Back To Course

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

Are you a student or a teacher?

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Joseph Vigil*

In this lesson, learn what fact families are and how they work to help you understand that numbers in a fact family are related. Gain a better of understanding of how addition and subtraction work together, and study the relationship between multiplication and division.

Just like a family starting with two people coming together, **fact families** in math start with two numbers coming together. Let's say, for example, 1 and 2 meet one day. Then, they come together to make 3. Here's their first family portrait:

1 + 2 = 3

But, in addition, we can switch the numbers we're adding and still get the same sum. So 1, 2, and 3 could also arrange themselves as:

2 + 1 = 3

And just like people in families, numbers can have different relationships with each other at different times. For example, 3, 2, and 1 could come together in a subtraction sentence. Since we're **subtracting** (or taking away from something), start with the largest number because it will be easiest to take away from.

Using our same three fact family members, we could start by subtracting 2 from 3, giving us this portrait of the three numbers:

3 - 2 = 1

And, of course, we could also subtract 1 from 3:

3 - 1 = 2

We can situate our three fact family numbers in four different ways using addition and subtraction. We can create two addition sentences because we can add numbers in any order (1 + 2 or 2 + 1). We can create two subtraction sentences because we can subtract either one of the smaller numbers from the largest number (3 - 1 or 3 - 2).

So, an **addition and subtraction fact family** consists of the four addition and subtraction sentences created using three numbers. The fact family shows the relationships between the numbers in it. All we need to create a fact family is two numbers that we can then add together and the sum of those two numbers.

Let's create another addition and subtraction fact family example. This time, we'll bring together **5 **and **10**.

When they come together in addition, they create 15. Here's their first family portrait:

5 + 10 = 15

Just like before, we can switch 5 and 10 in addition without changing the sum. In essence, the numbers are just rearranging themselves in their portrait:

10 + 5 =15

We can also make subtraction sentences with these three numbers. We'll subtract from the largest number in the fact family:

15 - 10 = 5

And we can also subtract the other smaller number from the largest, which in this case means taking 5 away from 15:

15 - 5 = 10

So the four number sentences in this fact family look like this:

5 + 10 = 15 so, 10 + 5 = 15. These are the two addition sentences for this fact family.

15 - 10 = 5 and 15 - 5 = 10. These are the two subtraction sentences for this fact family.

Four different number sentences all using the same three numbers; that's a fact family!

We can also bring numbers together with multiplication. Let's use the numbers 5 and 10 again. When we multiply them together, we get a product of 50. This gives us a new portrait:

5 * 10 = 50

Similar to when we're adding, we can switch the numbers we're multiplying and still get the same product. So, the numbers in this family can rearrange themselves for a second portrait:

10 * 5 = 50

10, 5, and 50 are a fact family when multiplying and dividing. Let's take the same three numbers and make a division sentence with them. Just like in subtraction, we'll start with the largest number and divide it by one of the smaller numbers:

50 / 5 = 10

We can also divide the largest number by the other smaller number for a fourth portrait:

50 / 10 = 5

We can situate the three fact family numbers in four different ways using multiplication and division. We can create two multiplication sentences because we can multiply numbers in any order (5 * 10 = 50 or 10 * 5 = 50). We can create two division sentences because we can divide the largest number by both of the smaller numbers (50 / 5 = 10 or 50 / 10 = 5).

So, a **multiplication and division fact family** consists of the four multiplication and division sentences we can create using three numbers. The fact family shows the relationships between the numbers in it. All we need to create them is two numbers that we can then multiply together and the product.

Let's multiply the numbers 8 and 12 for another example. We can then create four number sentences by multiplying, dividing, and rearranging the numbers just like we did in the previous example:

8 * 12 = 96

12 * 8 = 96

These are the two multiplication number sentences for this fact family.

96 / 8 = 12

96 / 12 = 8

These are the two division number sentences for this fact family. Altogether that is four number sentences showing the relationship between three numbers.

**Fact families** are number sentences that show the relationships between three different numbers. **Addition and subtraction fact families** make four number sentences that show the relationship between three numbers as you combine them and take them apart. **Multiplication and division fact families** make four number sentences that show the relationship between three numbers as you group them together and break those groups back apart.

Knowing the numbers within fact families shows understanding of number relationships. This means if you know 4 + 6 = 10, then you know 6 + 4 = 10. And if you remember that 4, 6, and 10 are a fact family, then you know that 10 - 4= 6, and 10 - 6 = 4. Similar relationships hold true for three numbers that you can use when multiplying and dividing. If you know that 6 * 7 = 42, then you can remember that 42 / 6 = 7.

