| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.54 |
| Score | 0% | 71% |
What is \( \frac{8}{3} \) - \( \frac{7}{11} \)?
| 2\(\frac{1}{33}\) | |
| \( \frac{3}{10} \) | |
| 1 \( \frac{7}{16} \) | |
| \( \frac{9}{33} \) |
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 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 11}{3 x 11} \) - \( \frac{7 x 3}{11 x 3} \)
\( \frac{88}{33} \) - \( \frac{21}{33} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{88 - 21}{33} \) = \( \frac{67}{33} \) = 2\(\frac{1}{33}\)
If a car travels 300 miles in 5 hours, what is the average speed?
| 60 mph | |
| 65 mph | |
| 30 mph | |
| 35 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)15 members of a bridal party need transported to a wedding reception but there are only 4 3-passenger taxis available to take them. How many will need to find other transportation?
| 3 | |
| 9 | |
| 1 | |
| 2 |
There are 4 3-passenger taxis available so that's 4 x 3 = 12 total seats. There are 15 people needing transportation leaving 15 - 12 = 3 who will have to find other transportation.
What is the distance in miles of a trip that takes 3 hours at an average speed of 35 miles per hour?
| 105 miles | |
| 440 miles | |
| 455 miles | |
| 110 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 = \( 35mph \times 3h \)
105 miles
If a rectangle is twice as long as it is wide and has a perimeter of 30 meters, what is the area of the rectangle?
| 50 m2 | |
| 18 m2 | |
| 72 m2 | |
| 32 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 30 meters so the equation becomes: 2w + 2h = 30.
Putting these two equations together and solving for width (w):
2w + 2h = 30
w + h = \( \frac{30}{2} \)
w + h = 15
w = 15 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 15 - 2w
3w = 15
w = \( \frac{15}{3} \)
w = 5
Since h = 2w that makes h = (2 x 5) = 10 and the area = h x w = 5 x 10 = 50 m2