| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.47 |
| Score | 0% | 69% |
What is \( \frac{4}{5} \) x \( \frac{2}{7} \)?
| \(\frac{1}{56}\) | |
| 1\(\frac{3}{5}\) | |
| \(\frac{8}{35}\) | |
| \(\frac{2}{9}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{5} \) x \( \frac{2}{7} \) = \( \frac{4 x 2}{5 x 7} \) = \( \frac{8}{35} \) = \(\frac{8}{35}\)
A factor is a positive __________ that divides evenly into a given number.
fraction |
|
improper fraction |
|
mixed number |
|
integer |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.
Simplify \( \frac{36}{64} \).
| \( \frac{7}{16} \) | |
| \( \frac{3}{8} \) | |
| \( \frac{9}{16} \) | |
| \( \frac{10}{19} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{36}{64} \) = \( \frac{\frac{36}{4}}{\frac{64}{4}} \) = \( \frac{9}{16} \)
The total water usage for a city is 20,000 gallons each day. Of that total, 25% is for personal use and 38% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 2,600 | |
| 9,000 | |
| 6,000 | |
| 850 |
38% of the water consumption is industrial use and 25% is personal use so (38% - 25%) = 13% more water is used for industrial purposes. 20,000 gallons are consumed daily so industry consumes \( \frac{13}{100} \) x 20,000 gallons = 2,600 gallons.
What is \( \frac{6}{4} \) + \( \frac{5}{12} \)?
| 1\(\frac{11}{12}\) | |
| \( \frac{5}{13} \) | |
| 1 \( \frac{1}{6} \) | |
| 1 \( \frac{2}{12} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] 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 4 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 3}{4 x 3} \) + \( \frac{5 x 1}{12 x 1} \)
\( \frac{18}{12} \) + \( \frac{5}{12} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{18 + 5}{12} \) = \( \frac{23}{12} \) = 1\(\frac{11}{12}\)