| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.97 |
| Score | 0% | 59% |
What is \( \frac{8}{2} \) - \( \frac{7}{4} \)?
| \( \frac{9}{14} \) | |
| 1 \( \frac{2}{8} \) | |
| 2\(\frac{1}{4}\) | |
| \( \frac{1}{4} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 2}{2 x 2} \) - \( \frac{7 x 1}{4 x 1} \)
\( \frac{16}{4} \) - \( \frac{7}{4} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{16 - 7}{4} \) = \( \frac{9}{4} \) = 2\(\frac{1}{4}\)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 20% off." If Roger buys two shirts, each with a regular price of $37, how much will he pay for both shirts?
| $66.60 | |
| $29.60 | |
| $53.65 | |
| $40.70 |
By buying two shirts, Roger will save $37 x \( \frac{20}{100} \) = \( \frac{$37 x 20}{100} \) = \( \frac{$740}{100} \) = $7.40 on the second shirt.
So, his total cost will be
$37.00 + ($37.00 - $7.40)
$37.00 + $29.60
$66.60
Convert x-5 to remove the negative exponent.
| \( \frac{-1}{-5x^{5}} \) | |
| \( \frac{1}{x^5} \) | |
| \( \frac{1}{x^{-5}} \) | |
| \( \frac{-5}{x} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 20 small cakes per hour. The kitchen is available for 3 hours and 22 large cakes and 260 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 14 | |
| 13 | |
| 11 | |
| 8 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 3 x 3 = 9 large cakes during that time. 22 large cakes are needed for the party so \( \frac{22}{9} \) = 2\(\frac{4}{9}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 20 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 20 x 3 = 60 small cakes during that time. 260 small cakes are needed for the party so \( \frac{260}{60} \) = 4\(\frac{1}{3}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 5 = 8 cooks.
Alex loaned Diane $400 at an annual interest rate of 6%. If no payments are made, what is the total amount owed at the end of the first year?
| $412 | |
| $404 | |
| $432 | |
| $424 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $400
i = 0.06 x $400
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $400 + $24