Answer to Question #114305 in Algebra for Felicia Ngubandze

Question

Design an activity that you will give to your learners so that they can apply the following properties of numbers:
1.1. Commutative properties
1.2. Associative properties
1.3. Distributive property
1.4. Density property
1.5. Identity property
2. Provide solutions for the activity in above

Answer 1

1. Commutativity:

In a red bucket lie two apples. And in a blue bucket lie two tangerines. If you add them together, you get 4 fruits - 2 apples and 2 tangerines.

Try swapping buckets so that apples are in blue and tangerines are in red. Fold and see how much fruit you get.

2.Associativity:

In a bucket lie two apples. On the table there is a tangerine. If you put a tangerine from a bucket on the table, then we get 3 fruits - 2 apples and 1 tangerine.

Try changing apples and tangerines - now there are two apples in the bucket, and one tangerine on the table. Fold and see how much fruit you get.

3.Distribution:

On the table there are two apples. Two tangerines and two pears lie in a bucket. For fruit salad, we need one bucket of tangerines and pears for each apple.

Since we have two apples, we take another bucket with two tangerines and two pears. Now if you add all the fruits, you get 4 tangerines (2 from each bucket),

4 pears (2 from each bucket) and 2 apples - 10 fruits. Now let's take two buckets for each apple - one with 2 pears and the other with 2 tangerines.

For two apples we will need 4 buckets - two buckets of 2 pears in each and two buckets of 2 tangerines in each. Count how many fruits will be now.

4.Density:

If you take a whole apple and divide it into two parts, you get 2 halves. Each half is 0.5 apples. We have two 0.5 apples each, and if we add them together, we get the whole apple, i.e. 1.

Now we divide each half into two and get 4 parts - 0.25 apples each. From two of these we can collect 0.5 apples, from 3 parts - 0.75 apples, and from 4 - a whole apple.

Try to divide each part of the apple into two more and tell us if we can get such a share of the apple that it will be more than 0.75, but less than 1.

5.Identity:

We have two apples and an empty bucket. How many apples will there be in a bucket if we put our two apples in it?

We have two apples and two empty buckets. We need to somehow distribute our apples in these two buckets. After distribution in each bucket - 1 apple.

If we have only one bucket, then how many apples will fall into it during distribution?

Answers:

1. Commutativity:

We still get 4 fruits.

2.Associativeness:

We get the same amount of fruit - 3 pieces.

3.Distribution:

We will also get 10 fruits in total.

4.Density:

Yes, after operations we can get 0.875 apples.

5.Identity:

If we put two apples in an empty bucket, then we will have 2 apples in a bucket.

If you divide two apples into 1 bucket, then in one bucket there will be 2 apples.