The Distributive Property in the Case of Multiplication

🏆Practice the distributive property for 7th grade

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

A- The Distributive Property in the Case of Multiplication

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Test yourself on the distributive property for 7th grade!

einstein

Solve the exercise:

84:4=

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More exercises to practice the distributive property in the case of multiplication

37×5=(30+7)×5=30×5+7×5=150+35=18537\times 5= ( 30+7) \times 5= 30\times 5 + 7 \times 5= 150+35= 185

48×6=(502)×6=50×62×6=30012=28848\times 6= (50-2) \times 6= 50\times 6-2\times 6= 300-12= 288


Exercises on The Distributive Property in the Case of Multiplication

Exercise 1

Assignment:

74:8= 74:8=

Solution:

We break down 72 72 into numbers divisible by 8 8

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

We arrange the exercise into simple fractions

728+28= \frac{72}{8}+\frac{2}{8}=

We divide accordingly

9+14=914 9+\frac{1}{4}=9\frac{1}{4}

Answer:

914 9\frac{1}{4}


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Exercise 2

Assignment:

What expression is equivalent to the exercise 14×3 14\times3 ?

Solution:

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

(151)×3= (15-1)\times3=

15×33×1= 15\times3-3\times1=

15×33 15\times3-3

Answer:

15×315\times3 Then subtract 3


Exercise 3

Assignment:

(40+70+357)×9= \left(40+70+35−7\right)×9=

Solution:

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

40×9+70×9+35×97×9= 40\times9+70\times9+35\times9-7\times9=

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

=360+630+(30+5)963 =360+630+(30+5)9-63

First, we solve the parentheses

360+630+270+4563= 360+630+270+45-63=

Now we add and subtract accordingly

990+270+4563= 990+270+45-63=

1260+4563= 1260+45-63=

130563=1242 1305-63=1242

Answer:

1242 1242


Do you know what the answer is?

Exercise 4

Assignment:

74×8= 74\times8=

Solution:

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

(70+4)×8= (70+4)\times8=

We solve the exercise accordingly

70×8+4×8= 70\times8+4\times8=

560+32=592 560+32=592

Answer:

592592


Exercise 5

Assignment:

35×4=35\times4=

Solution:

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

(30+5)×4= (30+5)\times4=

We solve the exercise accordingly

30×4+5×4= 30\times4+5\times4=

120+20=140 120+20=140

Answer:

140 140


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Review Questions

What is the distributive property of multiplication?

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

Distributive property of multiplication over subtraction.

a×(bc)=a×ba×c a\times\left(b-c\right)=a\times b-a\times c


What is the distributive property of division?

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:

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


Do you think you will be able to solve it?

What are some examples of the distributive property in multiplication?

Example 1

P

Assignment

(3+8)×5= \left(3+8\right)\times5=

(3+8)×5=3×5+8×5 \left(3+8\right)\times5=3\times5+8\times5

3×5+8×5=15+40 3\times5+8\times5=15+40

=55 =55

Answer

=55 =55


Example 2

Assignment 198×7= 198\times7=

We can break down 198 198 in the following way:

(100+90+8)×7= \left(100+90+8\right)\times7=

We apply the distributive property of multiplication

100×7+90×7+8×7= 100\times7+90\times7+8\times7=

=700+630+56 =700+630+56

=1386 =1386

Answer

=1386 =1386


What are some examples of the distributive property in division?

Example 1

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

Applying the distributive property of division

=222+142 =\frac{22}{2}+\frac{14}{2}

=11+7=18 =11+7=18

Result

=18 =18

Example 2

Assignment 250:5 250:5

We break down the 250 250 into two numbers

(30050):5 \left(300-50\right):5

We apply the distributive law of division with respect to subtraction

3005505=6010 \frac{300}{5}-\frac{50}{5}=60-10

=50 =50

Answer

=50 =50


Test your knowledge

Examples with solutions for 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 following exercise,

We will present two of them.

In both ways, we begin by decomposing the number 84 into smaller units; 80 and 4.

44=1 \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; 10×8 10\times8

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

And therefore, we are able to reduce the exercise as follows: 104×8 \frac{10}{4}\times8

Eventually we are left with2×10 2\times10

which is equal to 20

In the second method, we decompose 80 into the following smaller units:40+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 it in to our above answer:

20+1=21 20+1=21

Thus we are left with the following solution:844=21 \frac{84}{4}=21

Answer

21

Exercise #2

133+30= 133+30=

Video Solution

Step-by-Step Solution

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

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

We then use the distributive property for 33:

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

We rearrange the exercise into a more practical form:

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

We solve the middle exercise:

30+30=60 30+30=60

Which results in the final exercise as seen below:

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

Answer

163

Exercise #3

14070= 140-70=

Video Solution

Step-by-Step Solution

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

100+4070= 100+40-70=

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

10070+40= 100-70+40=

Lastly 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

94+72= 94+72=

Video Solution

Step-by-Step Solution

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= 90+4+70+2=

Using the associative property, we then rearrange the exercise to be more functional.

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

Which results in the following exercise:

160+6=166 160+6=166

Answer

166

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