Reviewing Fraction Operations with Mr. J

May 19, 2024

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Class Notes: Math with Mr. J - Fraction Review

Summary

In this session, Mr. J provided a review of operations with fractions including adding, subtracting, multiplying, and dividing. He emphasized on finding common denominators for addition and subtraction, simplifying fractions where possible, and the methods of 'keep, switch, flip' for division. The entire lesson is a refresher aimed at brushing up calculation skills with fractions.

Detailed Notes

  1. Adding Fractions

    • Example: ( \frac{5}{8} + \frac{1}{3} )
    • Steps:
      1. Find a common denominator, which is the least common multiple (LCM).
        • LCM of 8 and 3 is 24.
      2. Rewrite fractions with the common denominator.
        • ( \frac{5}{8} ) becomes ( \frac{15}{24} ) (Multiply both numerator and denominator by 3).
        • ( \frac{1}{3} ) becomes ( \frac{8}{24} ) (Multiply both numerator and denominator by 8).
      3. Add the numerators and keep the denominator.
        • ( 15 + 8 = 23 ), thus, ( \frac{23}{24} ).
      4. Check if the resulting fraction can be simplified. In this example, it cannot.

  2. Subtracting Fractions

    • Example: ( \frac{1}{2} - \frac{2}{5} )
    • Steps:
      1. Find the LCM of the denominators, which is 10.
      2. Convert each fraction to an equivalent fraction.
        • ( \frac{1}{2} ) becomes ( \frac{5}{10} ).
        • ( \frac{2}{5} ) becomes ( \frac{4}{10} ).
      3. Subtract the new numerators, keeping the denominator.
        • ( 5 - 4 = 1 ), giving ( \frac{1}{10} ).
      4. Check for simplification; it remains as ( \frac{1}{10} ).

  3. Multiplying Fractions

    • Example: ( \frac{2}{8} \cdot \frac{1}{4} )
    • Steps:
      1. Multiply numerators and denominators directly.
        • ( 2 \cdot 1 = 2 ) and ( 8 \cdot 4 = 32 ), resulting in ( \frac{2}{32} ).
      2. Simplify the result.
        • Divide both numerator and denominator by 2 to get ( \frac{1}{16} ).

  4. Dividing Fractions

    • Example: ( \frac{5}{6} \div \frac{2}{7} )
    • Steps:
      1. "Keep, switch, and flip" the second fraction. Change the division to a multiplication and flip the second fraction.
        • It becomes ( \frac{5}{6} \cdot \frac{7}{2} ).
      2. Multiply across.
        • ( 5 \cdot 7 = 35 ) and ( 6 \cdot 2 = 12 ), resulting in ( \frac{35}{12} ).
      3. Convert the improper fraction to a mixed number.
        • ( 35 \div 12 = 2 ) remainder 11, so the answer is ( 2 \frac{11}{12} ).
      4. Check for simplification; ( \frac{11}{12} ) cannot be simplified further.

Conclusion: This review offered a quick refresher on fraction calculations pertaining to basic operations. For deeper explanations or additional examples, refer to the links provided by Mr. J in the video description.

Feel free to revise these concepts and practice more problems to master fraction operations.

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