| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.38 |
| Score | 0% | 68% |
Which of the following is an improper fraction?
\({a \over 5} \) |
|
\({7 \over 5} \) |
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\(1 {2 \over 5} \) |
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\({2 \over 5} \) |
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.
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 3 to 2 and the ratio of baseball to basketball cards is 3 to 1, what is the ratio of football to basketball cards?
| 9:2 | |
| 7:1 | |
| 5:4 | |
| 1:4 |
The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. 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 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.
What is \( \frac{5}{9} \) - \( \frac{6}{15} \)?
| \(\frac{7}{45}\) | |
| 2 \( \frac{5}{12} \) | |
| 1 \( \frac{7}{15} \) | |
| 1 \( \frac{7}{12} \) |
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:
\( \frac{5 x 5}{9 x 5} \) - \( \frac{6 x 3}{15 x 3} \)
\( \frac{25}{45} \) - \( \frac{18}{45} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{25 - 18}{45} \) = \( \frac{7}{45} \) = \(\frac{7}{45}\)
Which of the following is a mixed number?
\({7 \over 5} \) |
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\(1 {2 \over 5} \) |
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\({a \over 5} \) |
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\({5 \over 7} \) |
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.
What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?
| 31 | |
| 39 | |
| 38 | |
| 26 |
The equation for this sequence is:
an = an-1 + 2(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 2(6 - 1)
a6 = 21 + 2(5)
a6 = 31