| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.72 |
| Score | 0% | 54% |
What is \( \frac{2}{2} \) + \( \frac{6}{10} \)?
| 1\(\frac{3}{5}\) | |
| 2 \( \frac{8}{11} \) | |
| 1 \( \frac{9}{15} \) | |
| 1 \( \frac{6}{15} \) |
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 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{2 x 5}{2 x 5} \) + \( \frac{6 x 1}{10 x 1} \)
\( \frac{10}{10} \) + \( \frac{6}{10} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{10 + 6}{10} \) = \( \frac{16}{10} \) = 1\(\frac{3}{5}\)
The __________ is the smallest positive integer that is a multiple of two or more integers.
greatest common factor |
|
absolute value |
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least common factor |
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least common multiple |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
Solve 3 + (3 + 3) ÷ 5 x 2 - 32
| \(\frac{1}{2}\) | |
| -3\(\frac{3}{5}\) | |
| \(\frac{8}{9}\) | |
| 1 |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
3 + (3 + 3) ÷ 5 x 2 - 32
P: 3 + (6) ÷ 5 x 2 - 32
E: 3 + 6 ÷ 5 x 2 - 9
MD: 3 + \( \frac{6}{5} \) x 2 - 9
MD: 3 + \( \frac{12}{5} \) - 9
AS: \( \frac{15}{5} \) + \( \frac{12}{5} \) - 9
AS: \( \frac{27}{5} \) - 9
AS: \( \frac{27 - 45}{5} \)
\( \frac{-18}{5} \)
-3\(\frac{3}{5}\)
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 13 small cakes per hour. The kitchen is available for 4 hours and 29 large cakes and 220 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?
| 8 | |
| 12 | |
| 6 | |
| 5 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 29 large cakes are needed for the party so \( \frac{29}{12} \) = 2\(\frac{5}{12}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 13 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 13 x 4 = 52 small cakes during that time. 220 small cakes are needed for the party so \( \frac{220}{52} \) = 4\(\frac{3}{13}\) 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 3 + 5 = 8 cooks.
A bread recipe calls for 2\(\frac{7}{8}\) cups of flour. If you only have \(\frac{1}{2}\) cup, how much more flour is needed?
| 2\(\frac{3}{8}\) cups | |
| 3\(\frac{1}{4}\) cups | |
| 1\(\frac{3}{4}\) cups | |
| \(\frac{7}{8}\) cups |
The amount of flour you need is (2\(\frac{7}{8}\) - \(\frac{1}{2}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{23}{8} \) - \( \frac{4}{8} \)) cups
\( \frac{19}{8} \) cups
2\(\frac{3}{8}\) cups