High School

Reduce the given fractions to their lowest terms:

(i) \(\frac{8}{10}\)

(ii) \(\frac{50}{75}\)

(iii) \(\frac{18}{81}\)

(iv) \(\frac{40}{120}\)

(v) \(\frac{105}{70}\)

Answer :

Final answer:

Reducing fractions involves dividing the numerator and denominator by their greatest common divisor (GCD). The reduced fractions of 8/10, 50/75, 18/81, 40/120 and 105/70 are 4/5, 2/3, 2/9, 1/3 and 3/2 or 1.5 respectively.

Explanation:

The process of reducing a fraction to its lowest terms involves finding the greatest common divisor (GCD) of the numerator and denominator and then dividing both by this value. Let's do this for each of your fractions.

  1. 8/10: The GCD of 8 and 10 is 2. Dividing both by 2, we get 4/5.
  2. 50/75: The GCD of 50 and 75 is 25. Dividing both by 25, we get 2/3.
  3. 18/81: The GCD of 18 and 81 is 9. Dividing both by 9, we get 2/9.
  4. 40/120: The GCD of 40 and 120 is 40. Dividing both by 40, we get 1/3.
  5. 105/70: The GCD of 105 and 70 is 35. Dividing both by 35, we get 3/2 or 1.5 in decimal form.

To find the GCD, list the factors of each number and find the largest number that appears in both lists. Then, divide the numerator and denominator by this number to get the reduced fraction.

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