| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.19 |
| Score | 0% | 64% |
What is \( \frac{3}{6} \) x \( \frac{1}{6} \)?
| \(\frac{1}{12}\) | |
| \(\frac{1}{2}\) | |
| \(\frac{1}{7}\) | |
| \(\frac{2}{9}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{6} \) x \( \frac{1}{6} \) = \( \frac{3 x 1}{6 x 6} \) = \( \frac{3}{36} \) = \(\frac{1}{12}\)
Which of the following statements about exponents is false?
b0 = 1 |
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b1 = 1 |
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all of these are false |
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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(b + c) = ab + ac defines which of the following?
commutative property for division |
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commutative property for multiplication |
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distributive property for division |
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distributive property for multiplication |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.
If the ratio of home fans to visiting fans in a crowd is 5:1 and all 49,000 seats in a stadium are filled, how many home fans are in attendance?
| 40,000 | |
| 40,833 | |
| 27,000 | |
| 28,800 |
A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:
49,000 fans x \( \frac{5}{6} \) = \( \frac{245000}{6} \) = 40,833 fans.
Simplify \( \frac{28}{80} \).
| \( \frac{7}{20} \) | |
| \( \frac{4}{17} \) | |
| \( \frac{5}{9} \) | |
| \( \frac{1}{2} \) |
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 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{80} \) = \( \frac{\frac{28}{4}}{\frac{80}{4}} \) = \( \frac{7}{20} \)