Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #2281 : Mathematical Relationships And Basic Graphs

Add the following numbers:  \(\displaystyle 419+841+542\)

Possible Answers:

\(\displaystyle 1820\)

\(\displaystyle 1702\)

\(\displaystyle 1792\)

\(\displaystyle 1798\)

\(\displaystyle 1802\)

Correct answer:

\(\displaystyle 1802\)

Explanation:

Add the ones digits.

\(\displaystyle 9+1+2 =12\)

The carryover is the tens place.

Add the tens digits.

\(\displaystyle 1+4+4+(1) = 10\)

The carryover for the next calculation is the tens place.

\(\displaystyle 4+8+5+(1) = 18\)

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

The answer is:  \(\displaystyle 1802\)

Example Question #2282 : Mathematical Relationships And Basic Graphs

Add the following numbers:  \(\displaystyle 1264+9811\)

Possible Answers:

\(\displaystyle 11075\)

\(\displaystyle 9895\)

\(\displaystyle 9975\)

\(\displaystyle 12075\)

\(\displaystyle 10075\)

Correct answer:

\(\displaystyle 11075\)

Explanation:

Add the ones digits.

\(\displaystyle 4+1=5\)

There is no carryover.

Add the tens digits.

\(\displaystyle 6+1=7\)

There is also no carryover.

Add the hundreds digits.

\(\displaystyle 2+8 = 10\)

The carryover is the tens digit.

Add the thousands digits with the carryover.

\(\displaystyle 1+9+(1) = 11\)

Combine this value with the ones digits of the previous calculations.

The answer is:  \(\displaystyle 11075\)

Example Question #2291 : Mathematical Relationships And Basic Graphs

Add the numbers:  \(\displaystyle 879+654\)

Possible Answers:

\(\displaystyle 1533\)

\(\displaystyle 1553\)

\(\displaystyle 1323\)

\(\displaystyle 1443\)

\(\displaystyle 1423\)

Correct answer:

\(\displaystyle 1533\)

Explanation:

Add the ones digits.

\(\displaystyle 9+4 = 13\)

The carryover is the tens digit.

Add the tens digits with the carryover.

\(\displaystyle 7+5+(1) =13\)

The carryover is the tens digit.

\(\displaystyle 8+6+(1) =15\)

Combine this value with the one digits of the previous calculations.

The answer is:  \(\displaystyle 1533\)

Example Question #2292 : Mathematical Relationships And Basic Graphs

Add the following numbers:  \(\displaystyle 318+219+797\)

Possible Answers:

\(\displaystyle 1324\)

\(\displaystyle \textup{The answer is not given.}\)

\(\displaystyle 1334\)

\(\displaystyle 1224\)

\(\displaystyle 1234\)

Correct answer:

\(\displaystyle 1334\)

Explanation:

Add the ones digits.

\(\displaystyle 8+9+7 = 24\)

Carry over the tens digit to the next calculation.

Add the tens digits with the carryover.

\(\displaystyle 1+1+9+(2) = 13\)

Repeat the process for the hundreds digits.

\(\displaystyle 3+2+7+(1) = 13\)

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

The answer is:  \(\displaystyle 1334\)

Example Question #2293 : Mathematical Relationships And Basic Graphs

Add the following numbers:  \(\displaystyle 49+81+79+24+99\)

Possible Answers:

\(\displaystyle 292\)

\(\displaystyle \textup{The answer is not given.}\)

\(\displaystyle 332\)

\(\displaystyle 342\)

\(\displaystyle 322\)

Correct answer:

\(\displaystyle 332\)

Explanation:

Add the ones digits.

\(\displaystyle 9+1+9+4+9 = 32\)

Add the tens digit with the carryover, 3.

\(\displaystyle 4+8+7+2+9+(3) = 33\)

Combine this number with the ones digit of the first number.

