| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.14 |
| Score | 0% | 63% |
What is \( \frac{8}{6} \) - \( \frac{9}{8} \)?
| 1 \( \frac{1}{24} \) | |
| \(\frac{5}{24}\) | |
| 2 \( \frac{1}{24} \) | |
| 1 \( \frac{6}{24} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 4}{6 x 4} \) - \( \frac{9 x 3}{8 x 3} \)
\( \frac{32}{24} \) - \( \frac{27}{24} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{32 - 27}{24} \) = \( \frac{5}{24} \) = \(\frac{5}{24}\)
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?
| 33 | |
| 1:1 | |
| 9:8 | |
| 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.
Simplify \( \frac{28}{44} \).
| \( \frac{1}{3} \) | |
| \( \frac{4}{11} \) | |
| \( \frac{2}{9} \) | |
| \( \frac{7}{11} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{44} \) = \( \frac{\frac{28}{4}}{\frac{44}{4}} \) = \( \frac{7}{11} \)
How many 1\(\frac{1}{2}\) gallon cans worth of fuel would you need to pour into an empty 9 gallon tank to fill it exactly halfway?
| 4 | |
| 6 | |
| 7 | |
| 3 |
To fill a 9 gallon tank exactly halfway you'll need 4\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:
cans = \( \frac{4\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 3
What is \( \sqrt{\frac{81}{49}} \)?
| \(\frac{7}{9}\) | |
| 1\(\frac{1}{3}\) | |
| 1\(\frac{3}{4}\) | |
| 1\(\frac{2}{7}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{81}{49}} \)
\( \frac{\sqrt{81}}{\sqrt{49}} \)
\( \frac{\sqrt{9^2}}{\sqrt{7^2}} \)
\( \frac{9}{7} \)
1\(\frac{2}{7}\)