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TACHS Math : Order of operations

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Example Questions

Example Question #1 : Order Of Operations

Evaluate:

$15 \times 8 - 12 + 25$ $\displaystyle 15 \times 8 - 12 + 25$

Possible Answers:

$\displaystyle 83$

157 $\displaystyle 157$

107 $\displaystyle 107$

133 $\displaystyle 133$

Correct answer:

133 $\displaystyle 133$

Explanation:

In the order of operations, in the absence of grouping symbols, multiplication takes precedence over addition and subtraction. Multiply 15 by 8 first:

$15 \times 8 - 12 + 25$ $\displaystyle 15 \times 8 - 12 + 25$

$\displaystyle =120 - 12 + 25$

Addition and subtraction have equal precedence and are worked in left-to-right order. Subtract 120 and 12 next:

$\displaystyle =108 + 25$

Now add:

= 133 $\displaystyle = 133$

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Example Question #1 : Order Of Operations

What is the value of $(3+1)^2\times 2-(2\times2)+15$ $\displaystyle (3+1)^2\times 2-(2\times2)+15$?

Possible Answers:

$\displaystyle 51$

$\displaystyle 22$

$\displaystyle 39$

$\displaystyle 43$

Correct answer:

$\displaystyle 43$

Explanation:

Make sure to follow the order of operations.

Start by simplifying what is found in the parentheses.

$(3+1)^2\times 2-(2\times2)+15=4^2\times 2-4+15$ $\displaystyle (3+1)^2\times 2-(2\times2)+15=4^2\times 2-4+15$

Next, simplify any exponents.

$4^2\times 2-4+15=16 \times 2-4+15$ $\displaystyle 4^2\times 2-4+15=16 \times 2-4+15$

Next, simplify any multiplication and division.

$16 \times 2-4+15=32-4+15$ $\displaystyle 16 \times 2-4+15=32-4+15$

Finally, simplify any addition and subtraction.

$\displaystyle 32-4+15=43$

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Example Question #21 : Tachs: Math And Ability

What is the value of $3+(7\times 4)\times (2+1)-10$ $\displaystyle 3+(7\times 4)\times (2+1)-10$?

Possible Answers:

$\displaystyle 81$

$\displaystyle 65$

$\displaystyle 91$

$\displaystyle 77$

Correct answer:

$\displaystyle 77$

Explanation:

Make sure you follow the order of operations (PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction—from the left to the right).

Start by simplifying what's found within the parentheses:

$3+(7\times 4)\times (2+1)-10=3+28 \times 3-10$ $\displaystyle 3+(7\times 4)\times (2+1)-10=3+28 \times 3-10$

Next, simplify any multiplication and division.

$3+28 \times 3-10=3+84-10$ $\displaystyle 3+28 \times 3-10=3+84-10$

Finally, simplify any addition and subtraction.

$\displaystyle 3+84-10=77$

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TACHS Math : Order of operations

Study concepts, example questions & explanations for TACHS Math

All TACHS Math Resources

Example Questions

Example Question #1 : Order Of Operations

Example Question #1 : Order Of Operations

Example Question #21 : Tachs: Math And Ability

All TACHS Math Resources

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