The answer is:  \(\displaystyle 332\)

Example Question #2294 : Mathematical Relationships And Basic Graphs

Subtract the following numbers:  \(\displaystyle 95-15-85-87-31\)

Possible Answers:

\(\displaystyle -96\)

\(\displaystyle -37\)

\(\displaystyle -103\)

\(\displaystyle -123\)

\(\displaystyle \textup{The answer is not given.}\)

Correct answer:

\(\displaystyle -123\)

Explanation:

We cannot subtract the numbers like how we can easily add numbers.  As a result, we will have to subtract each number at a time and this may be time consuming.

However, in order to save calculation time, we can simply take out a common factor of negative one so that we can add all the positive terms, and then subtract. 

\(\displaystyle 95-15-85-87-31 = -1(-95+[15+85+87+31])\)

\(\displaystyle = -1(-95+[218])\)

We can then rearrange the numbers to subtract.

\(\displaystyle -1(218-95)\)

Subtract the ones digits.

\(\displaystyle 8-5 = 3\)

Borrow a one from the 2 in 218 and then subtract the tens digits.  The hundreds digit becomes a 1.

\(\displaystyle 11-9 = 2\)

Combine the hundreds digit with the other ones digits.  The expression becomes:

\(\displaystyle -1(218-95) = -1(123) = -123\)

The answer is:  \(\displaystyle -123\)

Example Question #2295 : Mathematical Relationships And Basic Graphs

Add the following numbers:  \(\displaystyle 974+316+163\)

Possible Answers:

\(\displaystyle 1253\)

\(\displaystyle 1443\)

\(\displaystyle 1543\)

\(\displaystyle 1453\)

\(\displaystyle 1553\)

Correct answer:

\(\displaystyle 1453\)

Explanation:

Add the ones digits.

\(\displaystyle 4+6+3=13\)

Add the tens digits with the one as the carryover.

\(\displaystyle 7+1+6+(1)=15\)

Add the hundreds digits with the new carryover.

\(\displaystyle 9+3+1+(1) =14\)

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

The answer is:  \(\displaystyle 1453\)

Example Question #2296 : Mathematical Relationships And Basic Graphs

Add the numbers:  \(\displaystyle 974+978+192\)

Possible Answers:

\(\displaystyle 2244\)

\(\displaystyle 2034\)

\(\displaystyle 2114\)

\(\displaystyle 2144\)

\(\displaystyle 2054\)

Correct answer:

\(\displaystyle 2144\)

Explanation:

Add the ones digits.

\(\displaystyle 4+8+2 = 14\)

Add the tens digits with the one as the carryover.

\(\displaystyle 7+7+9+(1)= 24\)

Add the hundreds digits with the two as the carryover.

\(\displaystyle 9+9+1+(2) = 21\)

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

The answer is:  \(\displaystyle 2144\)

Example Question #81 : Addition And Subtraction

Add the following:  \(\displaystyle 644+494+911\)

Possible Answers:

\(\displaystyle 2039\)

\(\displaystyle \textup{The answer is not given.}\)

\(\displaystyle 2049\)

\(\displaystyle 1949\)

\(\displaystyle 2029\)

Correct answer:

\(\displaystyle 2049\)

Explanation:

Add the ones digits.

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

Add the tens digits.  There is no carryover.

\(\displaystyle 4+9+1 = 14\)

Add the hundreds digits.   The carryover is 1.

\(\displaystyle 6+4+9+(1) = 20\)

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

The answer is:  \(\displaystyle 2049\)

Example Question #2298 : Mathematical Relationships And Basic Graphs

Add the following numbers:  \(\displaystyle 856+196+877\)

Possible Answers:

\(\displaystyle \textup{The answer is not given.}\)

\(\displaystyle 1829\)

\(\displaystyle 1819\)

\(\displaystyle 1929\)

\(\displaystyle 1939\)

Correct answer:

\(\displaystyle 1929\)

Explanation:

Add the ones digits.

\(\displaystyle 6+6+7 = 19\)

Add the tens digits with the 1 as the carryover.

Add the tens digits.

\(\displaystyle 5+9+7+(1) = 22\)

Add the hundreds digits with the 2 as the carryover.

\(\displaystyle 8+1+8+(2) = 19\)

Combine this value with the ones digits of the first two calculations.

The answer is:  \(\displaystyle 1929\)

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