Order of Operations Practice Problems

Substitute the given values for the variables into the expression:

\(4a (3b+5) + 2b\) \(= 4 \times -6 (3 \times 7 + 5) + 2 \times 7\)

Compute the expression in the parentheses first. Remember that you must first multiply 3 by 7 and then add 5 in order to follow order of operations:

\(= 4 \times -6(21 + 5) + 2 \times 7\)

Next, add the values in the parentheses.

\(= 4 \times -6(26) + 2 \times 7\)

Simplify by multiplying the numbers outside the parenthesis:

\(= -24(26) + 14\)

Multiply -24 by 26:

\(= -624 +14\)

Finally, add:

\(= -610\)

Compute the product using the FOIL method.

\((a+b)(a-b)=a^2-ab+ba-b^2\)

Since \(ab\) is equal to \(ba\), the middle terms cancel out each other, which leaves \(a^2-b^2\).

Use the FOIL method to get rid of the parentheses:

\((2x – 20)(5x + 10)\) \(= 2x(5x) + 2x(10) – 20(5x) – 20(10)\) \(= 10x^2 + 20x – 100x – 200\)

Then, combine like terms to simplify the expression:

\(10x^2-80x-200\)

First, substitute the given values for \(x\) and \(y\) into the expression:

\(3x^2y + \frac{y}{2} \: – 6x\) \(= 3(4)^2 \times 10 + \frac{10}{2} \: – 6(4)\)

Then, calculate the value of the expression. According to the order of operations, any exponents must be evaluated first:

\(3(16)(10) + \tfrac{10}{2}\: – 6(4)\)

Then, perform any multiplication or division in order from left to right:

\(480+5-24\)

Then, any addition or subtraction should be completed:

\(485 – 24 = 461\)

First, substitute the given value of \(w\) into the expression each time it appears:

\(8w^2-12w+(4w-5)+6\) \(=8\times 7^2-12(7)+(4(7)-5)+6\)

According to the order of operations, any calculations inside of the brackets must be done first:

\(87^2-12(7)+(23)+6\)

Next, evaluate exponents and then perform multiplication:

\(849-12(7)+23+6\) \(=392-84+23+6\)

Finally, perform addition and subtraction:

\(392-84+23+6=337\)

First, simplify the expression inside the parentheses:

\(4(3)^2-(-2)\)

Next, simplify the exponent:

\(4(9)-(-2)\)

Then, multiply:

\(36-(-2)\)

Finally, subtract:

\(36-(-2)=36+2=38\)

Simplify the expression inside the parentheses first:

\(-11-(16-32)\)
\(-11–(-16)\)

Then subtract. When subtracting a negative integer, be sure to change the negative integer into a positive and then add it to the other number:

\(-11-(-16)=-11+16=5\)

Simplify the expression inside the parentheses first:

\(-3(25) + 2(-14) + 33\)

Then multiply and solve:

\(-75 + (-28) + 33 = -70\)

Use the FOIL method to simplify this expression:

\((3x+1)(7x+10)\) \(= (3x)(7x)+(3x)(10)+(1)(7x)+(1)(10)\)\(=21x^2+30x+7x+10\)

Combine like terms to get the answer:

\(21x^2+37x+10\)

First, simplify all operations inside the parentheses:

\(2(15)^2-12(12)\)

Second, simplify any exponential expressions:

\(2(225) – 12(12)\)

Third, perform all multiplication and division as they occur in the problem from left to right.

\(450 – 144\)

Finally, subtract and solve:

\(450 – 144 = 306\)