| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.09 |
| Score | 0% | 62% |
Which of the following is an improper fraction?
\({2 \over 5} \) |
|
\({a \over 5} \) |
|
\({7 \over 5} \) |
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\(1 {2 \over 5} \) |
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.
What is \( \frac{9y^5}{3y^4} \)?
| \(\frac{1}{3}\)y9 | |
| 3y | |
| 3y\(\frac{4}{5}\) | |
| \(\frac{1}{3}\)y |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{9y^5}{3y^4} \)
\( \frac{9}{3} \) y(5 - 4)
3y
What is \( \frac{1}{7} \) ÷ \( \frac{3}{6} \)?
| \(\frac{2}{7}\) | |
| \(\frac{1}{28}\) | |
| \(\frac{1}{10}\) | |
| 2 |
To divide fractions, invert the second fraction and then multiply:
\( \frac{1}{7} \) ÷ \( \frac{3}{6} \) = \( \frac{1}{7} \) x \( \frac{6}{3} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{7} \) x \( \frac{6}{3} \) = \( \frac{1 x 6}{7 x 3} \) = \( \frac{6}{21} \) = \(\frac{2}{7}\)
What is \( \frac{9}{3} \) - \( \frac{5}{9} \)?
| 2\(\frac{4}{9}\) | |
| 1 \( \frac{5}{11} \) | |
| \( \frac{8}{9} \) | |
| 2 \( \frac{5}{8} \) |
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:
\( \frac{9 x 3}{3 x 3} \) - \( \frac{5 x 1}{9 x 1} \)
\( \frac{27}{9} \) - \( \frac{5}{9} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{27 - 5}{9} \) = \( \frac{22}{9} \) = 2\(\frac{4}{9}\)
If a rectangle is twice as long as it is wide and has a perimeter of 18 meters, what is the area of the rectangle?
| 18 m2 | |
| 128 m2 | |
| 32 m2 | |
| 98 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 18 meters so the equation becomes: 2w + 2h = 18.
Putting these two equations together and solving for width (w):
2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 9 - 2w
3w = 9
w = \( \frac{9}{3} \)
w = 3
Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m2