| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
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.
In a class of 33 students, 14 are taking German and 15 are taking Spanish. Of the students studying German or Spanish, 6 are taking both courses. How many students are not enrolled in either course?
| 22 | |
| 12 | |
| 10 | |
| 24 |
The number of students taking German or Spanish is 14 + 15 = 29. Of that group of 29, 6 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 29 - 6 = 23 who are taking at least one language. 33 - 23 = 10 students who are not taking either language.
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?
| 1:1 | |
| 3:8 | |
| 3:2 | |
| 81:2 |
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.
Which of the following is an improper fraction?
\({7 \over 5} \) |
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\(1 {2 \over 5} \) |
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\({2 \over 5} \) |
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\({a \over 5} \) |
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.
If all of a roofing company's 12 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 9 complete crews out on jobs?
| 15 | |
| 6 | |
| 13 | |
| 8 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 12 workers at the company now and that's enough to staff 4 crews so there are \( \frac{12}{4} \) = 3 workers on a crew. 9 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 9 x 3 = 27 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 27 - 12 = 15 new staff for the busy season.