The Distributive Property in the Case of Multiplication

πŸ†Practice distributive property for seventh 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:
8Γ—5328\times 532

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

8Γ—532=8Γ—(500+30+2)8\times 532=8\times (500+30+2)

8Γ—500=40008\times 500=4000

+

8Γ—30=2408\times 30=240

+

8Γ—2=168\times 2=16

=

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

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Test yourself on distributive property for seventh grade!

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Solve the exercise:

84:4=

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

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

48Γ—6=(50βˆ’2)Γ—6=50Γ—6βˆ’2Γ—6=300βˆ’12=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 14Γ—3 14\times3 ?

Solution:

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

(15βˆ’1)Γ—3= (15-1)\times3=

15Γ—3βˆ’3Γ—1= 15\times3-3\times1=

15Γ—3βˆ’3 15\times3-3

Answer:

15Γ—315\times3 Then subtract 3


Exercise 3

Assignment:

(40+70+35βˆ’7)Γ—9= \left(40+70+35βˆ’7\right)Γ—9=

Solution:

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

40Γ—9+70Γ—9+35Γ—9βˆ’7Γ—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)9βˆ’63 =360+630+(30+5)9-63

First, we solve the parentheses

360+630+270+45βˆ’63= 360+630+270+45-63=

Now we add and subtract accordingly

990+270+45βˆ’63= 990+270+45-63=

1260+45βˆ’63= 1260+45-63=

1305βˆ’63=1242 1305-63=1242

Answer:

1242 1242


Do you know what the answer is?

Exercise 4

Assignment:

74Γ—8= 74\times8=

Solution:

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

(70+4)Γ—8= (70+4)\times8=

We solve the exercise accordingly

70Γ—8+4Γ—8= 70\times8+4\times8=

560+32=592 560+32=592

Answer:

592592


Exercise 5

Assignment:

35Γ—4=35\times4=

Solution:

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

(30+5)Γ—4= (30+5)\times4=

We solve the exercise accordingly

30Γ—4+5Γ—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.

aΓ—(b+c)=aΓ—b+aΓ—c a\times\left(b+c\right)=a\times b+a\times c

Distributive property of multiplication over subtraction.

aΓ—(bβˆ’c)=aΓ—bβˆ’aΓ—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)Γ—5= \left(3+8\right)\times5=

(3+8)Γ—5=3Γ—5+8Γ—5 \left(3+8\right)\times5=3\times5+8\times5

3Γ—5+8Γ—5=15+40 3\times5+8\times5=15+40

=55 =55

Answer

=55 =55


Example 2

Assignment 198Γ—7= 198\times7=

We can break down 198 198 in the following way:

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

We apply the distributive property of multiplication

100Γ—7+90Γ—7+8Γ—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

(300βˆ’50):5 \left(300-50\right):5

We apply the distributive law of division with respect to subtraction

3005βˆ’505=60βˆ’10 \frac{300}{5}-\frac{50}{5}=60-10

=50 =50

Answer

=50 =50


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