| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.58 |
| Score | 0% | 72% |
What is \( \frac{5}{3} \) + \( \frac{9}{7} \)?
| 1 \( \frac{1}{21} \) | |
| \( \frac{7}{21} \) | |
| 1 \( \frac{5}{10} \) | |
| 2\(\frac{20}{21}\) |
To add 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 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{5 x 7}{3 x 7} \) + \( \frac{9 x 3}{7 x 3} \)
\( \frac{35}{21} \) + \( \frac{27}{21} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{35 + 27}{21} \) = \( \frac{62}{21} \) = 2\(\frac{20}{21}\)
What is 3z5 - 7z5?
| -4z5 | |
| 10z5 | |
| 10z-10 | |
| -4z-5 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
3z5 - 7z5
(3 - 7)z5
-4z5
Which of the following is a mixed number?
\({a \over 5} \) |
|
\({5 \over 7} \) |
|
\({7 \over 5} \) |
|
\(1 {2 \over 5} \) |
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.
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 7 to 2 and the ratio of baseball to basketball cards is 7 to 1, what is the ratio of football to basketball cards?
| 49:2 | |
| 5:6 | |
| 3:6 | |
| 1:6 |
The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.
What is the next number in this sequence: 1, 2, 3, 4, 5, __________ ?
| 15 | |
| 6 | |
| 1 | |
| 3 |
The equation for this sequence is:
an = an-1 + 1
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 1
a6 = 5 + 1
a6 = 6