The Distributive Property of Division - Examples, Exercises and Solutions

The distributive property of division allows us to break down the first term of a division expression into a smaller number. This simplifies the division operation and allows us to solve the exercise without a calculator.

When using the distributive property of division, we begin by breaking down the number being divided by another, the dividend.

For example:

$54:3= (60-6):3= 60:3-6:3= 20-2=18$

We break down $54$ into $60-6$.
The value remains the same since $60-6=54$
Both $60$ and $6$ are divisible by $3$ and, therefore, the calculation is much easier.

examples with solutions for the distributive property of division

Exercise #1

Solve the exercise:

84:4=

Step-by-Step Solution

There are several ways to solve the exercise,

We will present two of them.

In both ways, in the first step we divide the number 84 into 80 and 4.

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

And thus we are left with only the 80.

From the first method, we will decompose 80 into$10\times8$

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

And therefore, we reduce the exercise $\frac{10}{4}\times8$

In fact, we will be left with$2\times10$

which is equal to 20

In the second method, we decompose 80 into$40+40$

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 them:

$20+1=21$

And thus we manage to decompose that:$\frac{84}{4}=21$

21

Exercise #2

$94+72=$

Step-by-Step Solution

To facilitate the resolution process, we break down 94 and 72 into smaller numbers. Preferably round numbers

We obtain:

$90+4+70+2=$

Using the associative property, we arrange the exercise in a more comfortable way:

$90+70+4+2=$

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

$90+70=160$

$4+2=6$

Now we obtain the exercise:

$160+6=166$

166

Exercise #3

$140-70=$

Step-by-Step Solution

To facilitate the resolution process, we use the distributive property for 140:

$100+40-70=$

Now we arrange the exercise using the substitution property in a more convenient way:

$100-70+40=$

We solve the exercise from left to right:

$100-70=30$

$30+40=70$

70

Exercise #4

$63-36=$

Step-by-Step Solution

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

27

Exercise #5

$133+30=$

Step-by-Step Solution

To solve the question, we first use the distributive property for 133:

$(100+33)+30=$

Now we use the distributive property for 33:

$100+30+3+30=$

We arrange the exercise in a more comfortable way:

$100+30+30+3=$

We solve the middle exercise:

$30+30=60$

Now we obtain the exercise:

$100+60+3=163$

163

examples with solutions for the distributive property of division

Exercise #1

$9\times33=$

Step-by-Step Solution

To facilitate the resolution process, we break down 33 into a smaller addition exercise with more comfortable numbers, preferably round:

$9\times(30+3)=$

We use the distributive property and multiply 9 by each of the terms in parentheses:

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

We solve each of the exercises in parentheses:

$270+27=297$

297

Exercise #2

$3\times56=$

Step-by-Step Solution

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 by 3 for each of the terms in parentheses:

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

We solve each of the exercises in parentheses and obtain:

$150+18=168$

168

Exercise #3

$3\times93=$

Step-by-Step Solution

To facilitate the resolution process, we break down 93 into a sum exercise with more comfortable numbers, preferably round.

We obtain:

$3\times(90+3)=$

We use the distributive property to solve the exercise.

We multiply by 3 each of the terms in parentheses:

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

We solve each of the terms in parentheses and obtain:

$270+9=279$

279

Exercise #4

$74\times8=$

Step-by-Step Solution

To facilitate the resolution process, we break down the number 74 into a smaller addition exercise.

It is easier to choose round whole numbers, therefore we get:

$(70+4)\times8=$

Now, we multiply each of the terms in parentheses by 8:

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

We solve the exercises in parentheses:

$560+32=592$

592

Exercise #5

$35\times4=$

Step-by-Step Solution

To facilitate the resolution process, we divide the number 35 into a smaller addition exercise.

It is easier to choose round whole numbers, therefore we get:

$(30+5)\times4=$

Now, we multiply each of the terms in parentheses by 4:

$(4\times30)+(4\times5)=$

We solve the exercises in parentheses:

$120+20=140$

140

examples with solutions for the distributive property of division

Exercise #1

$480\times3=$

Step-by-Step Solution

To facilitate the resolution process, we divide the number 480 into a smaller addition exercise:

$(400+80)\times3=$

Now, we multiply each of the terms in parentheses by 3:

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

We solve the exercises in parentheses and obtain:

$1200+240=1440$

1440

Exercise #2

$11\times34=$

Step-by-Step Solution

To make solving easier, we break down 11 into more comfortable numbers, preferably round ones.

We obtain:

$(10+1)\times34=$

We multiply 34 by each of the terms in parentheses:

$(34\times10)+(34\times1)=$

We solve the exercises in parentheses and obtain:

$340+34=374$

374

Exercise #3

$6\times29=$

Step-by-Step Solution

To make solving easier, we break down 29 into more comfortable numbers, preferably round ones.

We obtain:

$6\times(30-1)=$

We multiply 6 by each of the terms in parentheses:

$(6\times30)-(6\times1)=$

We solve the exercises in parentheses and obtain:

$180-6=174$

174

Exercise #4

$4\times53=$

Step-by-Step Solution

To make solving easier, we break down 53 into more comfortable numbers, preferably round ones.

We obtain:

$4\times(50+3)=$

We multiply 2 by each of the terms inside the parentheses:

$(4\times50)+(4\times3)=$

We solve the exercises inside the parentheses and obtain:

$200+12=212$

212

Exercise #5

Solve the exercise:

=74:4

Step-by-Step Solution

To make the resolution process easier for us, we break down the number 74 into a subtraction exercise:

We choose numbers divisible by:

$(80-6):4=$

Now we divide each of the terms in parentheses by 4:

$80:4=20$

$6:4=1.5$

Now we subtract the result we obtained:

$20-1.5=18.5$