High School

Reduce the following fractions to their lowest terms:

1. \(\frac{15}{20} = \frac{15 \div 5}{20 \div 5} = \frac{3}{4}\)
2. \(\frac{45}{60} = \)
3. \(\frac{12}{20} = \)
4. \(\frac{60}{80} = \)
5. \(\frac{125}{500} = \)
6. \(\frac{15}{75} = \)
7. \(\frac{70}{85} = \)
8. \(\frac{36}{48} = \)

Answer :

To reduce a fraction to its lowest terms, we need to find the greatest common divisor (GCD) of the numerator and the denominator and then divide both by that number. Here's how to solve each fraction step-by-step:

  1. [tex]\frac{15}{20} = \frac{15 \div 5}{20 \div 5} = \frac{3}{4}[/tex]

  2. [tex]\frac{45}{60}[/tex]:

    • Find the GCD of 45 and 60. The GCD is 15.
    • Divide both numerator and denominator by 15: [tex]\frac{45 \div 15}{60 \div 15} = \frac{3}{4}[/tex].

  3. [tex]\frac{12}{20}[/tex]:

    • Find the GCD of 12 and 20. The GCD is 4.
    • Divide both numerator and denominator by 4: [tex]\frac{12 \div 4}{20 \div 4} = \frac{3}{5}[/tex].

  4. [tex]\frac{60}{80}[/tex]:

    • Find the GCD of 60 and 80. The GCD is 20.
    • Divide both numerator and denominator by 20: [tex]\frac{60 \div 20}{80 \div 20} = \frac{3}{4}[/tex].

  5. [tex]\frac{125}{500}[/tex]:

    • Find the GCD of 125 and 500. The GCD is 125.
    • Divide both numerator and denominator by 125: [tex]\frac{125 \div 125}{500 \div 125} = \frac{1}{4}[/tex].

  6. [tex]\frac{15}{75}[/tex]:

    • Find the GCD of 15 and 75. The GCD is 15.
    • Divide both numerator and denominator by 15: [tex]\frac{15 \div 15}{75 \div 15} = \frac{1}{5}[/tex].

  7. [tex]\frac{70}{85}[/tex]:

    • Find the GCD of 70 and 85. The GCD is 5.
    • Divide both numerator and denominator by 5: [tex]\frac{70 \div 5}{85 \div 5} = \frac{14}{17}[/tex].

  8. [tex]\frac{36}{48}[/tex]:

    • Find the GCD of 36 and 48. The GCD is 12.
    • Divide both numerator and denominator by 12: [tex]\frac{36 \div 12}{48 \div 12} = \frac{3}{4}[/tex].

Always ensure to find the greatest common divisor correctly to reduce fractions to their simplest form.

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