A cookie factory uses 2/3 of a barrel of oatmeal in each batch of cookies. The factory used 1 1/3 barrels of oatmeal yesterday. How many batches of cookies did the factory make?

Question

Can you please show me how to do it and can u give me the answer plz!!

Answer 1

Imagine each barrel of oatmeal is represented by three barrels 🛢️🛢️🛢️(since the question has us breaking each barrel into three parts.

For each batch of cookies, the factory uses 2 out of 3 parts of a barrel (🛢️🛢️). Let's represent this with 🍪.

So two parts of a barrel equals one batch of cookies 🛢️🛢️ = 🍪

Yesterday, the factory used a total of 1 1/3 barrels, which can be represented as: 🛢️🛢️🛢️🛢️ (or 4 out of 3 barrels). We know this because 1 whole barrel is 3/3 parts (🛢️🛢️🛢️) and 1/3 is just one part (🛢️). So, 🛢️🛢️🛢️ + 🛢️ = 🛢️🛢️🛢️🛢️

Now, to figure out how many batches of cookies were made, we'll divide the total barrel parts used by the amount for each batch. We can represent this visually by counting how many batches it takes until we use four parts of a barrel.

First batch:

🛢️🛢️ = 🍪

Second batch:

🛢️🛢️ = 🍪

And now we've used up all four parts of the barrel! So, the factory made 2 batches of cookies yesterday.

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Another way to look at it, a bit more mathematically:

The cookie factory uses 2/3 of a barrel of oatmeal for each batch of cookies. So if you think of this as dividing the oatmeal into thirds, the factory uses 2 of those thirds for each batch.

Yesterday, the factory used a total of 1 1/3 barrels of oatmeal. When we see mixed numbers like this, it's often helpful to convert them to improper fractions to make the math a bit easier. So, 1 1/3 can be written as 3/3 + 1/3 = 4/3.

Now, to find out how many batches of cookies the factory made, we need to divide the total amount of oatmeal used (4/3) by the amount used for each batch (2/3).

So, we want to know how many 2/3 fit into 4/3. Since they have the same denominator, you can divide 4 by 2 to get the answer - 4/2 = 2.

Here's a more complete way to divide 4/3 by 2/3:

(4/3) ÷ (2/3) = (4/3) * (3/2) = 12/6 = 2