Associative Property: Addition, subtraction, multiplication and division

According to the order of operations, we first solve the division exercise, and then the subtraction:

$(6:2)+9-4=$

$6:2=3$

Now we place the subtraction exercise in parentheses:

$3+(9-4)=$

$3+5=8$

According to the rules of the order of operations, we first solve the division exercise:

$9:3=3$

Now we obtain the exercise:

$3-3=0$

According to the rules of the order of operations, we first solve the division exercise:

$6:2=3$

Now we get the exercise:

$-5+2-3=$

We solve the exercise from left to right:

$-5+2=-3$

$-3-3=-6$

According to the rules of the order of operations, we first solve the multiplication exercise:

$4\times2=8$

Now we obtain the exercise:

$8-5+4=$

We solve the exercise from left to right:

$8-5=3$

$3+4=7$

According to the order of operations, we solve the exercise from left to right since the only operation in the exercise is division:

$24:8=3$

$3:3=1$

First, we will find the sum of the fractions:

$\frac{3}{7}+\frac{4}{7}=\frac{3+4}{7}=\frac{7}{7}=1$

Now we get the exercise:

$2+1=3$

Given that in the exercise there is only multiplication, we add 9 and 7 to the numerator of the fraction as follows:

$\frac{9\times7\times3}{9}=$

We simplify the 9 in the numerator and denominator, and obtain:

$7\times3=21$

We add the 2 to the numerator of the fraction in the multiplication exercise, and the 4 in the denominator of the fraction we break it down into a smaller multiplication exercise:

$5-\frac{2\times3}{2\times2}=$

We simplify the 2 in the numerator and denominator:

$5-\frac{3}{2}=$

We convert the simple fraction into a mixed fraction:

$5-1\frac{1}{2}=3\frac{1}{2}$

We can use the substitutive property to reorder and make solving the equation simpler:

$\frac{2}{5}+\frac{3}{5}-2=$

We first add the fractions:

$\frac{2+3}{5}=\frac{5}{5}=1$

Now we obtain the exercise:

$1-2=-1$

According to the rules of the order of operations, we first solve the multiplication exercise:

$3+8+(4\times3)=$

$4\times3=12$

Now, we solve the addition exercise from left to right:

$3+8+12=$

$11+12=23$

According to the rules regarding the order of arithmetic operations, we first solve the multiplication exercise:

$5\times4=20$

We obtain the following exercise:

$3+4-20=$

We then solve the exercise from left to right:

$3+4=7$

$7-20=-13$

According to the rules of the order of arithmetic operations, we begin by enclosing the multiplication exercise inside parentheses:

$2-(5\times3)+4=$

We then solve the said exercise inside of the parentheses:

$5\times3=15$

We obtain the following:

$2-15+4=$

Lastly we solve the exercise from left to right:

$2-15=-13$

$-13+4=-9$

First, we solve the exercise within the parentheses:

$9+1=10$

Now we obtain the exercise:

$-5+3\times10=$

According to the order of operations, we solve the multiplication exercise:

$3\times10=30$

We obtain:

$-5+30=$

We use the substitution property:

$30-5=25$

We simplify the exercise in parentheses as follows:

$2x+(5\times x)-(5\times5)=$

We solve the exercises in parentheses:

$2x+5x-25=$

We add like terms:

$2x+5x=7x$

We obtain

$7x-25$

We can use the substitutive property and rearrange the exercise in a way that makes it easier for us to solve the exercise:

$2a-a+3-2=$

We solve the exercise from left to right:

$2a-a=a$

$3-2=1$

Therefore, we obtain:

$a+1$

We can use the substitutive property and arrange the exercise in a way that makes solving the exercise simpler:

$-2+4+3+4a-2a-2a=$

First, we solve the addition exercise:

$4+3=7$

We now obtain the exercise:

$-2+7+4a-2a-2a=$

We add the coefficients a:

$4a-2a=2a$

$2a-2a=0$

We now obtain the exercise:

$-2+7+0=$$$

We use the substitutive property:

$7-2+0=5+0=5$

We rewrite the division exercise as a fraction:

$\frac{4a}{a}+6=$

We simplify a in both the numerator and denominator, and we obtain:

$4+6=10$

According to the order of operations, we place the multiplication and division exercise within parentheses:

$(9:3)-(1.5\times2)=$

Now we solve the exercises within parentheses:

$9:3=3$

$1.5\times2=3$

And we obtain the exercise:

$3-3=0$

We simplify this expression paying attention to the order of operations which states that exponentiation comes before multiplication and division, and before addition and subtraction, and that parentheses precede all of them.

Therefore, we start by performing the multiplication within parentheses, then we carry out the division operation, and we finish by performing the subtraction operation:

$9-6:(4\cdot3)-1= \\ 9-6:12-1= \\ 9-0.5-1= \\ 7.5$

Therefore, the correct answer is option C.

According to the rules of the order of operations, we first solve the exercise within parentheses from left to right:

$8:4=2$

$2:2=1$

Now we get the exercise:

$1-3-1=$

We solve the exercise from left to right:

$1-3=-2$

$-2-1=-3$