The Distributive Property in the Case of Multiplication

There are several ways to solve the following exercise,

We will present two of them.

In both ways, we begin by decomposing the number 84 into smaller units; 80 and 4.

$\frac{4}{4}=1$

Subsequently we are left with only the 80.

Continuing on with the first method, we will then further decompose 80 into smaller units; $10\times8$

We know that:$\frac{8}{4}=2$

And therefore, we are able to reduce the exercise as follows: $\frac{10}{4}\times8$

Eventually we are left with$2\times10$

which is equal to 20

In the second method, we decompose 80 into the following smaller units:$40+40$

We know that: $\frac{40}{4}=10$

And therefore: $\frac{40+40}{4}=\frac{80}{4}=20=10+10$

which is also equal to 20

Now, let's remember the 1 from the first step and add it in to our above answer:

$20+1=21$

Thus we are left with the following solution:$\frac{84}{4}=21$

Apply the distributive property of division and proceed to split the number 24 into a sum of 12 and 12, which ultimately renders the division operation easier and allows us to solve the exercise without a calculator.

Note - it's best to choose to split the number based on knowledge of multiples. In this case of the number 12 because we need to divide by 12.

Reminder - The distributive property of division actually allows us to split the larger term in a division problem into a sum or difference of smaller numbers, which makes the division operation easier and allows us to solve the exercise without a calculator

We will use the formula of the distributive property

 (a+b):c=a:c+b:c 

$24:12=(12+12):12$

$(12+12):12=12:12+12:12$

$12:12+12:12=1+1$

$1+1=2$

Therefore the answer is section a - 2.

We will use the distributive property of division and split the number 93 into a sum of 90 and 3. This ultimately renders the division operation easier and allows us to solve the exercise without a calculator.

Note - it's best to choose to split the number based on knowledge of multiples. In this case, we use 3 because we need to divide by 3. Additionally splitting by tens and ones is suitable and makes the division operation easier.

Reminder - The distributive property of division essentially allows us to split the larger term in the division problem into a sum or difference of smaller numbers, which makes the division operation easier and allows us to solve the exercise without a calculator

We will use the formula of the distributive property

 (a+b):c=a:c+b:c 

$93:3=(90+3):3$

$(90+3):3=90:3+3:3$

$90:3+3:3=30+1$

$30+1=31$

Therefore, the answer is option B - 31.

In order to simplify the calculation , we first break down 94 and 72 into smaller and preferably round numbers.

We obtain the following exercise:

$90+4+70+2=$

Using the associative property, we then rearrange the exercise to be more functional.

$90+70+4+2=$

We solve the exercise in the following way, first the round numbers and then the small numbers.

$90+70=160$

$4+2=6$

Which results in the following exercise:

$160+6=166$

To solve the problem, first we will use the distributive property on the two numbers:

(60+3)-(30+6)

Now, we will use the substitution property to arrange the exercise in the way that is most convenient for us to solve:

60-30+3-6

It is important to pay attention that when we open the second parentheses, the minus sign moved to the two numbers inside.

30-3 = 

27