Algebra II : Elementary Operations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #2231 : Mathematical Relationships And Basic Graphs

Add the following numbers:  \displaystyle 1982+7189

Possible Answers:

\displaystyle 8061

\displaystyle 8171

\displaystyle 9161

\displaystyle 9171

\displaystyle 9071

Correct answer:

\displaystyle 9171

Explanation:

Add the ones digits.

\displaystyle 9+2 = 11

The tens place of this number is one, which is the carryover.

Add the tens digits with the carryover.

\displaystyle 8+8+(1)=17

The tens place of this number is also one, which is the carryover.

Add the hundreds digits with the carryover.

\displaystyle 9+1+(1) = 11

Add the thousands digits with the carryover.

\displaystyle 1+7+(1) = 9

Combine all the ones digits.

The answer is:  \displaystyle 9171

Example Question #4901 : Algebra Ii

Add the following numbers:  \displaystyle 1791+9497+9169+517

Possible Answers:

\displaystyle 19974

\displaystyle 19954

\displaystyle 20854

\displaystyle 19874

\displaystyle 20974

Correct answer:

\displaystyle 20974

Explanation:

Add the ones digits.

\displaystyle 1+7+9+7 = 24

Add the tens digits with the carryover, which is the tens place.

\displaystyle 9+9+6+1+(2)=27

Repeat the process for the hundreds digits.

\displaystyle 7+4+1+5+(2) =19

Add the thousands digits with the carryover.

\displaystyle 1+9+9+0+(1) = 20

Combine this number with the ones digits of the numbers from the previous calculation.

The answer is:  \displaystyle 20974

Example Question #4901 : Algebra Ii

Add the following numbers:  \displaystyle 236+973+389

Possible Answers:

\displaystyle 1468

\displaystyle 1698

\displaystyle 1478

\displaystyle 1598

\displaystyle 1488

Correct answer:

\displaystyle 1598

Explanation:

Add the ones digits.

\displaystyle 6+3+9 = 18

The carryover is the tens digit, one.

Add the tens digit with the carryover.

\displaystyle 3+7+8+(1) =19

The carryover is the tens digit, one.

Add the hundreds digit with the carryover.

\displaystyle 2+9+3+(1) = 15

Combine this number with the ones digits of the other two calculations.

The answer is:  \displaystyle 1598

Example Question #4902 : Algebra Ii

Add:  \displaystyle 238+574+8457+98

Possible Answers:

\displaystyle 12367

\displaystyle 8367

\displaystyle 9367

\displaystyle 12467

\displaystyle 9157

Correct answer:

\displaystyle 9367

Explanation:

Add the ones digits.

\displaystyle 8+4+7+8 = 27

The carryover is the tens digit, \displaystyle 2.

Add the tens digits with the carryover.

\displaystyle 3+7+5+9+(2) = 26

The carryover is the tens digit, \displaystyle 2.

Add the hundreds digits with the carryover.  The two digit number will have zero as the hundreds place.

\displaystyle 2+5+4+0+(2)= 13

The tens place is the carryover.

Add the thousands places with the carryover.

\displaystyle 0+0+8+0+(1)=9

The answer is:  \displaystyle 9367

Example Question #31 : Elementary Operations

Add:  \displaystyle 979+283+178

Possible Answers:

\displaystyle 1440

\displaystyle 1220

\displaystyle 1240

\displaystyle 1230

\displaystyle 1340

Correct answer:

\displaystyle 1440

Explanation:

Add the ones digits.

\displaystyle 9+3+8=20

The carryover is 2.

Add the tens digits with the carryover.

\displaystyle 7+8+7+(2)=24

The carryover is 2.

Add the hundreds digits with the carryover.

\displaystyle 9+2+1+(2)=14

Combine this number with the ones digits from the previous calculation.

The answer is:  \displaystyle 1440

Example Question #31 : Addition And Subtraction

Add the following numbers:  \displaystyle [128,92,57,93,177]

Possible Answers:

\displaystyle 547

\displaystyle 557

\displaystyle 467

\displaystyle 687

Correct answer:

\displaystyle 547

Explanation:

Write an expression to set up the problem.

\displaystyle 128+92+57+93+177

Add the ones digits.

\displaystyle 8+2+7+3+7 = 27

The carryover is tens place, which is two.

Add the tens digits.

\displaystyle 2+9+5+9+7+(2) =34

The carryover is three.

Add the hundreds places with the carryover.  The two digit numbers will have zero as the hundreds places.

\displaystyle 1+0+0+0+1+(3)=5

Combine the ones digits from each calculation.

The answer is:  \displaystyle 547

Example Question #33 : Elementary Operations

Add the following numbers:  \displaystyle 317+989+517

Possible Answers:

\displaystyle 1823

\displaystyle 1833

\displaystyle 1843

\displaystyle 1723

\displaystyle 1923

Correct answer:

\displaystyle 1823

Explanation:

Add the ones digits.

\displaystyle 7+9+7 = 23

The two is the carryover.

Add the tens digits with the carryover.

\displaystyle 1+8+1+(2) = 12

The one is the carryover.

Add the hundreds digits with the carryover.

\displaystyle 3+9+5+(1) = 18

Combine this number with the ones digits of the previous numbers.

The answer is:  \displaystyle 1823

Example Question #4906 : Algebra Ii

Subtract the following numbers:  \displaystyle 973-236

Possible Answers:

\displaystyle 637

\displaystyle 737

\displaystyle 757

\displaystyle 687

\displaystyle 747

Correct answer:

\displaystyle 737

Explanation:

Subtract the first two numbers by initially focusing on the ones digits.

\displaystyle 973-236

Borrow a one from the tens place of the first number to subtract the ones digits.  The tens place becomes a six.

\displaystyle 13-6=7

Subtract the tens place.

\displaystyle 6-3=3

Subtract the hundreds digits.  There's no need to borrow a one.

\displaystyle 9-2 = 7

Combine the numbers from hundreds place to the ones place.

The answer is:  \displaystyle 737

Example Question #31 : Elementary Operations

Add the fractions:  \displaystyle \frac{1}{5}+\frac{11}{25}

Possible Answers:

\displaystyle \frac{8}{25}

\displaystyle \frac{4}{5}

\displaystyle \frac{2}{5}

\displaystyle \frac{16}{25}

\displaystyle \frac{12}{25}

Correct answer:

\displaystyle \frac{16}{25}

Explanation:

In order to add the fractions, we will need to convert the first fraction with least common denominator of 25.

Multiply the top and bottom of this fraction by five.

\displaystyle \frac{1}{5}+\frac{11}{25} = \frac{1(5)}{5(5)}+\frac{11}{25} = \frac{5}{25}+\frac{11}{25}

Add the numerators.  The denominators will stay the same.

The answer is:  \displaystyle \frac{16}{25}

Example Question #4908 : Algebra Ii

Sum the numbers:  \displaystyle 296+344+187+92

Possible Answers:

\displaystyle 899

\displaystyle 819

\displaystyle 1029

\displaystyle 909

\displaystyle 919

Correct answer:

\displaystyle 919

Explanation:

Add the ones digits.

\displaystyle 6+4+7+2= 19

The carry over is the tens digit of this number.

Add the tens digits with the carryover.

\displaystyle 9+4+8+9+(1) = 31

The carry over for the next calculation is the tens digit of this number.

Add the hundreds digits with the carry over.

\displaystyle 2+3+1+0+(3) = 9

Combine the numbers.

The answer is:  \displaystyle 919

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