| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
What is the distance in miles of a trip that takes 6 hours at an average speed of 30 miles per hour?
| 140 miles | |
| 180 miles | |
| 390 miles | |
| 120 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 = \( 30mph \times 6h \)
180 miles
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
distributive |
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associative |
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PEDMAS |
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commutative |
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 \( \frac{-2a^7}{7a^4} \)?
| -\(\frac{2}{7}\)a-3 | |
| -\(\frac{2}{7}\)a\(\frac{4}{7}\) | |
| -\(\frac{2}{7}\)a3 | |
| -\(\frac{2}{7}\)a11 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-2a^7}{7a^4} \)
\( \frac{-2}{7} \) a(7 - 4)
-\(\frac{2}{7}\)a3
How many 1\(\frac{1}{2}\) gallon cans worth of fuel would you need to pour into an empty 6 gallon tank to fill it exactly halfway?
| 2 | |
| 2 | |
| 8 | |
| 4 |
To fill a 6 gallon tank exactly halfway you'll need 3 gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:
cans = \( \frac{3 \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 2
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 5 to 2 and the ratio of baseball to basketball cards is 5 to 1, what is the ratio of football to basketball cards?
| 25:2 | |
| 3:8 | |
| 9:2 | |
| 3:6 |
The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.