The Distributive Property for 7th Grade: Solving the problem

Apply the distributive property of division and proceed to split the number 88 into the sum of 80 and 8. Simplifying he division operation allows us to solve the exercise without a calculator

Reminder - The distributive property of division actually allows us to split the larger term in the division problem into a sum or difference of smaller numbers, which makes the division operation easier and allows us to solve the exercise without a calculator

$(80+8):4=$

Apply the formula of the distributive property $(a+b):c=a:c+b:c$

$(80:4)+(8:4)=$

Continue to solve the problem according to the order of operations

$20+2=22$

Therefore the answer is option C - 22.

Shown below are the various steps of our solution:

$88:4=(80+8):4=80:4+80:4=20+2=22$

Apply the distributive property of division and proceed to split the number 186 into the sum of 180 and 6. This ultimately makes the division operation easier and allows us to solve the exercise without a calculator

Reminder - The distributive property of division actually allows us to split the larger number in a division problem into a sum or difference of smaller numbers, which makes the division operation easier and allows us to solve the exercise without a calculator

$(180+6):6=$

Apply the formula of the distributive property $(a+b):c=a:c+b:c$

$180:6+6:6=$

Continue to solve the problem according to the order of operations

$30+1=31$

Therefore the answer is option D - 31.

Below are the various steps of our solution:

$186:6= (180+6):6= 180:6+6:6= 30+1=31$

Apply the distributive property of multiplication in order to break down the number 13 into a subtraction exercise with smaller numbers. This allows us to work with smaller numbers and ultimately simplify the operation

Reminder - The distributive property of multiplication actually allows us to break down the larger term in the multiplication exercise into a sum or difference of smaller numbers, which makes the multiplication operation easier and gives us the ability to solve the exercise even without a calculator

$13\times(10-2)=$

Apply the distributive property formula $a(b+c)=ab+ac$

$13\times10-13\times2=$

Proceed to solve the problem according to the order of operations

$130-26=$

Therefore the answer is option D - 104.

Shown below are the various stages of the solution:

$13\times8=13\times(10-2)=13\times10-13\times2=130-26=104$

Apply the distributive property of multiplication in order to split the number 17 into the sum of numbers 10 and 7. This ultimately allows us to work with smaller numbers and simplify the operation

Reminder - The distributive property of multiplication essentially allows us to split the larger term in a multiplication problem into a sum or difference of smaller numbers, which makes multiplication easier and gives us the ability to solve the problem even without a calculator

$(10+7)\times7=$

Apply the distributive property formula $a(b+c)=ab+ac$

$10\times7+7\times7=$

Proceed to solve according to the order of operations

$70+49=$

Therefore the answer is option C - 119.

Shown below are the various stages of the solution

$17\times7=(10+7)\times7=(10\times7)+(7\times7)=70+49=119$

Apply the distributive property of multiplication and proceed to split the number 36 into the sum of the numbers 30 and 6. This allows us to work with smaller numbers and simplify the operation

Reminder - The distributive property of multiplication essentially allows us to split the larger term in a multiplication problem into a sum or difference of smaller numbers, which makes multiplication easier and gives us the ability to solve the problem without a calculator

$3×(30+6)=$

Apply the distributive property formula $a(b+c)=ab+ac$

$3×30+3×6=$

Proceed to solve the problem according to the order of operations

$90+18= 108$

Therefore the answer is option D - 108.

Shown below are the various stages of our solution:

$3\times36=3\times(30+6)=(3\times30)+(3\times6)=90+18=108$

Apply the distributive property of division and proceed to split the number 72 into the sum of 60 and 12. Simplifying the division operation allows us to solve the exercise without a calculator

Reminder - The distributive property of division allows us to split the larger number in a division problem into a sum or difference of smaller numbers, which makes the division operation easier and allows us to solve the exercise without a calculator

$(60+12):6=$

Apply the formula of the distributive property $(a+b):c=a:c+b:c$

$(60:6)+(12:6)=$

Continue to solve according to the order of operations

$10+2=12$

Therefore the answer is option A - 12.

Shown below are the various steps of the solution:

$72:6=(60+12):6=60:6+12:6=10+2=12$

Apply the distributive property of division and proceed to split the number 93 into the sum of 90 and 3. This ultimately simplifies the division operation allowing us to solve the exercise without a calculator

Reminder - The distributive property of division actually allows us to split the larger term in the division problem into a sum or difference of smaller numbers, which makes the division operation easier and allows us to solve the exercise without a calculator

$(90+3):3=$

Apply the formula of the distributive property $(a+b):c=a:c+b:c$

$(90:3)+(3:3)=$

Continue to solve the problem according to the order of operations

$30+1=31$

Therefore the answer is option C - 31.

Shown below are the various steps of our solution:

$93:3=(90+3):3=90:3+3:3=30+1=31$

In order to render the process easier for ourselves, we will use the distributive property over 101:

$(100+1)\times17=$

We will multiply 17 by each of the terms in parentheses:

$(100\times17)+(1\times17)=$

Let's solve the expressions in parentheses:

$1,700+17=1,717$

Apply the distributive property of multiplication and proceed to split the number 12 that we obtained into a sum of 10 and 2. This allows us to work with smaller numbers and simplify the operation

Reminder - The distributive property of multiplication actually allows us to split the larger term in a multiplication problem into a sum or difference of smaller numbers, which makes multiplication easier and gives us the ability to solve the problem even without a calculator

$97×(10+2)=$

Apply the distributive property formula $a(b+c)=ab+ac$

$97×10+97×2=$

Solve according to the order of operations

$970+97×2=$

Apply the distributive property of multiplication again and split the number 97 into a sum of 90 and 7. This allows us to work with smaller numbers and simplify the operation

$970+2×(90+7)=$

Apply the distributive property formula once again $a(b+c)=ab+ac$

$970+90×2+7×2=$

Solve the problem according to the order of operations

$970+180+14=$

$1150+14=1164$

Therefore the answer is option C - 1164.

Shown below are the various steps of the solution:
$97×12= 97×(10+2)= 97×10+97×2= 970+(90+7)×2= 970+90×2+7×2= 970+180+14= 1150+14=1164$

Begin by applying the division distributive law in order to split the number 224 into the sum of 160 and 64. This ultimately simplifies the division operation allowing us to solve the exercise without a calculator

Reminder - The division distributive law essentially allows us to split the larger term in a division exercise into a sum or difference of smaller numbers, which makes the division operation easier and allows us to solve the exercise without a calculator

$(160+64):16=$

Apply the formula of the distributive law $(a+b):c=a:c+b:c$

Continue to solve according to the order of operations

$10+4=14$

Therefore the answer is option B - 14.

Shown below are the various steps of the solution

$224:16=(160+64):6=160:16+64:16=10+4=14$

To make it easier for us to solve, we will use the divisibility rule by 19:

$99\times(10+9)=$

Let's multiply 99 by each term in parentheses:

$(99\times10)+(99\times9)=$

Let's solve the expression in the first parentheses:

$990+(99\times9)=$

We'll separate the expression in parentheses in a way that uses the divisibility rule by 99:

$990+(90+9)\times9=$

Let's multiply 9 by each term in parentheses and we get:

$990+(90\times9)+(9\times9)=$

Let's solve each of the expressions in parentheses:

$990+810+81=$

Let's solve the expression from left to right.

We'll solve the left expression by adding vertically:

$990\\+810\\$

We'll make sure to follow the correct order when solving the expression, ones with ones, tens with tens, and so on, and we get:

$1,800$

Now we get the expression:

$1,800+81=1,881$