| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
What is \( \frac{2}{3} \) - \( \frac{7}{9} \)?
| \( \frac{4}{11} \) | |
| \( \frac{4}{13} \) | |
| 1 \( \frac{7}{12} \) | |
| -\(\frac{1}{9}\) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{2 x 3}{3 x 3} \) - \( \frac{7 x 1}{9 x 1} \)
\( \frac{6}{9} \) - \( \frac{7}{9} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{6 - 7}{9} \) = \( \frac{-1}{9} \) = -\(\frac{1}{9}\)
Cooks are needed to prepare for a large party. Each cook can bake either 2 large cakes or 17 small cakes per hour. The kitchen is available for 4 hours and 37 large cakes and 180 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?
| 8 | |
| 13 | |
| 6 | |
| 12 |
If a single cook can bake 2 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 2 x 4 = 8 large cakes during that time. 37 large cakes are needed for the party so \( \frac{37}{8} \) = 4\(\frac{5}{8}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 17 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 17 x 4 = 68 small cakes during that time. 180 small cakes are needed for the party so \( \frac{180}{68} \) = 2\(\frac{11}{17}\) 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 5 + 3 = 8 cooks.
How many 11-passenger vans will it take to drive all 93 members of the football team to an away game?
| 4 vans | |
| 16 vans | |
| 9 vans | |
| 7 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{93}{11} \) = 8\(\frac{5}{11}\)
So, it will take 8 full vans and one partially full van to transport the entire team making a total of 9 vans.
Frank loaned Charlie $1,300 at an annual interest rate of 6%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $45 | |
| $78 | |
| $28 | |
| $88 |
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 $1,300
i = 0.06 x $1,300
i = $78
If a mayor is elected with 54% of the votes cast and 30% of a town's 44,000 voters cast a vote, how many votes did the mayor receive?
| 8,052 | |
| 7,128 | |
| 6,996 | |
| 10,032 |
If 30% of the town's 44,000 voters cast ballots the number of votes cast is:
(\( \frac{30}{100} \)) x 44,000 = \( \frac{1,320,000}{100} \) = 13,200
The mayor got 54% of the votes cast which is:
(\( \frac{54}{100} \)) x 13,200 = \( \frac{712,800}{100} \) = 7,128 votes.