The distributive property of multiplication allows us to break down the highest term of the exercise into a smaller number. This simplifies the multiplication operation and we can solve the exercise without the need to use a calculator.

The distributive property of multiplication allows us to break down the highest term of the exercise into a smaller number. This simplifies the multiplication operation and we can solve the exercise without the need to use a calculator.

**Let's assume we have an exercise with a** **multiplication**** that is simple, but with large numbers, for example:**

$8\times 532$

**Thanks to the distributive property, we can break it down into simpler exercises:**

$8\times 532=8\times (500+30+2)$

$8\times 500=4000$

+

$8\times 30=240$

+

$8\times 2=16$

=

$4000+240+16=4256$

Question 1

Solve the exercise:

84:4=

Question 2

\( 94+72= \)

Question 3

\( 140-70= \)

Question 4

\( 63-36= \)

Question 5

\( 133+30= \)

Solve the exercise:

84:4=

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

$94+72=$

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

$140-70=$

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

$63-36=$

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

$133+30=$

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

Question 1

\( 9\times33= \)

Question 2

\( \)\( 3\times56= \)

Question 3

\( 3\times93= \)

Question 4

\( 74\times8= \)

Question 5

\( 35\times4= \)

$9\times33=$

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

$3\times56=$

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

$3\times93=$

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

$74\times8=$

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

$35\times4=$

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

Question 1

\( 480\times3= \)

Question 2

\( 11\times34= \)

Question 3

\( 6\times29= \)

Question 4

\( 4\times53= \)

Question 5

Solve the exercise:

=74:4

$480\times3=$

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

$11\times34=$

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

$6\times29=$

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

$4\times53=$

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

Solve the exercise:

=74:4

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:

$20-1.5=18.5$

18.5