| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.00 |
| Score | 0% | 60% |
What is \( \frac{2}{2} \) + \( \frac{7}{4} \)?
| 1 \( \frac{1}{8} \) | |
| \( \frac{9}{18} \) | |
| \( \frac{2}{4} \) | |
| 2\(\frac{3}{4}\) |
To add 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 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{2 x 2}{2 x 2} \) + \( \frac{7 x 1}{4 x 1} \)
\( \frac{4}{4} \) + \( \frac{7}{4} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{4 + 7}{4} \) = \( \frac{11}{4} \) = 2\(\frac{3}{4}\)
Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 15 small cakes per hour. The kitchen is available for 3 hours and 27 large cakes and 260 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?
| 9 | |
| 8 | |
| 5 | |
| 10 |
If a single cook can bake 5 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 5 x 3 = 15 large cakes during that time. 27 large cakes are needed for the party so \( \frac{27}{15} \) = 1\(\frac{4}{5}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 15 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 15 x 3 = 45 small cakes during that time. 260 small cakes are needed for the party so \( \frac{260}{45} \) = 5\(\frac{7}{9}\) 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 + 6 = 8 cooks.
What is \( \sqrt{\frac{36}{64}} \)?
| \(\frac{3}{4}\) | |
| \(\frac{7}{8}\) | |
| 1\(\frac{1}{3}\) | |
| \(\frac{1}{2}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{36}{64}} \)
\( \frac{\sqrt{36}}{\sqrt{64}} \)
\( \frac{\sqrt{6^2}}{\sqrt{8^2}} \)
\(\frac{3}{4}\)
The __________ is the greatest factor that divides two integers.
greatest common multiple |
|
absolute value |
|
least common multiple |
|
greatest common factor |
The greatest common factor (GCF) is the greatest factor that divides two integers.
Convert 4,263,000 to scientific notation.
| 4.263 x 107 | |
| 4.263 x 106 | |
| 4.263 x 10-5 | |
| 4.263 x 10-6 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
4,263,000 in scientific notation is 4.263 x 106