Distributive Property Practice Problems for 7th Grade Math

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

$100+40-70=$

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

$100-70+40=$

Lastly we solve the exercise from left to right:

$100-70=30$

$30+40=70$

We will use the distributive law and split the number 143 into a sum of 100 and 43.

The distributive law allows us to distribute, meaning, to split a number into two or more numbers. This actually allows us to work with smaller numbers and simplify the operation.

$(100+43)-43=$

We will operate according to the order of operations

We can remove parentheses and perform addition and subtraction operations in any order since there are only addition and subtraction operations in the equation

$100+43-43=100+0=100$

Therefore, the answer is option C - 100.

And now let's see the solution to the exercise in a centered format:

$143-43= (100+43)-43= 100+43-43=100+0=100$

In order to simplify the calculation , we first break down 94 and 72 into smaller and preferably round numbers.

We obtain the following exercise:

$90+4+70+2=$

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

$90+70+4+2=$

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

$90+70=160$

$4+2=6$

Which results in the following exercise:

$160+6=166$

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.

$\frac{4}{4}=1$

Subsequently we are left with only the 80.

Continuing on with the first method, we will then further decompose 80 into smaller units; $10\times8$

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

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

Eventually we are left with$2\times10$

which is equal to 20

In the second method, we decompose 80 into the following smaller units:$40+40$

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

And therefore: $\frac{40+40}{4}=\frac{80}{4}=20=10+10$

which is also equal to 20

Now, let's remember the 1 from the first step and add it in to our above answer:

$20+1=21$

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

Apply the distributive property of division and proceed to split the number 24 into a sum of 12 and 12, which ultimately renders the division operation easier and allows us to solve the exercise without a calculator.

Note - it's best to choose to split the number based on knowledge of multiples. In this case of the number 12 because we need to divide by 12.

Reminder - The distributive property of division actually allows us to split the larger term 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

We will use the formula of the distributive property

$(a+b):c=a:c+b:c$

$24:12=(12+12):12$

$(12+12):12=12:12+12:12$

$12:12+12:12=1+1$

$1+1=2$

Therefore the answer is section a - 2.