| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
Which of the following is a mixed number?
\({7 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({5 \over 7} \) |
|
\({a \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 |
|
a = -7 |
|
none of these is correct |
|
a = 7 or a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 7 to 2 and the ratio of baseball to basketball cards is 7 to 1, what is the ratio of football to basketball cards?
| 9:6 | |
| 1:8 | |
| 5:6 | |
| 49:2 |
The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.
A tiger in a zoo has consumed 32 pounds of food in 4 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 80 pounds?
| 8 | |
| 10 | |
| 6 | |
| 5 |
If the tiger has consumed 32 pounds of food in 4 days that's \( \frac{32}{4} \) = 8 pounds of food per day. The tiger needs to consume 80 - 32 = 48 more pounds of food to reach 80 pounds total. At 8 pounds of food per day that's \( \frac{48}{8} \) = 6 more days.
If all of a roofing company's 8 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 5 complete crews out on jobs?
| 12 | |
| 14 | |
| 5 | |
| 10 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 8 workers at the company now and that's enough to staff 2 crews so there are \( \frac{8}{2} \) = 4 workers on a crew. 5 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 5 x 4 = 20 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 20 - 8 = 12 new staff for the busy season.