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|---|---|---|
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1
A bread recipe calls for 3\(\frac{3}{8}\) cups of flour. If you only have \(\frac{1}{2}\) cup, how much more flour is needed?
| \(\frac{3}{4}\) cups | |
| 2\(\frac{3}{8}\) cups | |
| 2\(\frac{7}{8}\) cups | |
| 2\(\frac{1}{4}\) cups |
The amount of flour you need is (3\(\frac{3}{8}\) - \(\frac{1}{2}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{27}{8} \) - \( \frac{4}{8} \)) cups
\( \frac{23}{8} \) cups
2\(\frac{7}{8}\) cups
A factor is a positive __________ that divides evenly into a given number.
mixed number |
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improper fraction |
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fraction |
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integer |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.
Simplify \( \frac{28}{64} \).
| \( \frac{8}{19} \) | |
| \( \frac{7}{12} \) | |
| \( \frac{7}{16} \) | |
| \( \frac{4}{11} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{64} \) = \( \frac{\frac{28}{4}}{\frac{64}{4}} \) = \( \frac{7}{16} \)
a(b + c) = ab + ac defines which of the following?
distributive property for multiplication |
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commutative property for multiplication |
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commutative property for division |
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distributive property for division |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.