| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.19 |
| Score | 0% | 64% |
What is \( \frac{2}{4} \) + \( \frac{5}{12} \)?
| 2 \( \frac{3}{12} \) | |
| 1 \( \frac{8}{16} \) | |
| \( \frac{4}{9} \) | |
| \(\frac{11}{12}\) |
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:
\( \frac{2 x 3}{4 x 3} \) + \( \frac{5 x 1}{12 x 1} \)
\( \frac{6}{12} \) + \( \frac{5}{12} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{6 + 5}{12} \) = \( \frac{11}{12} \) = \(\frac{11}{12}\)
What is \( \frac{7}{3} \) - \( \frac{8}{9} \)?
| \( \frac{2}{9} \) | |
| \( \frac{1}{4} \) | |
| \( \frac{6}{9} \) | |
| 1\(\frac{4}{9}\) |
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:
\( \frac{7 x 3}{3 x 3} \) - \( \frac{8 x 1}{9 x 1} \)
\( \frac{21}{9} \) - \( \frac{8}{9} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{21 - 8}{9} \) = \( \frac{13}{9} \) = 1\(\frac{4}{9}\)
The total water usage for a city is 40,000 gallons each day. Of that total, 12% is for personal use and 28% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 1,950 | |
| 7,350 | |
| 5,700 | |
| 6,400 |
28% of the water consumption is industrial use and 12% is personal use so (28% - 12%) = 16% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{16}{100} \) x 40,000 gallons = 6,400 gallons.
Solve for \( \frac{6!}{2!} \)
| 1680 | |
| \( \frac{1}{8} \) | |
| 336 | |
| 360 |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{6!}{2!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{6 \times 5 \times 4 \times 3}{1} \)
\( 6 \times 5 \times 4 \times 3 \)
360
a(b + c) = ab + ac defines which of the following?
distributive property for division |
|
distributive property for multiplication |
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commutative property for division |
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commutative property for multiplication |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.