| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.14 |
| Score | 0% | 63% |
Which of the following is an improper fraction?
\(1 {2 \over 5} \) |
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\({2 \over 5} \) |
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\({7 \over 5} \) |
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\({a \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
The total water usage for a city is 25,000 gallons each day. Of that total, 20% is for personal use and 52% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 8,000 | |
| 5,700 | |
| 5,000 | |
| 12,800 |
52% of the water consumption is industrial use and 20% is personal use so (52% - 20%) = 32% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{32}{100} \) x 25,000 gallons = 8,000 gallons.
What is \( \frac{3}{8} \) + \( \frac{3}{12} \)?
| 2 \( \frac{3}{9} \) | |
| 2 \( \frac{8}{14} \) | |
| 1 \( \frac{8}{24} \) | |
| \(\frac{5}{8}\) |
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 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 3}{8 x 3} \) + \( \frac{3 x 2}{12 x 2} \)
\( \frac{9}{24} \) + \( \frac{6}{24} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{9 + 6}{24} \) = \( \frac{15}{24} \) = \(\frac{5}{8}\)
What is \( \frac{3}{8} \) ÷ \( \frac{3}{9} \)?
| 1\(\frac{1}{8}\) | |
| 9 | |
| \(\frac{1}{16}\) | |
| \(\frac{1}{27}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{3}{8} \) ÷ \( \frac{3}{9} \) = \( \frac{3}{8} \) x \( \frac{9}{3} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{8} \) x \( \frac{9}{3} \) = \( \frac{3 x 9}{8 x 3} \) = \( \frac{27}{24} \) = 1\(\frac{1}{8}\)
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
commutative property for multiplication |
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distributive property for division |
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distributive property for multiplication |
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commutative property for division |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).