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GED Math : Complex Operations

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Example Questions

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Example Question #31 : Order Of Operations

Simplify:

$(7-3)^2+9\div 3 \times 2-1$

Possible Answers:

16.5

Correct answer:

Explanation:

Make sure to follow the order of operations.

Start by simplifying anything found within parentheses.

$(7-3)^2+9\div 3 \times 2-1$

$=(4)^2+9\div 3 \times 2-1$

Next, take care of exponents.

$=16+9\div 3 \times 2-1$

Then, multiply and divide.

=16+6-1

Finally, add and subtract.

=21

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Example Question #31 : Order Of Operations

Simplify the following expression:

$(4-6)^2\times3+2\times 1+(9\div 3)$

Possible Answers:

Correct answer:

Explanation:

Recall the order of operations. Simplify the parenthetical terms first.

$(4-6)^2\times3+2\times 1+(9\div 3)=(-2)^2\times3+2\times 1+(3)$

Next, tackle the exponents.

$(-2)^2\times3+2\times 1+(3)=4\times3+2\times 1+(3)$

Then, multiply and divide where needed.

$4\times3+2\times 1+(3)=12+2+3$

Finally, add.

12+2+3=17

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Example Question #33 : Order Of Operations

Solve

$(1+2)\cdot3-4^2=?$

Possible Answers:

Correct answer:

Explanation:

Recall our order of operations, PEMDAS:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

So for our equation, let's do the parenthesis first

$(1+2)\cdot3-4^2=?$

$(3)\cdot3-4^2=?$

Now exponents

$(3)\cdot3-16=?$

Now multiplication

9-16=?

No division, no addition, so let's do subtraction

-7=?

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Example Question #31 : Complex Operations

Compute: 2^3+(4-2*5)+(-3)^2+(4)^2

Possible Answers:

Correct answer:

Explanation:

Use PEMDAS:

Parentheses, Exponents, Multiply, Divide, Add, Subtract

2^3+(4-2*5)+(-3)^2+(4)^2

Start with the parentheses:

2^3+(4-10)+(-3)^2+4^2

More parentheses:

2^3+(-6)+(-3)^2+16

Exponents:

8+(-6)+9+16

Add/Subtract:

$8-6+9+16\rightarrow 2+25=27$

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Example Question #1 : Proportions And Percentages

At a party, there are 7 women with blonde hair, 9 women with brown hair, and 5 women with red hair. What is the proportion of women with blonde hair?

Possible Answers:

$\small \frac{1}{2}$

$\small \frac{1}{3}$

$\small \frac{7}{9}$

$\small \frac{7}{5}$

Correct answer:

$\small \frac{1}{3}$

Explanation:

A proprotion is the number of a specific event (blonde women) divided by the total number of events (total number of women).

$\small \frac{7}{7+9+5}=\frac{7}{21}=\frac{1}{3}$

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Example Question #1 : Proportions And Percentages

Solve:

$14\%\ of\ 52=$

Possible Answers:

7.28

371.43

45.61

59.28

Correct answer:

7.28

Explanation:

$\small 14\%\ of \ 52=0.14\times 52=7.28$

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Example Question #1 : Proportions And Percentages

Solve:

$\small 23\%\ of\ 73=$

Possible Answers:

$\small 317.4$

$\small 59.3$

$\small 96$

$\small 16.8$

Correct answer:

$\small 16.8$

Explanation:

$\small 23\%\ of\ 73=0.23\times73=16.8$

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Example Question #1 : Proportions And Percentages

A bag contains $\small 7$ green marbles, $\small 2$ red marbles, and $\small 5$ blue marbles. What is the proportion of red marbles?

Possible Answers:

$\small \frac{1}{7}$

$\small \frac{2}{7}$

$\small \frac{2}{5}$

$\small \frac{1}{6}$

Correct answer:

$\small \frac{1}{7}$

Explanation:

The proportion is equal to the number of specific events (red marbles) divided by the total number of events (sum of all colors).

$\small P=\frac{2}{7+2+5}=\frac{2}{14}=\frac{1}{7}$

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Example Question #1 : Proportions And Percentages

What is $17\%$ of ?

Possible Answers:

199.6

170.6

4.9

33.9

Correct answer:

4.9

Explanation:

$17\%\ of\ 29=0.17\times 29=4.9$

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Example Question #1 : Proportions And Percentages

Sherry deposits $3,000 at 6% simple interest per year. How much will she have in this account after three years, assuming she does not make any withdrawals or deposits?

Possible Answers:

$\$3,054$

$\$3,540$

$\$3,180$

$\$3,018$

Correct answer:

$\$3,540$

Explanation:

Use the simple interest formula

I = Prt

with P = 3,000, r = 0.06, t = 3 :

$I = \$ 3,000 \cdot 0.06 \cdot 3 = \$540$

This is the simple interest earned. Add it to the original principal:

$\$ 3,000+\$540 = \$3,540$

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All GED Math Resources

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GED Math : Complex Operations

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #31 : Order Of Operations

Example Question #31 : Order Of Operations

Example Question #33 : Order Of Operations

Example Question #31 : Complex Operations

Example Question #1 : Proportions And Percentages

Example Question #1 : Proportions And Percentages

Example Question #1 : Proportions And Percentages

Example Question #1 : Proportions And Percentages

Example Question #1 : Proportions And Percentages

Example Question #1 : Proportions And Percentages

All GED Math Resources

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