The Distributive Property for 7th Grade: Applying the formula

To solve the equation, follow these steps:

1. Start by solving the expression inside the parentheses: $12 + 8$.

2. Calculate $12 + 8$ to get $20$.

3. Now divide the result by 4: $20 \div 4$.

4. Calculate $20 \div 4$ to get $5$.

Therefore, the final answer is $5$.

To solve the equation, follow these steps:

1. Start with the expression inside the parentheses: $50 - 10$.

2. Calculate $50 - 10$ to get $40$.

3. Now multiply the result by 2: $40 \times 2$.

4. Calculate $40 \times 2$ to get $80$.

Therefore, the final answer is $80$.

In order to simplify the resolution process, we begin by breaking down the number 480 into a smaller addition exercise:

$(400+80)\times3=$

We then multiply each of the terms within the parentheses by 3:

$(400\times3)+(80\times3)=$

Lastly we solve the exercises inside the parentheses and obtain the following:

$1200+240=1440$

In order to simplify the resolution process, we begin by breaking down the number 74 into a smaller addition exercise.

It is easier to choose round whole numbers, hence the following calculation:

$(70+4)\times8=$

We then multiply each of the terms within the parentheses by 8:

$(8\times70)+(8\times4)=$

Lastly we solve the exercises within the parentheses:

$560+32=592$

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 and proceed to multiply each term inside of the parentheses by 187:

$187\times8-187\times5=$

Solve the first multiplication problem vertically, making sure to solve it in the correct order (ones multiplied by ones, ones multiplied by tens, ones multiplied by hundreds )

$187\\\times8$

We should obtain the following result: 1496

Proceed to solve the second multiplication problem vertically, once again making sure to solve it in the correct order (ones multiplied by ones, ones multiplied by tens, ones multiplied by hundreds )

$187\\\times5$

We should obtain the following result: 935

Now to tackle the next problem:

$1496-935=$

We should once again solve this vertically. Make sure to align the digits properly, ones under ones, tens under tens, etc.:

$1496\\-935$

Subtract ones from ones, tens from tens, etc., to obtain the final result: $561$

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 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:

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

Let's simplify this expression while maintaining the order of operations.

Let's start by solving what's in the parentheses:

$29-4=25$

Now we get the expression:

$25:5=$

In the next step, to make the division easier, we'll break down 25 into two smaller factors that are divisible by 5:

$(20+5):5=$

Let's divide each factor in the parentheses by 5:

$(20:5)+(5:5)=$

We'll solve each expression in the parentheses and obtain:

$4+1=5$

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

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

In order to simplify the resolution process, we divide the number 35 into a smaller addition exercise.

It is easier to choose round whole numbers, hence the following calculation:

$(30+5)\times4=$

We then multiply each of the terms inside of the parentheses by 4:

$(4\times30)+(4\times5)=$Lastly we solve the exercises inside of the parentheses:

$120+20=140$

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:

$1,700+17=1,717$

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:

$1,800+81=1,881$

In order to simplify the resolution process, we begin by breaking down the number 12345 into a smaller addition exercise:

$(10000+2000+300+40+5)\times6=$

We multiply each term inside the parentheses by 6:

$(10000\times6)+(2000\times6)+(300\times6)+(40\times6)+(5\times6)=$

We then solve each of the exercises inside of the parentheses:

$60000+12000+1800+240+30=$

Lastly we solve the exercise from left to right:

$60000+12000=72000$

$72000+1800=73800$

$73800+240=74040$

$74040+30=74070$

We will use the distributive property and multiply each term in parentheses by 4:

$4\times18+4\times5+4\times10=$

We will solve the exercise from left to right.

We will solve the first multiplication exercise vertically. We will make sure to write correctly and multiply ones by ones, and ones by tens as follows:

$4\\\times18$

We get the result: 72.

Let's solve the remaining multiplication exercises:

$4\times5=20$

$4\times10=40$

Now we'll connect all the results in the following way:

$72+20+40=$

We will solve the exercise vertically, making sure to write correctly and add ones with ones and tens with tens, as follows:

$72\\+20\\40$

We'll add all the ones together and get: 2

We'll add all the tens together and get: 13

Therefore, we got the number:

$132$

In order to simplify the resolution process, we begin by breaking down 30 into a smaller addition exercise:

$(30+5)\times20=$

We then multiply each of the terms inside of the parentheses by 20:

$(30\times20)+(5\times20)=$

Lastly we solve the exercises inside of the parentheses as follows:

$600+100=700$

Let's simplify this expression while maintaining the order of operations.

Let's start by solving the expression in parentheses from left to right:

$6+1-5=7-5=2$

Now we get the expression:

$106:2=$

In the next step, to make the division easier for ourselves, we'll break down 106 into two smaller factors that are divisible by 2:

$(100+6):2=$

Let's divide each factor in parentheses by 5:

$(100:2)+(6:2)=$

We'll solve each expression in parentheses and obtain:

$50+3=53$

In order to simplify the resolution process, we first separate 458 into a smaller addition exercise and choose numbers that are divisible by 7:

$(420+38):7=$

We then further separate 38 into a smaller addition exercise and choose numbers that are divisible by 7:

$(420+35+3):7=$

We divide each of the terms inside of the parentheses by 7:

$\frac{420}{7}+\frac{35}{7}+\frac{3}{7}=$

Finally we solve the fractions as follows:

$60+5+\frac{3}{7}=65\frac{3}{7}$

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

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

In order to simplify the resolution process, we begin by breaking down the number 354 into a smaller addition exercise.

It is easier to choose round whole numbers, and also to consider numbers that are easily divisible by 3.

Hence the following calculation:

$(300+54):3=$

Once again, for the purpose of facilitating the resolution process, we break down 54 into a smaller addition exercise.

Just as in the previous calculation we choose round numbers and numbers divisible by 3.

We obtain the following:

$(300+30+24):3=$

We then divide each of the terms within the parentheses by 3:

$300:3=100$

$30:3=10$

$24:3=8$

We finish by adding up all the results we obtained:

$100+10+8=110+8=118$