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Algebra 1 : Real Numbers

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Example Questions

Example Question #81 : Integer Operations

Evaluate: $\frac{7^{2} + (-7)^{3} + (-7)^{4}}{7}$

Possible Answers:

301

238

350

399

287

Correct answer:

301

Explanation:

$\frac{7^{2} + (-7)^{3} + (-7)^{4}}{7} =\frac{49 + (-343)+ 2401}{7} = \frac{2107}{7} = 301$

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Example Question #82 : Integer Operations

Solve

$\left ( \frac{3}{4} \right)^{3}\times \left (\frac{2}{9}\right)^{2}$

Possible Answers:

$\frac{3}{144}$

$\frac{1}{48}$

$\frac{9}{432}$

$\frac{108}{5184}$

$\frac{18}{864}$

Correct answer:

$\frac{1}{48}$

Explanation:

First, distribute the exponents to the numerators and denominators:

$\frac{3^{3}}{4^{3}}\times\frac{2^{2}}{9^{2}}$ .

Then, rewrite the problem in expanded form:

$\frac{3\cdot3\cdot3}{4\cdot4\cdot4}\times\frac{2\cdot2}{9\cdot9}$

Next, rewrite the problem so that you only have prime factors in both numerators and denominators:

$\frac{3\cdot3\cdot3}{2\cdot2\cdot2\cdot2\cdot2\cdot2}\times\frac{2\cdot2}{3\cdot3\cdot3\cdot3}$ .

Last, simplify by "canceling out" like terms, leaving you with

$\frac{1}{2\cdot2\cdot2\cdot2}\times\frac{1}{3}$

and multiply across both numerators and denominators, which will give you $\frac{1}{48}$ .

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Example Question #83 : Integer Operations

$\sqrt2 \times \sqrt18$

Possible Answers:

$\sqrt20$

$2\sqrt18$

Correct answer:

Explanation:

$\fn_cm When\; multiplying \; radicals, \; multiply \; the \; numbers \; under \; the \; radical\; and \; keep\; the\; radical.$

$\: \sqrt2 \times \sqrt18 = \sqrt36 = 6$

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Example Question #84 : Integer Operations

Multiply and express the product in scientific notation:

$\left (5 \times 10^{20} \right ) \left (8\times 10^{9} \right )$

Possible Answers:

$40 \times 10^{30}$

$4 \times 10^{30}$

$40 \times 10^{29}$

$4 \times 10^{181}$

$40 \times 10^{180}$

Correct answer:

$4 \times 10^{30}$

Explanation:

Use your power properties to multiply these numbers.

$\left (5 \times 10^{20} \right ) \left (8\times 10^{9} \right )$

$=\left (5 \cdot 8 \right )\times \left (10^{20} \cdot 10^{9} \right )$

$=40 \times 10^{20+9}$

$=40 \times 10^{29}$

This is not in scientific notation, so adjust as follows:

$40 \times 10^{29}$

$=4 \times 10^{1} \times 10^{29}$

$=4 \times 10^{1+29}$

$=4 \times 10^{30}$

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Example Question #85 : Real Numbers

Multiply and express the product in scientific notation:

$\left (9.2 \times 10^{12} \right ) \left (1.5\times 10^{12} \right )$

Possible Answers:

$13.8 \times 10^{24}$

$1.38 \times 10^{25}$

$1.38 \times 10^{24}$

$0.138 \times 10^{26}$

$0.138 \times 10^{25}$

Correct answer:

$1.38 \times 10^{25}$

Explanation:

Use your power properties to multiply these numbers.

$\left (9.2 \times 10^{12} \right ) \left (1.5\times 10^{12} \right )$

$=\left (9.2 \cdot 1.5 \right )\times \left (10^{12} \cdot 10^{12} \right )$

$=13.8 \times 10^{12+12}$

$=13.8 \times 10^{24}$

This is not in scientific notation, so adjust as follows:

$13.8 \times 10^{24}$

$=1.38 \times 10^{1} \times 10^{24}$

$=1.38 \times 10^{1+24}$

$=1.38 \times 10^{25}$

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Example Question #83 : Integer Operations

Rewrite as a number in base ten: $243_{\textrm{five}}$

Possible Answers:

Correct answer:

Explanation:

$243_{\textrm{five}}$

$= 2 \cdot 5^{2} + 4 \cdot 5^{1 } + 3$

$= 2 \cdot 25 + 4 \cdot 5 + 3$

= 50 +20+3 = 73

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Example Question #87 : Real Numbers

Rewrite as a number in base ten: $231_{\textrm{six}}$

Possible Answers:

Correct answer:

Explanation:

$231_{\textrm{six}}$

$= 2 \cdot 6^{2} + 3 \cdot 6^{1} + 1$

$= 2 \cdot 36 + 3 \cdot 6 + 1$

= 72+ 18+ 1 =91

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Example Question #88 : Real Numbers

Simplify the following:

4+5*10^2-5

Possible Answers:

499

8095

104

2499

Correct answer:

499

Explanation:

In this problem, you need to use the proper order of operations to find the correct answer: PEMDAS (Parentheses, Exponents, Multiplication-Division, Addition-Subtraction).

Exponents show up first in this problem, so the first step is to simplify:

10^2 = 100

This results in:

4+5*100-5

The next step is the multiplication:

5*100=500

This results in:

4+500-5

The next step is to do the remaining addition and subtraction from left to right.

4+500-5=499

499 is your final answer.

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Example Question #1 : Mathematical Relationships

Evaluate the expression.

$\small (3+4)^2+(\frac{3+5}{2})+6\div 2$

Possible Answers:

Correct answer:

Explanation:

Follow the correct order of operations: parenthenses, exponents, multiplication, division, addition, subtraction.

$\small (3+4)^2+(\frac{3+5}{2})+6\div 2$

First, evaluate any terms in parenthesis.

$(7)^2+(\frac{8}{2})+6\div 2$

$7^2+4+6\div 2$

Next, evaluate the exponent.

$\small 49+4+6\div2$

Divide.

$\small 49+4+3$

Finally, add.

$\small 49+4+3=56$

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Example Question #11 : Proportionalities

The quantity x varies directly with y. If x is 26 when y is 100, find x when y is 200.

Possible Answers:

104

6.5

Correct answer:

Explanation:

We must set up a proportion. Since x varies directly with y, when y is multiplied by 2, x is also multiplied by 2. 26 times 2 is 52.

Direct variation: $\frac{x_1}{x_2}=\frac{y_1}{y_2}$

$\frac{26}{x_2}=\frac{100}{200}$

$\frac{26}{x_2}=\frac{1}{2}$

x_2=2(26)=52

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Algebra 1 : Real Numbers

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #81 : Integer Operations

Example Question #82 : Integer Operations

Example Question #83 : Integer Operations

Example Question #84 : Integer Operations

Example Question #85 : Real Numbers

Example Question #83 : Integer Operations

Example Question #87 : Real Numbers

Example Question #88 : Real Numbers

Example Question #1 : Mathematical Relationships

Example Question #11 : Proportionalities

All Algebra 1 Resources

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