High School

Reduce the following to lowest term:

1. \(\frac{38}{32}\)
2. \(\frac{9}{15}\)
3. \(\frac{21}{35}\)
4. \(\frac{24}{30}\)
5. \(\frac{18}{24}\)

Answer :

To reduce fractions to their lowest terms means to simplify them so that the numerator and the denominator have no common factors other than 1. Here’s how you can do it step-by-step for each fraction:

  1. [tex]\frac{38}{32}[/tex]

    • Find the Greatest Common Divisor (GCD): The GCD of 38 and 32 is 2.
    • Divide both the numerator and the denominator by their GCD:
      [tex]\frac{38}{32} = \frac{38 \div 2}{32 \div 2} = \frac{19}{16}[/tex]
    • So, [tex]\frac{38}{32}[/tex] reduces to [tex]\frac{19}{16}[/tex].

  2. [tex]\frac{9}{15}[/tex]

    • Find the GCD: The GCD of 9 and 15 is 3.
    • Simplify the fraction:
      [tex]\frac{9}{15} = \frac{9 \div 3}{15 \div 3} = \frac{3}{5}[/tex]
    • So, [tex]\frac{9}{15}[/tex] reduces to [tex]\frac{3}{5}[/tex].

  3. [tex]\frac{21}{35}[/tex]

    • Find the GCD: The GCD of 21 and 35 is 7.
    • Simplify the fraction:
      [tex]\frac{21}{35} = \frac{21 \div 7}{35 \div 7} = \frac{3}{5}[/tex]
    • So, [tex]\frac{21}{35}[/tex] reduces to [tex]\frac{3}{5}[/tex].

  4. [tex]\frac{24}{30}[/tex]

    • Find the GCD: The GCD of 24 and 30 is 6.
    • Simplify the fraction:
      [tex]\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}[/tex]
    • So, [tex]\frac{24}{30}[/tex] reduces to [tex]\frac{4}{5}[/tex].

  5. [tex]\frac{18}{24}[/tex]

    • Find the GCD: The GCD of 18 and 24 is 6.
    • Simplify the fraction:
      [tex]\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}[/tex]
    • So, [tex]\frac{18}{24}[/tex] reduces to [tex]\frac{3}{4}[/tex].

By finding the greatest common divisor and dividing both the numerator and the denominator by it, you can reduce any fraction to its simplest form.

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