Algebra 1 : Real Numbers

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #51 : Real Numbers

Find the difference between 644 and 134.

Possible Answers:

Correct answer:

Explanation:

Find the difference between 644 and 134.

Recall that difference is a clue to use subtraction. So, we need to find the following:

We can break it down one place value at a time:

Ones:

Tens:

Hundreds:

So our answer is 510

Example Question #25 : How To Subtract Integers

Subtract:  

Possible Answers:

Correct answer:

Explanation:

The ones digits currently cannot be subtracted.  One must borrowed from the tens place of .

Subtract 16 and 7.

This is the ones place of the final answer.

Subtract the tens digits.  Remember that since we borrowed a one, the eight becomes a seven.

Combine the tens and ones digit.

The answer is:  

Example Question #26 : How To Subtract Integers

Subtract .

Possible Answers:

Correct answer:

Explanation:

Subtract the ones place.

Since the five in the tens place cannot subtract the seven, borrow a one from the hundreds place.  Subtract the two numbers.

Combine the two numbers.

The answer is .

Example Question #27 : How To Subtract Integers

Subtract:  

Possible Answers:

Correct answer:

Explanation:

Borrow a one from the tens digit in order to subtract the ones digits.  The tens digit become an 8.

Subtract to find the ones digit.

Subtract the tens digits.  

The answer is:  

Example Question #4 : Operations In Expressions

When evaluating the expression 

,

which of the five operations must be carried out third?

Possible Answers:

Division

Squaring

Addition

Subtraction

Multiplication

Correct answer:

Squaring

Explanation:

By the order of operations, any operations within parentheses must be carried out first; there are two here, the addition and the subtraction. After this is done, the exponent, or squaring, must be worked before the other operations. Squaring, the third operation, is therefore the correct answer.

Example Question #3 : Order Of Operations And Pemdas

When evaluating the expression 

,

in which order must you work the three operations?

Possible Answers:

Subtraction, multiplication, cubing

Subtraction, cubing, multiplication

Cubing, multiplication, subtraction

Cubing, subtraction, multiplication

Multiplication, cubing, subtraction

Correct answer:

Cubing, multiplication, subtraction

Explanation:

By the order of operations, in the absence of grouping symbols, the exponent (represented here by cubing) must be worked first. The multiplication must be worked second, followed by the subtraction.

Example Question #28 : How To Subtract Integers

Subtract the following integers:  

Possible Answers:

Correct answer:

Explanation:

In order to subtract these numbers, we will need to subtract 36 from 59, and then add a negative sign in front.

Solve .

Subtract the ones digits.

Subtract the tens digits.

Combine the numbers and add a negative sign in front.

The answer is: 

Example Question #52 : Real Numbers

Subtract:  

Possible Answers:

Correct answer:

Explanation:

Subtract the ones digits.

Since we cannot subtract the tens digits, borrow a one from the hundreds digit.

Subtract.

The hundreds digits are zero.

The answer is:  

Example Question #53 : Real Numbers

Subtract the following integers:  

Possible Answers:

Correct answer:

Explanation:

Subtract the ones digits.

Subtract the tens digits.   Notice that the three cannot subtract seven.  Borrow a one from the hundreds digit of .

Now we can subtract to obtain the tens digit.

The hundreds digit will become a one.  The hundreds digit of  is zero.

The answer is:  

Example Question #54 : Real Numbers

Subtract:

Possible Answers:

Correct answer:

Explanation:

Borrow a one from the tens digit of the first number. Then subtract the ones digits.

This is the ones digit of the final answer.

The tens place of  becomes an eight since the number was borrowed.

Subtract the tens digits.

This is the tens digit of the final answer.

The final answer is:

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