High School

Reduce these fractions to their lowest terms:

a) 4/6
b) 10/12
c) 6/9
d) 12/16
e) 18/24
f) 32/40
g) -45/54
h) 20/40
i) 120/150
j) 2400/2800
k) 3600/27000
l) 4200/63000

Answer :

To reduce fractions to their lowest terms, you need to divide both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). Here’s how you can do this for each fraction:


  1. [tex]\frac{4}{6}[/tex]:


    • The GCD of 4 and 6 is 2.

    • Divide both by 2: [tex]\frac{4 \div 2}{6 \div 2} = \frac{2}{3}[/tex]



  2. [tex]\frac{10}{12}[/tex]:


    • The GCD of 10 and 12 is 2.

    • Divide both by 2: [tex]\frac{10 \div 2}{12 \div 2} = \frac{5}{6}[/tex]



  3. [tex]\frac{6}{9}[/tex]:


    • The GCD of 6 and 9 is 3.

    • Divide both by 3: [tex]\frac{6 \div 3}{9 \div 3} = \frac{2}{3}[/tex]



  4. [tex]\frac{12}{16}[/tex]:


    • The GCD of 12 and 16 is 4.

    • Divide both by 4: [tex]\frac{12 \div 4}{16 \div 4} = \frac{3}{4}[/tex]



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


    • The GCD of 18 and 24 is 6.

    • Divide both by 6: [tex]\frac{18 \div 6}{24 \div 6} = \frac{3}{4}[/tex]



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


    • The GCD of 32 and 40 is 8.

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



  7. [tex]\frac{-45}{54}[/tex]:


    • The GCD of 45 and 54 is 9.

    • Divide both by 9: [tex]\frac{-45 \div 9}{54 \div 9} = \frac{-5}{6}[/tex]



  8. [tex]\frac{20}{40}[/tex]:


    • The GCD of 20 and 40 is 20.

    • Divide both by 20: [tex]\frac{20 \div 20}{40 \div 20} = \frac{1}{2}[/tex]



  9. [tex]\frac{120}{150}[/tex]:


    • The GCD of 120 and 150 is 30.

    • Divide both by 30: [tex]\frac{120 \div 30}{150 \div 30} = \frac{4}{5}[/tex]



  10. [tex]\frac{2400}{2800}[/tex]:


    • The GCD of 2400 and 2800 is 400.

    • Divide both by 400: [tex]\frac{2400 \div 400}{2800 \div 400} = \frac{6}{7}[/tex]



  11. [tex]\frac{3600}{27000}[/tex]:


    • The GCD of 3600 and 27000 is 900.

    • Divide both by 900: [tex]\frac{3600 \div 900}{27000 \div 900} = \frac{4}{30}[/tex], which further reduces to [tex]\frac{2}{15}[/tex]



  12. [tex]\frac{4200}{63000}[/tex]:


    • The GCD of 4200 and 63000 is 2100.

    • Divide both by 2100: [tex]\frac{4200 \div 2100}{63000 \div 2100} = \frac{2}{30}[/tex], which further reduces to [tex]\frac{1}{15}[/tex]




Each of these fractions is now simplified to its lowest terms!

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