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This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
commutative |
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PEDMAS |
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distributive |
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associative |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 10 small cakes per hour. The kitchen is available for 3 hours and 39 large cakes and 190 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?
| 5 | |
| 10 | |
| 12 | |
| 6 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 3 x 3 = 9 large cakes during that time. 39 large cakes are needed for the party so \( \frac{39}{9} \) = 4\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 10 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 10 x 3 = 30 small cakes during that time. 190 small cakes are needed for the party so \( \frac{190}{30} \) = 6\(\frac{1}{3}\) 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 5 + 7 = 12 cooks.
Which of the following is an improper fraction?
\({7 \over 5} \) |
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\(1 {2 \over 5} \) |
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\({a \over 5} \) |
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\({2 \over 5} \) |
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 5,000 gallons each day. Of that total, 30% is for personal use and 59% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 2,250 | |
| 11,000 | |
| 7,200 | |
| 1,450 |
59% of the water consumption is industrial use and 30% is personal use so (59% - 30%) = 29% more water is used for industrial purposes. 5,000 gallons are consumed daily so industry consumes \( \frac{29}{100} \) x 5,000 gallons = 1,450 gallons.
What is \( \frac{4}{4} \) + \( \frac{9}{10} \)?
| 1\(\frac{9}{10}\) | |
| 2 \( \frac{9}{12} \) | |
| 2 \( \frac{3}{12} \) | |
| \( \frac{1}{5} \) |
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 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 5}{4 x 5} \) + \( \frac{9 x 2}{10 x 2} \)
\( \frac{20}{20} \) + \( \frac{18}{20} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{20 + 18}{20} \) = \( \frac{38}{20} \) = 1\(\frac{9}{10}\)