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The __________ is the greatest factor that divides two integers.
least common multiple |
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greatest common multiple |
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absolute value |
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greatest common factor |
The greatest common factor (GCF) is the greatest factor that divides two integers.
Which of these numbers is a factor of 20?
| 10 | |
| 21 | |
| 8 | |
| 13 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 20 are 1, 2, 4, 5, 10, 20.
What is \( \frac{4}{2} \) - \( \frac{8}{6} \)?
| \( \frac{1}{6} \) | |
| 1 \( \frac{7}{6} \) | |
| 1 \( \frac{4}{13} \) | |
| \(\frac{2}{3}\) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 3}{2 x 3} \) - \( \frac{8 x 1}{6 x 1} \)
\( \frac{12}{6} \) - \( \frac{8}{6} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{12 - 8}{6} \) = \( \frac{4}{6} \) = \(\frac{2}{3}\)
What is \( 3 \)\( \sqrt{50} \) + \( 9 \)\( \sqrt{2} \)
| 12\( \sqrt{2} \) | |
| 24\( \sqrt{2} \) | |
| 27\( \sqrt{50} \) | |
| 27\( \sqrt{100} \) |
To add these radicals together their radicands must be the same:
3\( \sqrt{50} \) + 9\( \sqrt{2} \)
3\( \sqrt{25 \times 2} \) + 9\( \sqrt{2} \)
3\( \sqrt{5^2 \times 2} \) + 9\( \sqrt{2} \)
(3)(5)\( \sqrt{2} \) + 9\( \sqrt{2} \)
15\( \sqrt{2} \) + 9\( \sqrt{2} \)
Now that the radicands are identical, you can add them together:
15\( \sqrt{2} \) + 9\( \sqrt{2} \)A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 15% off." If Ezra buys two shirts, each with a regular price of $44, how much will he pay for both shirts?
| $81.40 | |
| $57.20 | |
| $66.00 | |
| $59.40 |
By buying two shirts, Ezra will save $44 x \( \frac{15}{100} \) = \( \frac{$44 x 15}{100} \) = \( \frac{$660}{100} \) = $6.60 on the second shirt.
So, his total cost will be
$44.00 + ($44.00 - $6.60)
$44.00 + $37.40
$81.40