| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
What is \( \frac{1}{9} \) x \( \frac{3}{6} \)?
| \(\frac{1}{18}\) | |
| \(\frac{1}{28}\) | |
| \(\frac{4}{15}\) | |
| \(\frac{1}{2}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{9} \) x \( \frac{3}{6} \) = \( \frac{1 x 3}{9 x 6} \) = \( \frac{3}{54} \) = \(\frac{1}{18}\)
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for multiplication |
|
distributive property for division |
|
commutative property for multiplication |
|
commutative property for division |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
In a class of 32 students, 10 are taking German and 14 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 11 | |
| 13 | |
| 16 | |
| 15 |
The number of students taking German or Spanish is 10 + 14 = 24. Of that group of 24, 3 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 24 - 3 = 21 who are taking at least one language. 32 - 21 = 11 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?
| 7:4 | |
| 3:6 | |
| 81:2 | |
| 9:2 |
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.
What is \( \frac{9}{6} \) - \( \frac{2}{12} \)?
| 1 \( \frac{8}{11} \) | |
| \( \frac{2}{9} \) | |
| \( \frac{3}{12} \) | |
| 1\(\frac{1}{3}\) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 2}{6 x 2} \) - \( \frac{2 x 1}{12 x 1} \)
\( \frac{18}{12} \) - \( \frac{2}{12} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{18 - 2}{12} \) = \( \frac{16}{12} \) = 1\(\frac{1}{3}\)