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Fractions and GCD

  • Simplifying Ratios:
  • Problem: Express in simplest form the ratio of 36 yards to 40 yards.
  • Solution: Divide both numbers by their greatest common divisor (GCD). In this case, the GCD of 36 and 40 is 4.36
  • 36÷440÷4=91
  • Tip: The simplified ratio is 9:10.

  • Calculating Shares:

    • Problem: A couple earned $8800, and their shares are in the ratio 5:3. Find the smallest and largest shares.
    • Solution:
      • Smallest Share: Use the ratio to divide the earnings.
        • Smallest share fraction: 35+3=38\frac{3}{5+3} = \frac{3}{8}
        • Smallest share amount: 38×8800
      • Largest Share:
        • Largest share fraction: 55+3=58\frac{5}{5+3} = \frac{5}{8}
        • Largest share amount: 58×8800

  • Storage Fee Calculation:

    • Problem: UMA farmers charged $64 for every 900 tons of products. Calculate the storage fee per ton and round to the nearest hundredth.
    • Solution:
      • Storage fee per ton: 64900
      • Rounded fee: $0.07 per ton.

  • Defective Engine Calculation:

    • Problem: An automobile assembly plant produced 243 engines, of which 27 were defective. Find the number of defective engines in 4130 engines produced.
    • Solution:
      • Defective rate: 27243=19\frac{27}{243} = \frac{1}{9}
      • Defective engines in 4130: 19×4130
      • Rounded result: 459 defective engines.

  • Simplifying Time Ratios:

    • Problem: Express in simplest form the ratio of 18 seconds to 15 seconds.
    • Solution: Divide both numbers by their GCD.
      • 1815=18÷315÷3=65\frac{18}{15} = \frac{18 \div 3}{15 \div 3} = \frac{6}{5}
    • Tip: The simplified ratio is 6:5.
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