## Multiplying by 9

Intended Audience: Teachers and Parents of K-5 students.

In this video, 6-year-old Autumn shows how easy it is to multiply by 9. Watch her multiply 18×9 in her head and explain how she did it!

Parents and teachers may also want to watch Autumn’s and my 3-part video series on learning how to multiply along with this video (Part I, Part II, Part III).  In the 3-part series, Autumn shows the basics of learning to skip count while keeping track of the number of skip counts on her fingers. This method helps young children learn what multiplication means and gives them a way to confidently find products of two numbers where one of the numbers is 2, 3, 4, 5, and 10. That, together with the commutative property (i.e., 6×7 is the same as 7×6), leaves the following products:

6×6, 6×7, 6×8, 6×9, 7×7, 7×8, 7×9, 8×8, 8×9, 9×9.

This list can be reduced to just 6 facts by learning how to multiply by 9, i.e., the content of this video.  The multiplication by 9 method in this video can be easily seen using unit math: 9×7 means finding  “9 sevens.”  But just as “9 apples = 10 apples – 1 apple,” the same holds for sevens:

9 sevens = 10 sevens – 1 seven.

Of course, 10 sevens = 70 is easy, so 9×7 = 70 – 7.

As you watch Autumn, note that an important prerequisite to this technique is how to take away a 1-digit number from a multiple of 10, for example, 70-7, 80-8, 90-9, etc. This skill in turn comes out of learning to work with “10 combinations,” i.e., 2 and 8 make 10, 3 and 7 make 10, 4 and 6 make 10, etc. All of these prerequisite skills are learned and practiced in the Eureka Math/EngageNY math curriculum in grades K-2 using joyful mental math/counting activities and number bonds (take a look!).

With multiplication by 9 understood, that only leaves the six “most troublesome” facts:

6×6, 6×7, 6×8, 7×7, 7×8, 8×8.

You can watch Autumn explain in another video how to find some of these products just knowing that “6×7=42” by following this link. 