Question

For the problem 135 divided by 5 draw two different ways to break apart the array. Use the distributive property to write products for each different way

Answer 1

To use an array for a divide, make a box and put the total in it (135). Put 5 along the top. Then break up the left hand side of the box, using multiplication. One way is to have 20 (x5 = 100) and 7 (x 5 = 35) as in total this makes 135. Another is to have 10 (x5 = 50), 10 (x5 = 50), 6 (x5 = 30) and 1 (x5 = 5).

Answer 2

The distributive property will show you how you can state the arrays.

1) Make 135 = 100 + 35

⇒ 135 ÷ 5 = (100 + 35 ) ÷ 5

Distributive property → 100 ÷ 5 + 35 ÷ 5 =

⇒ 20 + 7 = 27

This means that 27 is the result of the division 135 ÷ 35

Then you can make one array with 20 rows of 5 tiles each, and 7 rows of 5 tiles each.

2) For the second array you can make 135 = 50 + 50 + 30 + 5

⇒ 135 ÷ 5 = (50 + 50 + 30 + 5) ÷ 5

Distributive property → 50 ÷ 5 + 50 ÷ 5 + 30 ÷ 5 + 5 ÷ 5

⇒ 10 + 10 + 6 + 1 = 27

Which also shows that 27 is the result of 135 ÷ 5

Therefore, you can make an array with 10 rows plus 10 rows, plus 6 rows, plus 1 row, each of 5 tiles.