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GED Math : Complex Operations

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Example Questions

Example Question #331 : Numbers And Operations

Evaluate:

$6 \times 3 + 4 ^{2}$

Possible Answers:

1,764

484

294

Correct answer:

Explanation:

Work the operations in this order: Square first, multiply second, add third.

$6 \times 3 + 4 ^{2} = 6 \times 3 +\left ( 4 \times 4 \right ) = 6 \times 3 + 16 = 18 + 16 = 34$

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Example Question #331 : Numbers And Operations

Solve:

$3-4+2^{3}*3$

Possible Answers:

Correct answer:

Explanation:

When solving this problem, you need to remember order of operations, which tells us which operation has to be done first.

When following order of operations, you complete operations in the following order:

1. Parenthesis - Complete any operation in parenthesis first

2. Exponents - Solve exponents second

3. Multiplication and Division - Multiply or Divide (whichever one comes first from left to right)

4. Addition and Subtraction - Add or Subtract (whichever one comes first from left to right)

Keeping order of operations in mind, the steps to solve $3-4+2^{3}*3$ are below

$3-4+2^{3}*3 \textup{ } (\textup{Solve for the exponent})$

$3-4+8*3 \textup{ } (\textup{Multiply } 8 \textup{ and }3)$

$3-4+24 \textup{ } (\textup{Subtract } 3 \textup{ and }4)$

$-1+24 \textup{ } (\textup{Add } -1 \textup{ and }24)$

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Example Question #1 : Complex Operations

Define an operation $\bigstar$ on the real numbers as follows:

$a \bigstar b = \frac{a + 5}{a + b + 5}$

Evaluate $6 \bigstar (- 6)$

Possible Answers:

$2\frac{1}{5}$

$-\frac{1}{6}$

$-\frac{1}{5}$

Undefined

Correct answer:

$2\frac{1}{5}$

Explanation:

Substitute 6 for and for :

$a \bigstar b = \frac{6 + 5}{6 + (-6) + 5}= \frac{11}{0 + 5} = \frac{11}{5} = 2\frac{1}{5}$

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Example Question #2 : Order Of Operations

Define an operation $\bigstar$ on the real numbers as follows:

$a \bigstar b = \frac{a + 5}{a + b + 5}$

Evaluate $7 \bigstar \left (- 12 \right )$

Possible Answers:

$\frac{1}{2}$

Undefined

$-\frac{7}{24}$

$-\frac{1}{2}$

Correct answer:

Undefined

Explanation:

Substitute 7 for and - for :

$a \bigstar b = \frac{a + 5}{a + b + 5}$

$7 \bigstar -12 = \frac{7 + 5}{7 + (-12)+ 5} = \frac{12}{-5+ 5} = \frac{12}{0}$

Any fraction with a zero denominator - such as this one - is an undefined quantity.

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Example Question #1 : Order Of Operations

Solve: $-2 + 3\times6-12\div3+2$

Possible Answers:

$-\frac{6}{5}$

$\frac{10}{3}$

Correct answer:

Explanation:

This problem involves order of operations.

Use the acronym for the correct order:

PEMDAS-Parenthesis, Exponents, Multiply, Divide, Add, Subtract

(Please Excuse My Dear Aunt Sally)

Start by grouping what needs to be solved first.

$-2 + 3\times6-12\div3+2$

$-2 +\left ( 3\times6 \right )-\left (12\div3 \right )+2$

-2+18-4+2

The answer is 14.

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Example Question #3 : Order Of Operations

In order to calculate

$50 - 20 \div 5 + 8^{2}$

what step must you take first?

Possible Answers:

Subtracting twenty from fifty

Calculating the square of eight

Dividing twenty by five

Adding five and eight

Correct answer:

Calculating the square of eight

Explanation:

By the order of operations, in the absence of grouping symbols, exponents must be carried out before any other operations. The correct choice is that eight must be squared.

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Example Question #1 : Order Of Operations

Evaluate $y ^{2} - 6y + 7$ for y = 0.5 .

Do not use a calculator.

Possible Answers:

6.5

-7.5

4.25

-9.75

Correct answer:

4.25

Explanation:

Substitute 0.5 for and follow the order of operations:

$y ^{2} - 6y + 7$

$=0.5 ^{2} - 6(0.5) + 7$

=0.25- 6(0.5) + 7

=0.25 - 3 + 7

= -2.75 + 7

= 4.25

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Example Question #3 : Order Of Operations

Evaluate -7x + 13 for x = -6 . Do NOT use a calculator.

Possible Answers:

133

Correct answer:

Explanation:

Substitute for in the expression and folllow the order of operations:

-7x + 13

= -7 (-6) + 13

$= +(7 \cdot 6)+ 13$

= 42 + 13

= 55

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Example Question #4 : Order Of Operations

Evaluate $-7 + x^{2}$ for x = 7

Do not use a calculator.

Possible Answers:

Correct answer:

Explanation:

Substitute 7 for in the expression and evaluate, paying attention to the order of operations:

$-7 + x^{2}$

$= -7 + 7^{2}$

= -7 + 49

$= +\left ( 49 - 7 \right )$

=42

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Example Question #5 : Complex Operations

Evaluate:

800 - 281 + 154 - 165 + 342

Do not use a calculator.

Possible Answers:

850

166

542

Correct answer:

850

Explanation:

In the order of operations, additions and subtractions are carried out from left to right:

800 - 281 + 154 - 165 + 342

=519 + 154 - 165 + 342

=673 - 165 + 342

=508 + 342

= 850

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GED Math : Complex Operations

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #331 : Numbers And Operations

Example Question #331 : Numbers And Operations

Example Question #1 : Complex Operations

Example Question #2 : Order Of Operations

Example Question #1 : Order Of Operations

Example Question #3 : Order Of Operations

Example Question #1 : Order Of Operations

Example Question #3 : Order Of Operations

Example Question #4 : Order Of Operations

Example Question #5 : Complex Operations

All GED Math Resources

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