**Fact Families**: number sentences showing the relationship between three different numbers**Addition & Subtraction Fact Families**: four number sentences that show the relationship between three numbers as you take them apart or combine them**Multiplication and Division Fact Families**: four number sentences that display the relationship between three numbers as you break them apart or group them together

All that you learn about fact families from this lesson can be drawn upon when you subsequently:

- Recognize a fact family
- Build addition and subtraction fact families
- Display knowledge of fact families for multiplication and division
- Create multiplication sentences and division sentences

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackDid you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
17 in chapter 1 of the course:

Back To Course

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

- What are the Different Types of Numbers? 6:56
- What Is The Order of Operations in Math? - Definition & Examples 5:50
- How to Find the Prime Factorization of a Number 5:36
- How to Find the Greatest Common Factor 4:56
- How to Find the Least Common Multiple 5:37
- How to Build and Reduce Fractions 3:55
- How to Find Least Common Denominators 4:30
- Comparing and Ordering Fractions 7:33
- Estimation Problems using Fractions 7:37
- How to Solve Complex Fractions 5:20
- Calculations with Ratios and Proportions 5:35
- What is a Percent? - Definition & Examples 4:20
- Changing Between Decimals and Percents 4:53
- Changing Between Decimals and Fractions 7:17
- Mathematical Sets: Elements, Intersections & Unions 3:02
- Ruler Postulate: Definition & Examples 5:19
- What is a Fact Family? - Definition & Examples 6:09
- What is a Positive Integer? - Definition & Examples 3:56
- Basic Arithmetic: Rules & Concepts 5:02
- How to Do Double Digit Multiplication: Steps & Practice Problems 4:27
- How to Teach Double Digit Multiplication
- Double Digit Multiplication Strategies 5:10
- Counting On in Math: Definition & Strategy
- What are Turn Around Facts in Math? 3:48
- Go to Basic Math Review: Help and Review

- Introduction to SQL
- Computer Science 203: Defensive Security
- GRE Information Guide
- Computer Science 310: Current Trends in Computer Science & IT
- Earth Science 105: Introduction to Oceanography
- Views, Indexes & Triggers in SQL
- Joins & Subqueries in SQL
- Intro to Databases & SQL
- SQL Data Types & Syntax
- Removing Data Using SQL
- What is the ASCP Exam?
- ASCPI vs ASCP
- MEGA Exam Registration Information
- MEGA & MoGEA Prep Product Comparison
- PERT Prep Product Comparison
- MTLE Prep Product Comparison
- What is the MTLE Test?

- Separation Methods Used in Biology Labs
- Job Enrichment: Definition, Advantages, Disadvantages & Examples
- Measurement Lesson for Kids
- How Plants Grow: Lesson for Kids
- How a Bill Becomes a Law Lesson Plan
- Computer Technology Lesson Plan
- Responsibility-Based A/R Reporting in Health: Definition & Purpose
- Quiz & Worksheet - Southern Early Childhood Association
- Quiz & Worksheet - Bleak House
- Quiz & Worksheet - Psychological Impact of Social Media
- Quiz & Worksheet - Intonation & Stress in Speaking
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Common Core Math Standards
- Reading Comprehension

- Biology: Credit Recovery
- CLEP History of the United States I: Study Guide & Test Prep
- DSST Technical Writing: Study Guide & Test Prep
- Molecular Biology: Help & Review
- High School US History Textbook
- Praxis Middle School Social Studies: U.S. Federalism
- Praxis Middle School Social Studies: 1970s America
- Quiz & Worksheet - Basic Algebra Rules & Equations
- Quiz & Worksheet - References and Allusions to The Bible in Literature
- Quiz & Worksheet - African Religious Systems
- Quiz & Worksheet - U.S. Rule & Acquisition of Puerto Rico
- Quiz & Worksheet - Calculating Hydrostatic Pressure

- Total War: Definition & Examples
- Practical Application: Identifying Types of Contracts
- Sequencing Activities for 2nd Grade
- How to Pass the Series 7 Exam
- National History Day Projects
- Women's History Month
- Speaking & Listening Rubrics for the Classroom
- Sequencing Activities for 3rd Grade
- Is the SAT a Standardized Test?
- Persuasive Writing Prompts: 4th Grade
- Life Cycle of a Frog Lesson Plan
- How to Succeed in Nursing School

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject