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Fractions, Decimals & Percentages

75 cards · 🇺🇸 English

Converting between fractions, decimals and percentages, and operating on them.

arithmeticfractionsdecimalspercentages

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Question

What does the word 'fraction' derive from?

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  1. 1What does the word 'fraction' derive from?
    From Latin 'fractus,' meaning 'broken'
  2. 2Numerator in a fraction
    The number of equal parts being described (top number), from Latin 'numerātor' meaning 'counter' or 'numberer'
  3. 3Denominator in a fraction
    The type or variety of parts (bottom number), from Latin 'dēnōminātor' meaning 'thing that names or designates'
  4. 4the 3 in the fraction 3/4
    The numerator, indicating 3 equal parts
  5. 5the 4 in the fraction 3/4
    The denominator, indicating that 4 parts make up a whole
  6. 6Simple (or common or vulgar) fraction
    A rational number written as a/b where a and b are both integers and b is non-zero
  7. 7Unit fraction
    A common fraction with a numerator of 1 (e.g., 1/7)
  8. 8Dyadic fraction
    A common fraction where the denominator is a power of two (e.g., 1/8 = 1/2³)
  9. 9Example of a proper fraction
    2/3, 3/4, or 4/9 - any fraction where the numerator is smaller than the denominator
  10. 10Example of an improper fraction
    9/4, 4/3, or 3/3 - any fraction where the numerator is greater than or equal to the denominator
  11. 11Reciprocal of a fraction
    Another fraction with the numerator and denominator exchanged (e.g., the reciprocal of 3/7 is 7/3)
  12. 12Product of a fraction and its reciprocal
    1 (one), which is why the reciprocal is called the multiplicative inverse
  13. 13'invisible denominator'
    The number 1, which any integer can be divided by to express it as a fraction (e.g., 17 = 17/1)
  14. 14Mixed number
    The sum of a non-zero integer and a proper fraction, written by juxtaposition (e.g., 2¾)
  15. 15a mixed number → an improper fraction
    Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator
  16. 162¾ → an improper fraction
    11/4 (calculated as: 2×4 + 3 = 11, placed over 4)
  17. 17an improper fraction → a mixed number
    Use division with remainder: the quotient becomes the whole number, and the remainder over the divisor becomes the fraction
  18. 1811/4 → a mixed number
    2¾ (11 ÷ 4 = 2 remainder 3, so 2 and 3/4)
  19. 19Decimal fraction
    A fraction whose denominator is an integer power of ten, commonly expressed using decimal notation (e.g., 0.75 = 75/100)
  20. 20The implied denominator in the decimal 0.75
    100 (10 to the power of 2, because there are two digits after the decimal point)
  21. 21a percentage
    A fraction with an implied denominator of 100 (from Latin 'per centum' meaning 'per hundred')
  22. 22What does 51% mean as a fraction?
    51/100
  23. 233/4 → a percentage
    75% (3/4 = 0.75 = 75/100)
  24. 240.25 → a percentage
    25% (0.25 = 25/100)
  25. 25Permille (ppt)
    Parts per thousand, meaning a denominator of 1000
  26. 26What happens when you multiply the numerator and denominator of a fraction by the same number?
    You get an equivalent fraction with the same value (e.g., 1/2 = 2/4 = 50/100)
  27. 27Simplifying (or reducing) a fraction
    Dividing both the numerator and denominator by their greatest common divisor to get the lowest terms
  28. 286/9
    2/3 (divide both by their GCD of 3)
  29. 29What does it mean when a fraction is in 'lowest terms'?
    The numerator and denominator share no common factor greater than 1
  30. 30Is 3/8 in lowest terms?
    Yes, because the only positive integer that divides both 3 and 8 is 1

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