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Pre-Algebra : Order of Operations

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Example Questions

Example Question #92 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

First subtract and , then multiply by .

Possible Answers:

$20-5\times7$

$(20-5)\div7$

$(20+5)\times7$

$20-(5\times7)$

$(20-5)\times7$

Correct answer:

$(20-5)\times7$

Explanation:

Because we want to subtract and first, we need to set that off into parentheses due to the order of operation rules. Then we can do the multiplication of .

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Example Question #82 : Order Of Operations

Simplify the following expression:

$6*2^{2}+6(2+3)-1$

Possible Answers:

198

203 Fol

173

Correct answer:

Explanation:

Follow the rules of order of operations. An easy way to remember them is to remember PEMDAS.

P - parenthesis

E - exponents

M/D - multiplication and division, done in order from left to right

A/S - addition and subtraction, done in order from left to right

By following this, we first evaluate what's in the parenthesis:

$6*2^{2}+6(5)-1$

Next we evaluate the exponent:

6(4)+6(5)-1

Now we multiply from left to right:

24+30-1

Lastly, we add and subtract from left to right:

54-1=53

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Example Question #81 : Order Of Operations

Simplify: $8x[-14x\div 7x]^3-6x$

Possible Answers:

60x

None of the other answers.

-64x

-70x

-58x

Correct answer:

-70x

Explanation:

To solve this problem you must follow the order of operations which are a set of rules that say some mathematical operations are performed sooner than others. The most common acronym to keep track of the order is PEMDAS which stands for Parentheses, Exponents, Multiplication, Division, Addition, and lastly Subtraction. Deal with each operation and move onto the next.

$8x[-14x\div 7x]^3-6x$

Paretheses:

8x[-2]^3-6x

Exponents:

8x[-8]-6x

Multiplication:

-64x-6x

Subtraction:

-64x-6x=-70x

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Example Question #83 : Order Of Operations

$6+3^2\div 9-3+(2\cdot 8)$

Simplify.

Possible Answers:

$\frac{16}{3}$

Correct answer:

Explanation:

Follow PEMDAS.

Simplify parentheses: (2*8)=16

Evaluate exponent: 3^2=9

Divide: 9/9=1

6+1-3+16=20

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Example Question #84 : Order Of Operations

$9^{2}-72\div4+6\times11-56$

Simplify.

Possible Answers:

Correct answer:

Explanation:

Follow PEMDAS.

Evaluate exponent: 9^2=81

Divide: 72/4=18

Multiply: 6(11)=66

81-18+66-55=74

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Example Question #85 : Order Of Operations

$32-8\left ( 1+2\right )^{2}+72$

Simplify.

Possible Answers:

293

Correct answer:

Explanation:

Follow PEMDAS.

Simplify parenthese: (1+2)=3

Evaluate exponent: 3^2=9

Multiply: 8(9)=72

32-72+77=37

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Example Question #87 : Order Of Operations

Solve the equation using order of operations.

24 + (5*-3) - 2^3 =

Possible Answers:

Correct answer:

Explanation:

24 + (5*-3) - 2^3 =

24 + (5 * -3) -8 =

24 + (-15) -8 =

9 - 8 =

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Example Question #88 : Order Of Operations

Simplify: 3-2(6-3)^2

Possible Answers:

Correct answer:

Explanation:

Evaluate the inner parentheses first.

3-2(6-3)^2= 3-2(3)^2

Square the quantity inside the parentheses.

3-2(3)^2 = 3-2(9)

Multiply the number before the parentheses with the inner quantity.

3-2(9) = 3-18

Subtract.

3-18=-15

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Example Question #81 : Order Of Operations

Solve: $\left(\frac{3(-2)}{3-2(3-2)}\right)^2$

Possible Answers:

$\frac{1}{36}$

Correct answer:

Explanation:

Evaluate the inner parentheses first.

$\left(\frac{3(-2)}{3-2(3-2)}\right)^2= \left(\frac{-6}{3-2(1)}\right)^2$

Simplify the denominator.

$\left(\frac{-6}{3-2(1)}\right)^2 = \left(\frac{-6}{1}\right)^2 =(-6)^2 = 36$

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Example Question #82 : Order Of Operations

Solve: 2-(1-4)^3

Possible Answers:

127

Correct answer:

Explanation:

Evaluate the quantity in the parentheses first by order of operations.

2-(1-4)^3 = 2-(-3)^3

Cube the quantity in the parentheses and simplify.

Remember, subtracting a negative number makes it positive.

2-(-3)^3 = 2-(-27) = 2+27=29

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Pre-Algebra : Order of Operations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #92 : Common Core Math: Grade 5

Example Question #82 : Order Of Operations

Example Question #81 : Order Of Operations

Example Question #83 : Order Of Operations

Example Question #84 : Order Of Operations

Example Question #85 : Order Of Operations

Example Question #87 : Order Of Operations

Example Question #88 : Order Of Operations

Example Question #81 : Order Of Operations

Example Question #82 : Order Of Operations

All Pre-Algebra Resources

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