Basic Operations Practice Questions 2

  1. What is the difference between 3.8 and 0.571?
  1. 0.73
  2. 2.567
  3. 3.229
  4. 4.262
Show Answer
The correct answer is C!

The word difference signifies a subtraction problem. When subtracting decimals, align the decimals vertically:

 

  1. What is 2.567 rounded to the nearest hundredth?
  1. 2.6
  2. 3.0
  3. 2.56
  4. 2.57
Show Answer
The correct answer is D!

Look at the digit in the thousandths place. In this case, it is a 7. Since the number is 5 or greater, round up the digit in the hundredths place to get 2.57.

 

  1. Dividing a number by 2 is the same as multiplying that number by…
  1. 2
  2. 1
  3. 0.25
  4. 0.5
Show Answer
The correct answer is D!

Division is the opposite, or the reciprocal, of multiplication. If you divide a number by 2, you have to multiply it by \(\tfrac{1}{2}\) (0.5) to get the same result.

 

  1. Arrange the following numbers in order from the least to greatest:
23, 42, 60, 9, 101
  1. 23, 42, 60, 9, 101
  2. 60, 9, 101, 23, 42
  3. 101, 23, 60, 9, 42
  4. 60, 23, 9, 101, 42
Show Answer
The correct answer is D!

When a number is raised to a power, it is multiplied by itself as many times as the power indicates. For example:

\(2^3=2\times 2\times2=8\)

A number raised to the power of 0 is always equal to 1, so 60 is the smallest number shown. Similarly, for the other numbers:

  • \(9=9\)
  • \(10^1=10\)
  • \(4^2=4\times 4=16\)

 

  1. If \(a = -6\) and \(b = 7\), then \(4a (3b+5) + 2b =\) ?
  1. -610
  2. 610
  3. 624
  4. -638
Show Answer
The correct answer is A!

Substitute the given values for the variables into the expression:

\(4a (3b+5) + 2b\) \(= 4 \times -6 (3 \times 7 + 5) + 2 \times 7\)

Compute the expression in the parentheses first. Remember that you must first multiply 3 by 7 and then add 5 in order to follow order of operations:

\(= 4 \times -6(21 + 5) + 2 \times 7\)

Next, add the values in the parentheses.

\(= 4 \times -6(26) + 2 \times 7\)

Simplify by multiplying the numbers outside the parenthesis:

\(= -24(26) + 14\)

Multiply -24 by 26:

\(= -624 +14\)

Finally, add:

\(= -610\)

 

  1. If one person consumes eight glasses of water on a daily basis, how many glasses of water will 18 people consume?
  1. 26
  2. 64
  3. 128
  4. 144
Show Answer
The correct answer is D!

To find the total amount that will be consumed, multiply the number of glasses consumed by one person by the number of people indicated in the question:

\(8 \times 18 = 144\)

 

  1. A person weighs 145 pounds. They gain 12 pounds one month and six pounds the next month. What is their new weight?
  1. 151 pounds
  2. 163 pounds
  3. 167 pounds
  4. 173 pounds
Show Answer
The correct answer is B!

To calculate their new weight, add their weight increases to their original weight:

\(145 \text{ lb} + 12 \text{ lb} + 6 \text{ lb} = 163 \text{ lb}\)

 

  1. Expand the following expression:
\((2x – 20) (5x + 10)\)
  1. \(10x^2-80x-200\)
  2. \(70x-200\)
  3. \(10x^2-80x+200\)
  4. \(10x^2-120x-200\)
Show Answer
The correct answer is A!

Use the FOIL method (first, outside, inside, and last) to get rid of the parentheses:

\((2x – 20)(5x + 10)\) \(= 2x(5x) + 2x(10) – 20(5x) – 20(10)\) \(= 10x^2 + 20x – 100x – 200\)

Then, combine like terms to simplify the expression:

\(10x^2 – 80x – 200\)

 

  1. For what real number \(x\) is it true that \(3(2x – 10) = x\) ?
  1. 5
  2. 6
  3. -5
  4. -6
Show Answer
The correct answer is B!

To solve \(3(2x – 10) = x\), first multiply out the left side of the equation using distribution:

\(6x – 30 = x\)

After subtracting \(x\) from both sides, we have \(5x – 30 = 0\).

Finally, adding 30 to both sides results in \(5x = 30\), and therefore \(x = 6\).

 

  1. Owen is three times as old as Lacy. Two years ago, Owen was five times as old as Lacy. How old is Owen now? ?
  1. 4
  2. 8
  3. 12
  4. 16
Show Answer
The correct answer is C!

To solve this problem, first let \(h\) represent Owen’s age and let \(t\) represent Lacy’s age.

Since Owen is three times as old as Lacy, then \(h = 3t\). Note that two years ago, Owen’s and Lacy’s ages would be \(h – 2\) and \(t – 2\), respectively.

Then, since Owen was five times as old as Lacy two years ago, we have \(h – 2 = 5(t – 2)\).

By substituting \(3t\) for \(h\), we can solve the following equation:

\(3t – 2 = 5(t – 2)\)
\(3t – 2 = 5t – 10\)
\(8 = 2t\)
\(t = 4\)

So, Lacy is four years old and Owen is three times Lacy’s age, or age 12.