Courtni is multiplying 3.2 x 30. Explain how Courtni can use expanded form and properties of multiplication to solve this problem mentally. What is the product of 3.2 x 30?

Answer 1

Expanded form is breaking a number down to digits times place value. Therefore, 30 in expanded form is (3x10).

Next you use the distributive property to multiply 3x3.2. The distributive property says that for any number (a) times the sum of any number (b) plus any number (c) is equal to the product of (a) times (b) plus the product of (b) times (c).

Example: Let a = 3, b = 3, c = 0.2

So: 3 x (3 + 0.2) = (3x3) + (3x0.2)

Multiply: 9 + 0.6

Add: 9.6

Now you have to go back to expanded form and remember to multiply times 10. 9.6 x 10 = 96

Answer 2

Not sure exactly what is meant by "Expanded Form," But what I would do to solve it mentally with the properties of multiplication is this:

So, 3.2 is just 3 + 0.2.

I would use use the distributive property of multiplication:

30(3 + 0.2)

0.2 = 1/5, so I can divide 30 by 5 to get 6.

Then, 30 * 3 = 90, pretty easily.

Lastly, add those 2 numbers together:

90+6 = 96.