Order of Operations - GED Math

Card 0 of 20

Question

Evaluate:

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

Answer

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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Question

Solve:

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

Answer

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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Question

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

$a \bigstar b = a^{2}+b -7$ for all real .

Evaluate $7\bigstar8$ .

Answer

Substitute 7 for and 8 for :

$a \bigstar b = a^{2}+b -7$

$7\bigstar 8 = 7^{2}+8 -7$

By order of operations, square, then add, then subtract.

$7\bigstar 8 = 49+8 -7$

$7\bigstar 8 =57 -7$

$7\bigstar 8 =50$

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Question

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

$a \bigstar b = a+b^{2} - 9$ for all real $a\textup{ and }b$ .

Evaluate $5\bigstar 7$ .

Answer

Substitute 5 for and 7 for :

$a \bigstar b = a+b^{2} - 9$

$5 \bigstar 7 = 5+7^{2} - 9$

By order of operations, square, then add, then subtract:

$5+7^{2} - 9 = 5 + 49 - 9 = 54 - 9 = 45$

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Question

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

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

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

Answer

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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Question

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

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

Evaluate $6 \bigstar (- 6)$

Answer

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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Question

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

Answer

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.

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

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

The answer is 14.

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Question

Suppose the values of all of the variables in the expression

$a - b \div c \cdot d +e$

are known. In order to evaluate this expression, what would be the first step?

Answer

In the absence of grouping symbols, the first operations that should be carried out are exponentiations, of which there are none here.

The next operations to be carried out are the multiplications and divisions, from left to right. The division is to the left, so it is executed first.

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Question

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

Do not use a calculator.

Answer

Substitute 0.5 for and follow the order of operations:

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

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

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Question

Jeff went to the casino with $1,000 in his pocket. He lost $400 of it playing blackjack, won $900 playing craps, then left the casino. How much money did he leave with?

Do not use a calculator.

Answer

A loss is a subtraction; a win is an addition. Jeff leaves the casino with

.

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Question

In order to calculate

$250 - 200 \div \left (6+4 \right )^{2}$

what step must you take first?

Answer

By the order of operations, the operation(s) within grouping symbols - here, the addition of six and four - must be carried out first.

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Question

In order to calculate

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

what step must you take first?

Answer

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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Question

Evaluate for . Do NOT use a calculator.

Answer

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

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

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Question

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

Do not use a calculator.

Answer

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

$-7 + x^{2}$

$= -7 + 7^{2}$

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

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Question

Evaluate:

Do not use a calculator.

Answer

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

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Question

Evaluate:

$10,000 \div 200 \times 8 \div 4 \times 2$

Do not use a calculator.

Answer

In the order of operations, multiplications and divisions have equal rank and, collectively, are carried out from left to right, as follows:

$10,000 \div 200 \times 8 \div 4 \times 2$

$=50 \times 8 \div 4 \times 2$

$=400 \div 4 \times 2$

$=100 \times 2$

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Question

Which of the following operations might yield a negative result?

Answer

The square of a positive number, as the product of two positive factors, must be positive.

Adding the square of a positive number to a positive number is adding two positive numbers; the sum must be positive. The same happens when multiplying and dividing; in both cases, both numbers are positive and the result must be positive.

Subtracting the square of a positive number from a positive number can yield a negative result. For example:

$5 - 4^{2} = 5 - 16 = -11$

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Question

Solve:

Answer

Simplify the parentheses first. Notice that there is an exponent in the first parentheses.

The expression becomes:

Simplify the terms inside the parentheses by subtraction.

Multiply the terms.

The answer is:

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Question

Simplify:

Answer

Evaluate the terms of the inner parentheses.

The inner parentheses become:

Replace the terms.

The answer is:

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Question

Solve:

Answer

Simplify by distributing the coefficient through the binomial.

Distribute the negative through the second binomial.

Combine the terms.

The answer is:

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