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### Course: 3rd grade (Eureka Math/EngageNY) > Unit 1

Lesson 6: Topic F: Distributive property and problem solving using units of 2–5 and 10- Properties of multiplication
- Visualize distributive property
- Distributive property when multiplying
- Distributive property
- 2-step word problem: theater
- 2-step word problem: truffles
- 2-step word problem: running
- 2-step estimation problem: marbles
- 2-step word problems

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# Distributive property when multiplying

Sal uses the distributive property to break up 4x7 into smaller numbers.

## Want to join the conversation?

- What is the easiest way to learn my 7 times table? This is very hard.(4 votes)
- Many kids have difficulty with 7’s, but this does not have to be you if you use a strategy.

There are multiple strategies. Here are three of them. These strategies come from the idea that multiplication is the same as counting groups of objects (distributive property).

1) If you’re good with 2’s and 5’s, a possible way to multiply a number by 7 is to multiply it by 2, multiply it by 5, then add the results. This is based on the fact that 2 + 5 = 7.

Example: let’s do 8 x 7.

8 x 2 = 16

8 x 5 = 40

16 + 40 =**56**, the answer.

2) If you’re good with 10’s and 3’s, a possible way to multiply a number by 7 is to multiply it by 10, multiply it by 3, then subtract the results. This is based on the fact that 10 - 3 = 7.

Example: let’s do 8 x 7 again.

8 x 10 = 80

8 x 3 = 24

80 - 24 =**56**, the answer.

3) lf you’re good with 6’s, a possible way to multiply a number by 7 is to multiply it by 6 and add the original number. This is based on the fact that 6 + 1 = 7.

Example: let’s do 8 x 7 again.

8 x 6 = 48

original number = 8

48 + 8 =**56**, the answer.

These are not the only strategies. From looking at the ideas in the three strategies l wrote, you might even come up with your own strategy that you like better.

Have a blessed, wonderful day!(65 votes)

- I'm learning times table, I need to memorize them fast, how do I memorize them fast?(14 votes)
- Use strategies if you forget some of them.

Example of a strategy: many kids are good with 5's and 2's but have trouble with 7's. Using the fact that 5+2 = 7 helps here. For the problem 7x8, think "7 groups of 8 is 5 groups of 8 plus 2 groups of 8. So you can do 5x8 = 40, 2x8 = 16, and then add 40+16 = 56. So 7x8 = 56.

Also look for patterns. For example, the 9's have an easy pattern. For 9x1 all the way through 9x10, the tens digit is one less than the number being multiplied by 9, and the units and tens digits add to 9. So for 9x6, the tens digit is 6-1=5, and the units digit is 4 because 5+4 = 9. So 9x6 = 54.

This is not the only strategy and pattern. You might even try to come up with some strategies and patterns of your own.

Have a blessed, wonderful day!(12 votes)

- how do we do distributive property in multiplying, i don't understand?? Such a 7x4(5 votes)
- Using the distributive property can help you figure out multiplication facts that you forget.

For example, if you remember your 2’s and 5’s but forget your 7’s, you can use this property to help you figure out your 7’s (because 2 + 5 = 7).

For example:

7x4 = (5+2)x4 = (5x4)+(2x4) = 20+8 = 28.

The idea is that 7 fours equals 5 fours plus 2 fours.

Have a blessed, wonderful day!(22 votes)

- another day of angry cats and a bunch on multipacation.(9 votes)
- Why is the cat angry?(5 votes)
- I love cats if you love cats vote(4 votes)
- why won't it let me watch the video?(2 votes)
- honestly I don't know(2 votes)

- mini quiz

1. 2 x 3 =

2. 8 x 1 =

3. 4 x 4 =

4. 7 x 2 =

5. 8 x 4 =

6. 4 x 6 =

7. 6 x 7 =

8. 9 x 9 =

9. 10 x 2 =

10. 5 x 3 =(2 votes)- 1. 6

2. 8

3. 16

4. 14

5. 32

6. 24

7. 42

8. 81

9. 20

10. 15(2 votes)

- Why do we use x for math(2 votes)

