

Let's apply the commutative property to some problems:

1). 4 + 6 = 10, so 6 + 4 = 10 (the commutative property works)

2). 3 * 2 = 6, so 2 * 3 = 6 (the commutative property works)

3). 10 / 5 = 2, *but* 5 / 10 does *not* equal 2 (the commutative property does not work)

4). 8 - 4 = 4, *but* 4 - 8 does *not* equal 4 (the commutative property does not work)

Now that you know about turnaround facts and the commutative property, let's take a moment and determine whether some statements are true or false:

Statement |
True or False |
Reason |
---|---|---|

If 5 * 2= 10, then 2 * 5 = 10 | True | The commutative property works with factors in a multiplication problem |

If 6 + 1 = 7, then 1 + 6 = 7 | True | The commutative property works with addends in an addition problem |

If 3 + 4 = 7, then 7 + 4 = 3 | False | Based on our knowledge of turnaround facts and the commutative property, only the addends can be turned around: the sum cannot become an addend |

Turnaround facts mean that the addends in an addition problem and the factors in a multiplication problem can be 'turned around' or reversed, and you will still get the same answer. The commutative property also allows for the ability to move the addends in addition or the factors in multiplication and still get the same answer. Remember, however, these do not apply to division or subtraction operations.

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SAT Mathematics Level 2: Help and Review22 chapters | 225 lessons

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