| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.08 |
| Score | 0% | 62% |
Which of the following is a mixed number?
\({7 \over 5} \) |
|
\({5 \over 7} \) |
|
\(1 {2 \over 5} \) |
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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.
A tiger in a zoo has consumed 66 pounds of food in 6 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 132 pounds?
| 9 | |
| 1 | |
| 12 | |
| 6 |
If the tiger has consumed 66 pounds of food in 6 days that's \( \frac{66}{6} \) = 11 pounds of food per day. The tiger needs to consume 132 - 66 = 66 more pounds of food to reach 132 pounds total. At 11 pounds of food per day that's \( \frac{66}{11} \) = 6 more days.
What is \( \frac{4}{3} \) + \( \frac{2}{11} \)?
| 2 \( \frac{3}{9} \) | |
| \( \frac{6}{33} \) | |
| 1\(\frac{17}{33}\) | |
| 2 \( \frac{3}{33} \) |
To add 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 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 11}{3 x 11} \) + \( \frac{2 x 3}{11 x 3} \)
\( \frac{44}{33} \) + \( \frac{6}{33} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{44 + 6}{33} \) = \( \frac{50}{33} \) = 1\(\frac{17}{33}\)
Cooks are needed to prepare for a large party. Each cook can bake either 4 large cakes or 16 small cakes per hour. The kitchen is available for 4 hours and 21 large cakes and 170 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 10 | |
| 5 | |
| 14 | |
| 6 |
If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 21 large cakes are needed for the party so \( \frac{21}{16} \) = 1\(\frac{5}{16}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 16 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 16 x 4 = 64 small cakes during that time. 170 small cakes are needed for the party so \( \frac{170}{64} \) = 2\(\frac{21}{32}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 3 = 5 cooks.
What is 4x6 + 2x6?
| 6x6 | |
| -2x-6 | |
| 6x36 | |
| 2x-6 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
4x6 + 2x6
(4 + 2)x6
6x6