Maths - to distribute or not - help!!!

[Wafflesandcrepes]

Hi all,

DD, who is usually good at maths, is struggling with when she can distribute or not.

For example, she knows that x(2+y) = 2x + xy

The problem is that she applies the same “logic”
if she has x(2•y) and she’ll go 2x•xy, which is incorrect.

i simply can’t get it out of her head and been looking for resources that might help but can’t find anything.

Can anyone help, please?

Thank you.

Think of the x as banana, the y as milk, and if you multiply a banana by milk (xy) you get a banana smoothie.

So the first equation means:
Banana times (2 + milk) = 2 bananas and a banana smoothie

The second one is:
banana times (2 milks) = 2 banana smoothies

You can also plug numbers in to explain it. For example, let x = 3, and let y = 4.

The first equation is x(2+y) = 3(2 + 4) = 3(6) =18
Her expanded version was 2x + xy = 6 + 12 = 18 (correct)

The second equation is x(2•y) = 3(8) = 24
Her expanded version was 2x•xy = 6•12 = 72 (incorrect)

Does she understand that in the second example its just multiplication? It doesn’t natter what order you multiply in. So 2 x 3 x 4 is the same as 3 x 4 x 2. The brackets are not needed in your second example.

But if you mix adding and multiplying then the brackets are necessary because 2 x 3 + 4 is not the same as 2 x (3 + 4).

You can show thus in real world examples to help her understand. For example, I have two boxes each containing 6 packets of biscuits. There are 12 biscuits in each pack. How many biscuits do I have? What if I have 6 boxes each with 12 packets and each packet has two biscuits?

Now for the adding one. Im painting a room with two identical walls. For the first wall i use two full tins plus 100 ml. How much paint will i need for two walls? Clearly i need to multiply both the two tins and the 100 ml by two.

I think it's useful to get the hang of what we mean by a term in maths. A term might be a single number or variable, or numbers and/or variables multiplied together. Terms will be separated by +/- signs.
So (2 +y) contains two separate terms, but 2•y is a single term.
When we multiply out a bracket, we multiply each term by what's in front.