## Video transcript

- [Instructor] What we're
going to do in this video is dig a little bit deeper into our understanding of multiplication. And just as an example, we're going to use four times seven. And some of you might know
what four times seven is, but even in this case, I think you might get
something from this video because we're gonna think
about how you can break down a multiplication question
into simpler parts, and that's going to be useful
well beyond four times seven. It's going to be useful in your future when you're tackling more
and more complicated things. Now there's a couple of
ways that we can visualize four times seven. My favorite way is to
visualize it with angry cats, so let's bring on the angry cats. (imitates cats meowing) Yep, they're still angry. And we can see that
this is a representation of four times seven. We have four rows right over here. Four rows, and each of those rows have seven cats. And so you can see that right over here, each of those rows has seven cats. Some people would call
this a four by seven grid or four by seven array, however you want to view it, but if someone were to ask
you what's the total number of cats, it would be four
rows times seven columns, four times seven. Now another way to
represent four times seven is also with a tape diagram. You might see something like this, where here, we're visualizing
it as seven fours, or you could view it as
four plus four plus four plus four plus four plus four plus four. Now that's all well and good
and you can add that up, if you like, but what I promised you is
that we would figure out ways to break down things that might simplify things in the future. Well what if you didn't know
what four times seven is, but you knew what four times five is and you knew what four times two is? Well what's interesting is
that seven is five plus two, so what if we tried to first
figure out this many cats, so four rows and five
columns right over there, and then we tried to figure out this many cats? Four rows and two columns. And you can see that it's the
exact same number of cats. So one way to think about
it is four times seven is the exact same thing as four times, and I'm gonna use parentheses,
and that just means to do that part first,
is equal to four times, instead of seven, I could write that as five plus two, 'cause that's what seven is, so all this is saying is four time seven is the same thing as
four times five plus two, where you do the five plus two first, 'cause we have those
parentheses around it, and five plus two is,
indeed, equal to seven, and we can see that that is
equivalent to the total number of cats that we have here, which we could view as
what we just circled off in this orangeish pink color which would be four rows of five, so that would be equal to four times five. Four times five, and then to that, we can add
this second group of cat heads or angry cat heads, and that is four rows of two. So that's four times two, and we could put parentheses if we want, just to make it a little
bit more readable. Now why did I do that? Well, some folks might
find four times five a little bit more straightforward. I could skip count by five. I can go five, 10, 15, 20. Also four times two might be a little bit more straightforward, and so it could be easier to say hey, this is just going to be four times five, which is 20, plus four times
two, which is equal to eight, and so that is just
going to be equal to 28. And you could have thought
about it the same way down here with what is sometimes
called a tape diagram. We could say, all right, if I have five fours, that's this mount right over here. That is the four times the five, and then I could add
that to the two fours, the four times the two right over here, and that's another way to
get to four times seven. So the big picture here is
even if you're not dealing with four times seven,
if you're not dealing with angry cats, and in most of our lives, we actually try to avoid angry cats, there might be a way to
break down the numbers that you're multiplying into ones that you might be more familiar with. I'll give you one more example. Let's say someone were to ask you, well, what is six times nine? Pause this video and see
if you can break this down in some useful way. Well, maybe you know what six times 10 is, and you also know what six times one is, so you could rerwrite nine as 10 minus one. Well then this would
mean that six times nine is the same thing as
six times 10 minus one. Based on exactly what we just did up here, that says that this whole thing is going to be the same
thing as six times 10. Six times 10 minus six times one. One way to think about it is, I just distributed the six. That's the distributive
property right over there, and then six times 10 is equal to 60, and then six times one is equal to six. And it might be easier for me to say, hey, 16 minus six in my head, that's equal to 54. So I know what some of you are thinking. Six times nine seems so clean, and now I've involved all
of this other symbolism, symbols, and I've written
down more numbers, but at the end of the day, I'm trying to give you skills for breaking down problems and including ways that you might want to do it in your head. If you're like, hey, I'm kind of foggy on what six times nine is, but six times 10, hey, I know that's 60, and six times one, of course, that's six, well what if I view this
as six times 10 minus one? And then I could tackle it and get 54. And once again, you might know six times nine. You might know four times seven, but in the future, it might be useful for
bigger and bigger numbers to think about how
could I break this down?