| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.85 |
| Score | 0% | 57% |
a(b + c) = ab + ac defines which of the following?
distributive property for division |
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commutative property for division |
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commutative property for multiplication |
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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 2:1 and all 36,000 seats in a stadium are filled, how many home fans are in attendance?
| 39,200 | |
| 28,667 | |
| 27,750 | |
| 24,000 |
A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:
36,000 fans x \( \frac{2}{3} \) = \( \frac{72000}{3} \) = 24,000 fans.
Convert b-2 to remove the negative exponent.
| \( \frac{1}{b^2} \) | |
| \( \frac{2}{b} \) | |
| \( \frac{-1}{-2b^{2}} \) | |
| \( \frac{-2}{-b} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 9 to 2 and the ratio of baseball to basketball cards is 9 to 1, what is the ratio of football to basketball cards?
| 5:6 | |
| 81:2 | |
| 3:1 | |
| 5:8 |
The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. 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 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.
Cooks are needed to prepare for a large party. Each cook can bake either 4 large cakes or 16 small cakes per hour. The kitchen is available for 4 hours and 37 large cakes and 260 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 8 | |
| 7 | |
| 9 | |
| 12 |
If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 37 large cakes are needed for the party so \( \frac{37}{16} \) = 2\(\frac{5}{16}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 16 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 16 x 4 = 64 small cakes during that time. 260 small cakes are needed for the party so \( \frac{260}{64} \) = 4\(\frac{1}{16}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 5 = 8 cooks.