Fractions: 41 flashcards
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1. What is a fraction?
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A number that represents a part of a whole, written as $\frac{a}{b}$ where $b \neq 0$.
2. In $\frac{3}{4}$, what is the numerator and what is the denominator?
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Numerator = 3, Denominator = 4.
3. What does the denominator represent in a fraction?
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The total number of equal parts the whole is divided into.
4. What does the numerator represent in a fraction?
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The number of equal parts being considered.
5. What is a proper fraction?
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A fraction where the numerator is less than the denominator, e.g., $\frac{2}{5}$.
6. What is an improper fraction?
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A fraction where the numerator is greater than or equal to the denominator, e.g., $\frac{7}{4}$.
7. What is a mixed number?
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A number consisting of a whole number and a proper fraction, e.g., $2\frac{1}{3}$.
8. Convert $2\frac{1}{3}$ to an improper fraction.
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$\frac{7}{3}$
9. Convert $\frac{11}{4}$ to a mixed number.
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$2\frac{3}{4}$
10. What are equivalent fractions?
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Fractions that represent the same value, e.g., $\frac{1}{2} = \frac{2}{4} = \frac{3}{6}$.
11. How do you simplify $\frac{18}{24}$?
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$\frac{3}{4}$
12. How do you add fractions with the same denominator?
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Add the numerators and keep the denominator: $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$.
13. How do you subtract fractions with the same denominator?
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Subtract the numerators and keep the denominator: $\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$.
14. How do you add fractions with different denominators?
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Find a common denominator, convert each fraction, then add the numerators.
15. Compute $\frac{1}{2} + \frac{1}{3}$.
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$\frac{5}{6}$
16. Compute $\frac{3}{4} - \frac{1}{6}$.
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$\frac{7}{12}$
17. How do you multiply two fractions?
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Multiply numerators and denominators: $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$.
18. Compute $\frac{2}{3} \times \frac{3}{5}$.
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$\frac{2}{5}$
19. How do you divide two fractions?
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Multiply the first fraction by the reciprocal of the second: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$.
20. Compute $\frac{3}{4} \div \frac{2}{5}$.
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$\frac{15}{8}$ or $1\frac{7}{8}$
21. What is the reciprocal of $\frac{5}{7}$?
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$\frac{7}{5}$
22. How do you compare fractions with the same denominator?
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Compare numerators: the fraction with the larger numerator is greater.
23. How do you compare fractions with the same numerator?
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Compare denominators: the fraction with the smaller denominator is greater.
24. Compare $\frac{2}{3}$ and $\frac{3}{5}$.
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$\frac{2}{3} > \frac{3}{5}$
25. What is a unit fraction?
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A fraction with numerator 1, e.g., $\frac{1}{4}$.
26. What is a decimal representation of $\frac{1}{4}$?
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0.25
27. Convert 0.6 to a fraction in simplest form.
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$\frac{3}{5}$
28. What is $\frac{1}{2}$ as a percent?
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50%
29. What is 25% as a fraction in simplest form?
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$\frac{1}{4}$
30. What is the rule for finding a fraction of a quantity?
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Multiply the quantity by the fraction: e.g., $\frac{2}{3}$ of 15 = $\frac{2}{3} \times 15 = 10$.
31. Find $\frac{3}{4}$ of 20.
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15
32. What is the commutative property of addition for fractions?
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$\frac{a}{b} + \frac{c}{d} = \frac{c}{d} + \frac{a}{b}$
33. What is the associative property of addition for fractions?
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$\left(\frac{a}{b} + \frac{c}{d}\right) + \frac{e}{f} = \frac{a}{b} + \left(\frac{c}{d} + \frac{e}{f}\right)$
34. What is the additive identity for fractions?
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0, because $\frac{a}{b} + 0 = \frac{a}{b}$.
35. What is the multiplicative identity for fractions?
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1, because $\frac{a}{b} \times 1 = \frac{a}{b}$.
36. What is the multiplicative inverse (reciprocal) of a non-zero fraction $\frac{a}{b}$?
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$\frac{b}{a}$
37. Simplify $\frac{2}{3} \times \frac{9}{4}$.
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$\frac{3}{2}$ or $1\frac{1}{2}$
38. Compute $\frac{5}{6} - \frac{1}{3}$.
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$\frac{1}{2}$
39. Arrange in ascending order: $\frac{1}{2}, \frac{2}{5}, \frac{3}{10}$.
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$\frac{3}{10}, \frac{2}{5}, \frac{1}{2}$
40. What is $\frac{0}{7}$?
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0
41. What is $\frac{7}{0}$?
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Undefined
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