Commutative, distributive and associative properties - Examples, Exercises and Solutions

$12:(2\times2)=$

According to the order of operations, we first solve the exercise within parentheses:

$2\times2=4$

Now we divide:

$12:4=3$

$3$

$5\cdot5\cdot5\cdot2\cdot2\cdot2=?$

We use the substitution property and organize the exercise in the following order:

$5\times2\times5\times2\times5\times2=$

We place parentheses in the exercise:

$(5\times2)\times(5\times2)\times(5\times2)=$

We solve from left to right:

$10\times10\times10=$

$(10\times10)\times10=$

$100\times10=1000$

1000

$7-(4+2)=$

According to the order of operations, we first solve the exercise within parentheses:

$4+2=6$

Now we solve the rest of the exercise:

$7-6=1$

$1$

$8-(2+1)=$

According to the order of operations, we first solve the exercise within parentheses:

$2+1=3$

Now we solve the rest of the exercise:

$8-3=5$

$5$

$13-(7+4)=$

According to the order of operations, we first solve the exercise within parentheses:

$7+4=11$

Now we subtract:

$13-11=2$

$2$

$38-(18+20)=$

According to the order of operations, first we solve the exercise within parentheses:

$18+20=38$

Now, the exercise obtained is:

$38-38=0$

$0$

$28-(4+9)=$

According to the order of operations, we first solve the exercise within parentheses:

$4+9=13$

Now we obtain the exercise:

$28-13=15$

$15$

$55-(8+21)=$

According to the order of operations, we first solve the exercise within parentheses:

$8+21=29$

Now we obtain the exercise:

$55-29=26$

$26$

$37-(4-7)=$

According to the order of operations, we first solve the exercise within parentheses:

$4-7=-3$

Now we obtain:

$37-(-3)=$

Remember that the product of a negative and a negative results in a positive, therefore:

$-(-3)=+3$

Now we obtain:

$37+3=40$

$40$

$80-(4-12)=$

According to the order of operations, we first solve the exercise within parentheses:

$4-12=-8$

Now we obtain the exercise:

$80-(-8)=$

Remember that the product of plus and plus gives us a positive:

$-(-8)=+8$

Now we obtain:

$80+8=88$

$88$

$100-(30-21)=$

According to the order of operations, we first solve the exercise within parentheses:

$30-21=9$

Now we obtain:

$100-9=91$

$91$

$22-(28-3)=$

According to the order of operations, we first solve the exercise within parentheses:

$28-3=25$

Now we obtain the exercise:

$22-25=-3$

$-3$

$60:(5\times3)=$

We write the exercise in fraction form:

$\frac{60}{5\times3}$

We break down 60 into a multiplication exercise:

$\frac{20\times3}{5\times3}=$

We simplify the 3s and obtain:

$\frac{20}{5}$

We break down the 5 into a multiplication exercise:

$\frac{5\times4}{5}=$

We simplify the 5 and obtain:

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

$4$

$2+4-3=$

We solve the exercise from left to right, we place the addition exercise in parentheses and then subtract:

$(2+4)-3=$

$6-3=3$

3

$-3-2+10=$

First, we place the subtraction exercise in parentheses, and then we add:

$(-3-2)+10=$

$-5+10=$

We use the substitution property to make solving the exercise easier:

$10-5=5$

5