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:**

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

$8\times 500=4000$

+

$8\times 30=240$

+

$8\times 2=16$

=

$4000+240+16=4256$

Solve the exercise:

84:4=

$37\times 5= ( 30+7) \times 5= 30\times 5 + 7 \times 5= 150+35= 185$

$48\times 6= (50-2) \times 6= 50\times 6-2\times 6= 300-12= 288$

**Assignment:**

$74:8=$

**Solution:**

We break down $72$ into numbers divisible by $8$

$\left(72+2\right):8=$

We arrange the exercise into simple fractions

$\frac{72}{8}+\frac{2}{8}=$

We divide accordingly

$9+\frac{1}{4}=9\frac{1}{4}$

**Answer:**

$9\frac{1}{4}$

Test your knowledge

Question 1

Solve the following exercise

?=24:12

Question 2

Solve the following exercise

?=93:3

Question 3

\( 133+30= \)

**Assignment:**

What expression is equivalent to the exercise $14\times3$?

**Solution:**

We break down the exercise into 2 multiplication operations to facilitate the calculation

$(15-1)\times3=$

$15\times3-3\times1=$

$15\times3-3$

**Answer:**

$15\times3$ Then subtract 3

**Assignment:**

$\left(40+70+35−7\right)×9=$

**Solution:**

First, we multiply the element inside the parentheses by $9$

$40\times9+70\times9+35\times9-7\times9=$

To facilitate the calculation, we break down $35$ into $2$ numbers and the rest of the exercise can be multiplied

$=360+630+(30+5)9-63$

First, we solve the parentheses

$360+630+270+45-63=$

Now we add and subtract accordingly

$990+270+45-63=$

$1260+45-63=$

$1305-63=1242$

**Answer:**

$1242$

Do you know what the answer is?

Question 1

\( 140-70= \)

Question 2

\( 143-43= \)

Question 3

\( 63-36= \)

**Assignment:**

$74\times8=$

**Solution:**

We break down $74$ into $2$ numbers to make the calculation easier

$(70+4)\times8=$

We solve the exercise accordingly

$70\times8+4\times8=$

$560+32=592$

**Answer:**

$592$

**Assignment:**

$35\times4=$

**Solution:**

We break down $35$ into $2$ numbers to make the calculation easier

$(30+5)\times4=$

We solve the exercise accordingly

$30\times4+5\times4=$

**$120+20=140$**

**Answer:**

$140$

Check your understanding

Question 1

\( 94+72= \)

Question 2

\( 13\times8= \)

Question 3

\( 17\times7= \)

The distributive property of multiplication over addition or subtraction is the property that helps us simplify and more easily carry out an operation where it is expressed with grouping symbols and related to the order of operations. We can express it as:

Distributive property of multiplication over addition.

$a\times\left(b+c\right)=a\times b+a\times c$

Distributive property of multiplication over subtraction.

$a\times\left(b-c\right)=a\times b-a\times c$

Just like the distributive property of multiplication, the distributive property of division with respect to addition and subtraction helps us to simplify an operation, and it can be expressed as:

$\left(a+b\right):c=a:c+b:c$

Do you think you will be able to solve it?

Question 1

\( 186:6= \)

Question 2

\( 187\times(8-5)= \)

Question 3

\( (29-4):5= \)

P

**Assignment**

$\left(3+8\right)\times5=$

$\left(3+8\right)\times5=3\times5+8\times5$

$3\times5+8\times5=15+40$

$=55$

**Answer**

$=55$

**Assignment** $198\times7=$

We can break down $198$ in the following way:

$\left(100+90+8\right)\times7=$

We apply the distributive property of multiplication

$100\times7+90\times7+8\times7=$

$=700+630+56$

$=1386$

**Answer**

$=1386$

**Assignment** $\left(22+14\right):2=$

Applying the distributive property of division

$=\frac{22}{2}+\frac{14}{2}$

$=11+7=18$

**Result**

$=18$

**Assignment** $250:5$

We break down the $250$ into two numbers

$\left(300-50\right):5$

We apply the distributive law of division with respect to subtraction

$\frac{300}{5}-\frac{50}{5}=60-10$

$=50$

**Answer**

$=50$

Test your knowledge

Question 1

\( 3\times36= \)

Question 2

\( 72:6= \)

Question 3

Solve the exercise:

84:4=