| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.94 |
| Score | 0% | 59% |
What is \( \frac{2}{6} \) + \( \frac{8}{14} \)?
| \( \frac{3}{42} \) | |
| \(\frac{19}{21}\) | |
| \( \frac{5}{8} \) | |
| \( \frac{7}{42} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{2 x 7}{6 x 7} \) + \( \frac{8 x 3}{14 x 3} \)
\( \frac{14}{42} \) + \( \frac{24}{42} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{14 + 24}{42} \) = \( \frac{38}{42} \) = \(\frac{19}{21}\)
Which of the following is an improper fraction?
\(1 {2 \over 5} \) |
|
\({2 \over 5} \) |
|
\({a \over 5} \) |
|
\({7 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
What is \( 3 \)\( \sqrt{75} \) + \( 9 \)\( \sqrt{3} \)
| 27\( \sqrt{225} \) | |
| 12\( \sqrt{3} \) | |
| 27\( \sqrt{75} \) | |
| 24\( \sqrt{3} \) |
To add these radicals together their radicands must be the same:
3\( \sqrt{75} \) + 9\( \sqrt{3} \)
3\( \sqrt{25 \times 3} \) + 9\( \sqrt{3} \)
3\( \sqrt{5^2 \times 3} \) + 9\( \sqrt{3} \)
(3)(5)\( \sqrt{3} \) + 9\( \sqrt{3} \)
15\( \sqrt{3} \) + 9\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
15\( \sqrt{3} \) + 9\( \sqrt{3} \)Which of these numbers is a factor of 28?
| 8 | |
| 29 | |
| 30 | |
| 7 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 28 are 1, 2, 4, 7, 14, 28.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 45% off." If Ezra buys two shirts, each with a regular price of $13, how much will he pay for both shirts?
| $18.85 | |
| $5.85 | |
| $14.95 | |
| $20.15 |
By buying two shirts, Ezra will save $13 x \( \frac{45}{100} \) = \( \frac{$13 x 45}{100} \) = \( \frac{$585}{100} \) = $5.85 on the second shirt.
So, his total cost will be
$13.00 + ($13.00 - $5.85)
$13.00 + $7.15
$20.15