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Fractions Toolkit

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課程筆記

Basic Fractions

  • A fraction is written as \frac{a}{b} where a (numerator) and b (denominator) are integers.
  • The denominator shows how many parts each whole is split into; the numerator shows how many parts you have.
  • A fraction is less than 1 if numerator < denominator; greater than 1 if numerator > denominator.
  • To find a fraction of an amount: divide by denominator, multiply by numerator (e.g., \frac{2}{5} of 60: 60 ÷ 5 = 12, 12 × 2 = 24).
  • Equivalent fractions represent the same amount; multiply top and bottom by the same number to find them.
  • Simplify a fraction by dividing numerator and denominator by a common factor (e.g., \frac{12}{18} = \frac{2}{3}).

Mixed Numbers & Improper Fractions

  • A mixed number has an integer part and a fraction part (e.g., 3\frac{3}{4}).
  • An improper fraction (top-heavy) has numerator ≥ denominator (e.g., \frac{15}{4}).
  • To convert a mixed number to an improper fraction: multiply the whole number by the denominator, add the numerator, write over the denominator.
  • To convert an improper fraction to a mixed number: divide numerator by denominator; the quotient is the whole number, remainder over denominator is the fraction.
  • Always convert mixed numbers to improper fractions before adding, subtracting, multiplying, or dividing.

Adding & Subtracting Fractions

  • Find the lowest common denominator (LCD) of the fractions.
  • Rewrite each fraction as an equivalent fraction with the LCD.
  • Add or subtract the numerators; keep the denominator the same.
  • Simplify the result by cancelling common factors.
  • If mixed numbers are involved, convert them to improper fractions first, then add/subtract, and convert back if needed.

Multiplying Fractions

  • Cancel any common factors between numerators and denominators before multiplying.
  • Multiply the numerators together and the denominators together.
  • Simplify the resulting fraction if possible.
  • If a mixed number is involved, convert it to an improper fraction first.
  • Example: \frac{4}{15} \times \frac{25}{11} = \frac{4 \times 25}{15 \times 11} = \frac{100}{165} = \frac{20}{33} after cancelling.

Dividing Fractions

  • To divide, flip the second fraction (find its reciprocal) and change ÷ to ×.
  • Then follow the multiplication steps: cancel, multiply numerators, multiply denominators.
  • If a mixed number is involved, convert it to an improper fraction first.
  • Example: 3\frac{1}{4} \div \frac{3}{8} = \frac{13}{4} \times \frac{8}{3} = \frac{13 \times 8}{4 \times 3} = \frac{104}{12} = \frac{26}{3} = 8\frac{2}{3}.

Working with Fractions of Amounts

  • To find a fraction of an amount, multiply the amount by the fraction.
  • Write the amount as a fraction over 1 (e.g., 60 = \frac{60}{1}).
  • Then multiply the fractions as usual.
  • Alternatively, divide by denominator then multiply by numerator.

Simplifying Fractions

  • A fraction is in its simplest form when numerator and denominator have no common factors other than 1.
  • Divide both numerator and denominator by their highest common factor (HCF).
  • Your calculator can simplify fractions automatically, but show the factor you divided by if working is required.

Common Mistakes & Tips

  • When adding/subtracting, do not add denominators.
  • Always simplify final answers unless stated otherwise.
  • Convert mixed numbers to improper fractions before any operation.
  • Remember "flip'n'times" for division: flip the second fraction and multiply.

投影片

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練習題

免費預覽——56 題中的 8 題。註冊即可查看全部。
  1. 1.What is a fraction?

    Easy
    • AA number written as a/b where a and b are integers
    • BA number with a decimal point
    • CA number less than 1
    • DA number greater than 1
  2. 2.What is the numerator in the fraction 3/5?

    Easy
    • A3
    • B5
    • C8
    • D2
  3. 3.Which of the following is an improper fraction?

    Easy
    • A7/4
    • B3/5
    • C2/3
    • D1/2
  4. 4.Convert 5 2/7 into an improper fraction.

    Easy
    • A37/7
    • B35/7
    • C12/7
    • D33/7
  5. 5.Convert 22/3 into a mixed number.

    Easy
    • A7 1/3
    • B7 2/3
    • C6 1/3
    • D7 1/2
  6. 6.Simplify 12/18 to its lowest terms.

    Easy
    • A2/3
    • B3/4
    • C1/2
    • D4/6
  7. 7.Work out 2/5 of 60.

    Easy
    • A24
    • B12
    • C30
    • D150
  8. 8.Which fraction is equivalent to 3.875?

    Medium
    • A31/8
    • B15/4
    • C29/8
    • D15/8

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