| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.01 |
| Score | 0% | 60% |
The __________ is the greatest factor that divides two integers.
greatest common factor |
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greatest common multiple |
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absolute value |
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least common multiple |
The greatest common factor (GCF) is the greatest factor that divides two integers.
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 34,000 seats in a stadium are filled, how many home fans are in attendance?
| 40,000 | |
| 25,500 | |
| 30,667 | |
| 32,500 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
34,000 fans x \( \frac{3}{4} \) = \( \frac{102000}{4} \) = 25,500 fans.
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?
| 1:1 | |
| 5:4 | |
| 7:2 | |
| 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.
What is \( \frac{21\sqrt{16}}{3\sqrt{4}} \)?
| 4 \( \sqrt{\frac{1}{7}} \) | |
| \(\frac{1}{7}\) \( \sqrt{\frac{1}{4}} \) | |
| \(\frac{1}{4}\) \( \sqrt{\frac{1}{7}} \) | |
| 7 \( \sqrt{4} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{21\sqrt{16}}{3\sqrt{4}} \)
\( \frac{21}{3} \) \( \sqrt{\frac{16}{4}} \)
7 \( \sqrt{4} \)
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
commutative |
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associative |
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PEDMAS |
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distributive |
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.