The Distributive Property in the Case of Multiplication - Examples, Exercises and Solutions

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:

$160+6=166$

In order to simplify the resolution process, we begin by using the distributive property for 140:

$100+40-70=$

We then rearrange the exercise using the substitution property into a more practical form:

$100-70+40=$

Lastly we solve the exercise from left to right:

$100-70=30$

$30+40=70$

In order to solve the question, we first use the distributive property for 133:

$(100+33)+30=$

We then use the distributive property for 33:

$100+30+3+30=$

We rearrange the exercise into a more practical form:

$100+30+30+3=$

We solve the middle exercise:

$30+30=60$

Which results in the final exercise as seen below:

$100+60+3=163$

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:$\frac{84}{4}=21$

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

We will use the distributive law and split the number 143 into a sum of 100 and 43.

The distributive law allows us to distribute, meaning, to split a number into two or more numbers. This actually allows us to work with smaller numbers and simplify the operation.

$(100+43)-43=$

We will operate according to the order of operations

We can remove parentheses and perform addition and subtraction operations in any order since there are only addition and subtraction operations in the equation

$100+43-43=100+0=100$

Therefore, the answer is option C - 100.

And now let's see the solution to the exercise in a centered format:

$143-43= (100+43)-43= 100+43-43=100+0=100$

We will use the distributive property of division and split the number 24 into a sum of 12 and 12, which makes 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, which makes 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, in this case, 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 facilitate the resolution process, we break down 56 into an exercise with smaller, preferably round, numbers.

$3\times(50+6)=$

We use the distributive property and multiply each of the terms in parentheses by 3:

$(3\times50)+(3\times6)=$

We then solve each of the exercises inside of the parentheses and obtain the following result:

$150+18=168$

In order to facilitate the resolution process, we first break down 33 into a smaller addition exercise with more manageable and preferably round numbers:

$9\times(30+3)=$

Using the distributive property we then multiply each of the terms in parentheses by 9:

$(9\times30)+(9\times3)=$

Finally we solve each of the exercises inside of the parentheses:

$270+27=297$

In order to simplify our calculation, we first break down 93 into smaller, more manageable parts. (Preferably round numbers )

We obtain the following:

$3\times(90+3)=$

We then use the distributive property in order to find the solution.

We multiply each of the terms in parentheses by 3:

$(3\times90)+(3\times3)=$

Lastly we solve each of the terms in parentheses and obtain:

$270+9=279$

In order to simplify the resolution process, we begin by breaking down the number 480 into a smaller addition exercise:

$(400+80)\times3=$

We then multiply each of the terms within the parentheses by 3:

$(400\times3)+(80\times3)=$

Lastly we solve the exercises inside the parentheses and obtain the following:

$1200+240=1440$

In order to simplify the resolution process, we begin by breaking down the number 74 into a smaller addition exercise.

It is easier to choose round whole numbers, hence the following calculation:

$(70+4)\times8=$

We then multiply each of the terms within the parentheses by 8:

$(8\times70)+(8\times4)=$

Lastly we solve the exercises within the parentheses:

$560+32=592$

In order to simplify the resolution process we begin by breaking down the number 74 into a subtraction exercise:

We choose numbers divisible by:

$(80-6):4=$

Next we divide each of the terms inside of the parentheses by 4:

$80:4=20$

$6:4=1.5$

Lastly we subtract the result that we obtained:

$20-1.5=18.5$

In order to simplify the resolution process, we divide the number 35 into a smaller addition exercise.

It is easier to choose round whole numbers, hence the following calculation:

$(30+5)\times4=$

We then multiply each of the terms inside of the parentheses by 4:

$(4\times30)+(4\times5)=$Lastly we solve the exercises inside of the parentheses:

$120+20=140$