| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
In a class of 16 students, 6 are taking German and 6 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 16 | |
| 15 | |
| 8 | |
| 12 |
The number of students taking German or Spanish is 6 + 6 = 12. Of that group of 12, 4 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 12 - 4 = 8 who are taking at least one language. 16 - 8 = 8 students who are not taking either language.
What is \( \frac{6}{3} \) - \( \frac{4}{9} \)?
| 1\(\frac{5}{9}\) | |
| 2 \( \frac{7}{12} \) | |
| \( \frac{1}{9} \) | |
| \( \frac{4}{9} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 3}{3 x 3} \) - \( \frac{4 x 1}{9 x 1} \)
\( \frac{18}{9} \) - \( \frac{4}{9} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{18 - 4}{9} \) = \( \frac{14}{9} \) = 1\(\frac{5}{9}\)
If all of a roofing company's 10 workers are required to staff 5 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?
| 16 | |
| 4 | |
| 2 | |
| 17 |
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 10 workers at the company now and that's enough to staff 5 crews so there are \( \frac{10}{5} \) = 2 workers on a crew. 7 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 7 x 2 = 14 total workers to staff the crews during the busy season. The company already employs 10 workers so they need to add 14 - 10 = 4 new staff for the busy season.
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?
| 3:1 | |
| 9:1 | |
| 9:2 | |
| 7:2 |
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.
a(b + c) = ab + ac defines which of the following?
distributive property for division |
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commutative property for multiplication |
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distributive property for multiplication |
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commutative property for division |
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.