- What is the difference between 3.8 and 0.571?
- 0.73
- 2.567
- 3.229
- 4.262
The word difference signifies a subtraction problem. When subtracting decimals, align the decimals vertically:
- What is 2.567 rounded to the nearest hundredth?
- 2.6
- 3.0
- 2.56
- 2.57
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.
- Dividing a number by 2 is the same as multiplying that number by…
- 2
- 1
- 0.25
- 0.5
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.
- Arrange the following numbers in order from the least to greatest:
- 23, 42, 60, 9, 101
- 60, 9, 101, 23, 42
- 101, 23, 60, 9, 42
- 60, 23, 9, 101, 42
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:
- \(9=9\)
- \(10^1=10\)
- \(4^2=4\times 4=16\)
- If \(a = -6\) and \(b = 7\), then \(4a (3b+5) + 2b =\) ?
- -610
- 610
- 624
- -638
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:
\(= -610\)
- If one person consumes eight glasses of water on a daily basis, how many glasses of water will 18 people consume?
- 26
- 64
- 128
- 144
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:
\(8 \times 18 = 144\)
- A person weighs 145 pounds. They gain 12 pounds one month and six pounds the next month. What is their new weight?
- 151 pounds
- 163 pounds
- 167 pounds
- 173 pounds
To calculate their new weight, add their weight increases to their original weight:
\(145 \text{ lb} + 12 \text{ lb} + 6 \text{ lb} = 163 \text{ lb}\)
- Expand the following expression:
- \(10x^2-80x-200\)
- \(70x-200\)
- \(10x^2-80x+200\)
- \(10x^2-120x-200\)
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:
\(10x^2 – 80x – 200\)
- For what real number \(x\) is it true that \(3(2x – 10) = x\) ?
- 5
- 6
- -5
- -6
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 \(x = 6\).
- Owen is three times as old as Lacy. Two years ago, Owen was five times as old as Lacy. How old is Owen now? ?
- 4
- 8
- 12
- 16
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.