| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.78 |
| Score | 0% | 76% |
How many 10-passenger vans will it take to drive all 95 members of the football team to an away game?
| 5 vans | |
| 7 vans | |
| 10 vans | |
| 8 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{95}{10} \) = 9\(\frac{1}{2}\)
So, it will take 9 full vans and one partially full van to transport the entire team making a total of 10 vans.
What is the next number in this sequence: 1, 10, 19, 28, 37, __________ ?
| 38 | |
| 48 | |
| 50 | |
| 46 |
The equation for this sequence is:
an = an-1 + 9
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 9
a6 = 37 + 9
a6 = 46
What is the distance in miles of a trip that takes 3 hours at an average speed of 75 miles per hour?
| 495 miles | |
| 140 miles | |
| 225 miles | |
| 180 miles |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 75mph \times 3h \)
225 miles
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
commutative |
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PEDMAS |
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associative |
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distributive |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
What is \( \frac{6}{8} \) - \( \frac{5}{12} \)?
| \(\frac{1}{3}\) | |
| \( \frac{1}{24} \) | |
| 2 \( \frac{8}{12} \) | |
| 2 \( \frac{4}{24} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 3}{8 x 3} \) - \( \frac{5 x 2}{12 x 2} \)
\( \frac{18}{24} \) - \( \frac{10}{24} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{18 - 10}{24} \) = \( \frac{8}{24} \) = \(\frac{1}{3}\)