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

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.

Example of an exercise where the distributive property is applied with multiplications

Let's assume we have an exercise with a multiplication that is simple, but with large numbers, for example:
8×5328\times 532

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

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

8×500=40008\times 500=4000

+

8×30=2408\times 30=240

+

8×2=168\times 2=16

=

4000+240+16=42564000+240+16=4256

Practice The Distributive Property in the Case of Multiplication

Exercise #1

Solve the exercise:

84:4=

Video Solution

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.

44=1 \frac{4}{4}=1

And thus we are left with only the 80.

 

From the first method, we will decompose 80 into10×8 10\times8

We know that:84=2 \frac{8}{4}=2

And therefore, we reduce the exercise 104×8 \frac{10}{4}\times8

In fact, we will be left with2×10 2\times10

which is equal to 20

In the second method, we decompose 80 into40+40 40+40

We know that: 404=10 \frac{40}{4}=10

And therefore: 40+404=804=20=10+10 \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 20+1=21

And thus we manage to decompose that:844=21 \frac{84}{4}=21

Answer

21

Exercise #2

94+72= 94+72=

Video Solution

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= 90+4+70+2=

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

90+70+4+2= 90+70+4+2=

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

90+70=160 90+70=160

4+2=6 4+2=6

Now we obtain the exercise:

160+6=166 160+6=166

Answer

166

Exercise #3

14070= 140-70=

Video Solution

Step-by-Step Solution

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

100+4070= 100+40-70=

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

10070+40= 100-70+40=

We solve the exercise from left to right:

10070=30 100-70=30

30+40=70 30+40=70

Answer

70

Exercise #4

6336= 63-36=

Video Solution

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

Answer

27

Exercise #5

133+30= 133+30=

Video Solution

Step-by-Step Solution

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

(100+33)+30= (100+33)+30=

Now we use the distributive property for 33:

100+30+3+30= 100+30+3+30=

We arrange the exercise in a more comfortable way:

100+30+30+3= 100+30+30+3=

We solve the middle exercise:

30+30=60 30+30=60

Now we obtain the exercise:

100+60+3=163 100+60+3=163

Answer

163

Exercise #1

9×33= 9\times33=

Video Solution

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×(30+3)= 9\times(30+3)=

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

(9×30)+(9×3)= (9\times30)+(9\times3)=

We solve each of the exercises in parentheses:

270+27=297 270+27=297

Answer

297

Exercise #2

3×56= 3\times56=

Video Solution

Step-by-Step Solution

To facilitate the resolution process, we break down 56 into an exercise with smaller, preferably round, numbers.

3×(50+6)= 3\times(50+6)=

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

(3×50)+(3×6)= (3\times50)+(3\times6)=

We solve each of the exercises in parentheses and obtain:

150+18=168 150+18=168

Answer

168

Exercise #3

3×93= 3\times93=

Video Solution

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×(90+3)= 3\times(90+3)=

We use the distributive property to solve the exercise.

We multiply by 3 each of the terms in parentheses:

(3×90)+(3×3)= (3\times90)+(3\times3)=

We solve each of the terms in parentheses and obtain:

270+9=279 270+9=279

Answer

279

Exercise #4

74×8= 74\times8=

Video Solution

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)×8= (70+4)\times8=

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

(8×70)+(8×4)= (8\times70)+(8\times4)=

We solve the exercises in parentheses:

560+32=592 560+32=592

Answer

592

Exercise #5

35×4= 35\times4=

Video Solution

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)×4= (30+5)\times4=

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

(4×30)+(4×5)= (4\times30)+(4\times5)=

We solve the exercises in parentheses:

120+20=140 120+20=140

Answer

140

Exercise #1

480×3= 480\times3=

Video Solution

Step-by-Step Solution

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

(400+80)×3= (400+80)\times3=

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

(400×3)+(80×3)= (400\times3)+(80\times3)=

We solve the exercises in parentheses and obtain:

1200+240=1440 1200+240=1440

Answer

1440

Exercise #2

11×34= 11\times34=

Video Solution

Step-by-Step Solution

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

We obtain:

(10+1)×34= (10+1)\times34=

We multiply 34 by each of the terms in parentheses:

(34×10)+(34×1)= (34\times10)+(34\times1)=

We solve the exercises in parentheses and obtain:

340+34=374 340+34=374

Answer

374

Exercise #3

6×29= 6\times29=

Video Solution

Step-by-Step Solution

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

We obtain:

6×(301)= 6\times(30-1)=

We multiply 6 by each of the terms in parentheses:

(6×30)(6×1)= (6\times30)-(6\times1)=

We solve the exercises in parentheses and obtain:

1806=174 180-6=174

Answer

174

Exercise #4

4×53= 4\times53=

Video Solution

Step-by-Step Solution

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

We obtain:

4×(50+3)= 4\times(50+3)=

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

(4×50)+(4×3)= (4\times50)+(4\times3)=

We solve the exercises inside the parentheses and obtain:

200+12=212 200+12=212

Answer

212

Exercise #5

Solve the exercise:

=74:4

Video Solution

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:

(806):4= (80-6):4=

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

80:4=20 80:4=20

6:4=1.5 6:4=1.5

Now we subtract the result we obtained:

201.5=18.5 20-1.5=18.5

Answer

18.5

Topics learned in later sections

  1. The Distributive Property
  2. The Distributive Property for Seventh Graders
  3. The commutative properties of addition and multiplication, and the distributive property
  4. Advanced Arithmetic Operations
  5. Division of Whole Numbers Within Parentheses Involving Division