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7th grade foundations (Eureka Math/EngageNY)

Course: 7th grade foundations (Eureka Math/EngageNY) > Unit 2

Lesson 3: Topic C: Foundations
Math
7th grade foundations (Eureka Math/EngageNY)
Module 2: Foundations
Topic C: Foundations
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Intro to distributive property

Google Classroom
Practice decomposing the factors in multiplication problems and see how it affects the product.

Breaking up multiplication

This array is made up of 3 rows with 6 dots in each row. The dots show 3×6=18.
If we add a line dividing the dots into two groups, the total number of dots does not change.
The top group has 1 row with 6 dots. The dots show 1×6.
The bottom group has 2 rows with 6 dots in each row. The dots show 2×6.
We still have a total of 18 dots.

Distributive property

The math rule that allows us to break up multiplication problems is called the distributive property.
The distributive property says that in a multiplication problem, when one of the factors is rewritten as the sum of two numbers, the product does not change.
Using the distributive property allows us to solve two simpler multiplication problems.
In the example with the dots we started with 3×6.
We broke the 3 down into 1+2. We can do this because 1+2=3
We used the distributive property to change the problem from 3×6 to (1+2)×6.
The 6 gets distributed to the 1 and 2 and the problem changes to:
(1×6)+(2×6)
Now we need to find the two products:
6+12
And finally, the sum:
6+12=18
3×6=18 and
(1+2)×6=18
Practice problem 1
Which expressions are the same as 4×9?
Choose all answers that apply:

Small numbers

Some numbers like 1,2,5, and 10 are easier to multiply. The distributive property allows us to change a multiplication problem so that we can use these numbers as one of the factors.
For example, we can change 4×12 into 4×(10+2).
The array of dots on the left shows (4×10). The array of dots on the right shows (4×2).
Now we can add the expressions to find the total.
(4×10)+(4×2)
=40+8
=48
Since 10 and 2 are both easy to multiply, using the distributive property for this problem made finding the product easier.

Practice problem 2

The dots represent 9×4.
Problem 2, part A
Which expression shows the dots above the dotted line?
Choose 1 answer:

Problem 2, Part B
Which expression shows the dots below the dotted line?
Choose 1 answer:

Problem 2, Part C
(5×4)
(4×4)= total number of dots

More practice

Problem 3A
The dots represent 3×8.
Which expression can we use to calculate the total number of dots?
Choose 1 answer:

Working with large numbers

The distributive property is very helpful when multiplying larger numbers. Look at how we can use the distributive property to simplify 15×8.
We will start by breaking 15 into 10+5. Then we will distribute the 8 to both of these numbers.
15×8=(10×8)+(5×8)
15×8= 80+40
15×8= 120
Problem 4
Use the distributive property to find the product.
18×3=(10×3)+( 
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
×3)
18×3= 30+
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
18×3= 
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

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