| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.68 |
| Score | 0% | 54% |
What is \( \frac{2}{9} \) - \( \frac{6}{15} \)?
| -\(\frac{8}{45}\) | |
| 1 \( \frac{3}{9} \) | |
| \( \frac{2}{8} \) | |
| 2 \( \frac{9}{45} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{2 x 5}{9 x 5} \) - \( \frac{6 x 3}{15 x 3} \)
\( \frac{10}{45} \) - \( \frac{18}{45} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{10 - 18}{45} \) = \( \frac{-8}{45} \) = -\(\frac{8}{45}\)
Betty scored 91% on her final exam. If each question was worth 3 points and there were 270 possible points on the exam, how many questions did Betty answer correctly?
| 82 | |
| 95 | |
| 83 | |
| 69 |
Betty scored 91% on the test meaning she earned 91% of the possible points on the test. There were 270 possible points on the test so she earned 270 x 0.91 = 246 points. Each question is worth 3 points so she got \( \frac{246}{3} \) = 82 questions right.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 65% larger than the original. By what percentage has the area of the logo increased?
| 32\(\frac{1}{2}\)% | |
| 27\(\frac{1}{2}\)% | |
| 25% | |
| 20% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 65% the radius (and, consequently, the total area) increases by \( \frac{65\text{%}}{2} \) = 32\(\frac{1}{2}\)%
Which of the following statements about exponents is false?
all of these are false |
|
b1 = 1 |
|
b0 = 1 |
|
b1 = b |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
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 | |
| 1:4 | |
| 3:1 |
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.