| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
Which of the following is an improper fraction?
\({2 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
|
\({7 \over 5} \) |
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.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 70% larger than the original. By what percentage has the area of the logo increased?
| 30% | |
| 20% | |
| 35% | |
| 32\(\frac{1}{2}\)% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 70% the radius (and, consequently, the total area) increases by \( \frac{70\text{%}}{2} \) = 35%
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 40% off." If Roger buys two shirts, each with a regular price of $11, how much will he pay for both shirts?
| $4.40 | |
| $6.60 | |
| $12.10 | |
| $17.60 |
By buying two shirts, Roger will save $11 x \( \frac{40}{100} \) = \( \frac{$11 x 40}{100} \) = \( \frac{$440}{100} \) = $4.40 on the second shirt.
So, his total cost will be
$11.00 + ($11.00 - $4.40)
$11.00 + $6.60
$17.60
Which of the following is a mixed number?
\(1 {2 \over 5} \) |
|
\({7 \over 5} \) |
|
\({5 \over 7} \) |
|
\({a \over 5} \) |
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 \( 6 \)\( \sqrt{125} \) - \( 6 \)\( \sqrt{5} \)
| 36\( \sqrt{5} \) | |
| 36\( \sqrt{25} \) | |
| 24\( \sqrt{5} \) | |
| 0\( \sqrt{125} \) |
To subtract these radicals together their radicands must be the same:
6\( \sqrt{125} \) - 6\( \sqrt{5} \)
6\( \sqrt{25 \times 5} \) - 6\( \sqrt{5} \)
6\( \sqrt{5^2 \times 5} \) - 6\( \sqrt{5} \)
(6)(5)\( \sqrt{5} \) - 6\( \sqrt{5} \)
30\( \sqrt{5} \) - 6\( \sqrt{5} \)
Now that the radicands are identical, you can subtract them:
30\( \sqrt{5} \) - 6\( \sqrt{5} \)