| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
What is \( \frac{5}{8} \) + \( \frac{7}{16} \)?
| \( \frac{8}{16} \) | |
| 2 \( \frac{4}{12} \) | |
| 2 \( \frac{4}{16} \) | |
| 1\(\frac{1}{16}\) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{5 x 2}{8 x 2} \) + \( \frac{7 x 1}{16 x 1} \)
\( \frac{10}{16} \) + \( \frac{7}{16} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{10 + 7}{16} \) = \( \frac{17}{16} \) = 1\(\frac{1}{16}\)
The __________ is the smallest positive integer that is a multiple of two or more integers.
least common multiple |
|
absolute value |
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greatest common factor |
|
least common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 35% off." If Ezra buys two shirts, each with a regular price of $17, how much will he pay for both shirts?
| $11.05 | |
| $5.95 | |
| $20.40 | |
| $28.05 |
By buying two shirts, Ezra will save $17 x \( \frac{35}{100} \) = \( \frac{$17 x 35}{100} \) = \( \frac{$595}{100} \) = $5.95 on the second shirt.
So, his total cost will be
$17.00 + ($17.00 - $5.95)
$17.00 + $11.05
$28.05
If a car travels 350 miles in 7 hours, what is the average speed?
| 70 mph | |
| 45 mph | |
| 25 mph | |
| 50 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)What is \( \frac{8}{3} \) - \( \frac{3}{7} \)?
| 2\(\frac{5}{21}\) | |
| 1 \( \frac{1}{21} \) | |
| 2 \( \frac{3}{21} \) | |
| \( \frac{7}{21} \) |
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 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:
\( \frac{8 x 7}{3 x 7} \) - \( \frac{3 x 3}{7 x 3} \)
\( \frac{56}{21} \) - \( \frac{9}{21} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{56 - 9}{21} \) = \( \frac{47}{21} \) = 2\(\frac{5}{21}\)