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|---|---|---|
| Questions | 5 | 5 |
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A factor is a positive __________ that divides evenly into a given number.
fraction |
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integer |
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improper fraction |
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mixed number |
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.
What is \( \frac{9}{9} \) - \( \frac{6}{15} \)?
| 2 \( \frac{7}{16} \) | |
| 1 \( \frac{8}{17} \) | |
| \( \frac{2}{45} \) | |
| \(\frac{3}{5}\) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 5}{9 x 5} \) - \( \frac{6 x 3}{15 x 3} \)
\( \frac{45}{45} \) - \( \frac{18}{45} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{45 - 18}{45} \) = \( \frac{27}{45} \) = \(\frac{3}{5}\)
Which of the following is not an integer?
1 |
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\({1 \over 2}\) |
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-1 |
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0 |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
A triathlon course includes a 400m swim, a 30.7km bike ride, and a 14.5km run. What is the total length of the race course?
| 58.6km | |
| 45.6km | |
| 32.8km | |
| 39.2km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.4km + 30.7km + 14.5km
total distance = 45.6km
Simplify \( \frac{28}{56} \).
| \( \frac{2}{7} \) | |
| \( \frac{8}{13} \) | |
| \( \frac{1}{2} \) | |
| \( \frac{5}{12} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 6 factors [1, 2, 4, 7, 14, 28] making 28 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{56} \) = \( \frac{\frac{28}{28}}{\frac{56}{28}} \) = \( \frac{1}{2} \)