High School

Which of these fractions are equivalent to \( \frac{6}{15} \)?

\( \frac{10}{16} \)
\( \frac{12}{21} \)
\( \frac{32}{40} \)
\( \frac{8}{16} \)

Answer :

To find which of the given fractions are equivalent to [tex]\frac{6}{15}[/tex], we need to simplify each fraction to see if they reduce to the same fraction.


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


    • The greatest common divisor (GCD) of 6 and 15 is 3.

    • Divide both the numerator and the denominator by 3:
      [tex]\frac{6 \div 3}{15 \div 3} = \frac{2}{5}[/tex]

    • So, [tex]\frac{6}{15} = \frac{2}{5}[/tex].



  2. Checking [tex]\frac{10}{16}[/tex]:


    • The GCD of 10 and 16 is 2.

    • Divide both numerator and denominator by 2:
      [tex]\frac{10 \div 2}{16 \div 2} = \frac{5}{8}[/tex]

    • [tex]\frac{10}{16} \neq \frac{2}{5}[/tex].



  3. Checking [tex]\frac{12}{21}[/tex]:


    • The GCD of 12 and 21 is 3.

    • Divide both numerator and denominator by 3:
      [tex]\frac{12 \div 3}{21 \div 3} = \frac{4}{7}[/tex]

    • [tex]\frac{12}{21} \neq \frac{2}{5}[/tex].



  4. Checking [tex]\frac{32}{40}[/tex]:


    • The GCD of 32 and 40 is 8.

    • Divide both numerator and denominator by 8:
      [tex]\frac{32 \div 8}{40 \div 8} = \frac{4}{5}[/tex]

    • [tex]\frac{32}{40} \neq \frac{2}{5}[/tex].



  5. Checking [tex]\frac{8}{16}[/tex]:


    • The GCD of 8 and 16 is 8.

    • Divide both numerator and denominator by 8:
      [tex]\frac{8 \div 8}{16 \div 8} = \frac{1}{2}[/tex]

    • [tex]\frac{8}{16} \neq \frac{2}{5}[/tex].




None of the given fractions are equivalent to [tex]\frac{6}{15}[/tex] after simplification.

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