In order to express 6/10 as a fraction, we need to simplify it to its lowest terms. This means that we need to find the greatest common factor of the numerator and denominator, and then divide both by that factor.
To find the greatest common factor, we can factor the numerator and denominator into their prime factors. The prime factors of 6 are 2 and 3, while the prime factors of 10 are 2 and 5. We can then find the greatest common factor by finding the intersection of these sets of prime factors, which is just 2.
Now that we have found the greatest common factor, we can divide both the numerator and denominator by 2 to simplify the fraction. This gives us:
6/10 = (6 ÷ 2) / (10 ÷ 2) = 3/5
So 6/10 is equivalent to 3/5.
In general, to express a fraction as its simplest form, we need to find the greatest common factor of the numerator and denominator, and then divide both by that factor. This process is called simplification or reduction.
For example, let’s say we want to simplify the fraction 12/24. The prime factors of 12 are 2, 2, and 3, while the prime factors of 24 are 2, 2, 2, and 3. The greatest common factor of 12 and 24 is 2 × 2 × 3 = 12. We can then divide both the numerator and denominator by 12 to simplify the fraction:
12/24 = (12 ÷ 12) / (24 ÷ 12) = 1/2
So 12/24 is equivalent to 1/2.
Another example is 25/35. The prime factors of 25 are 5 and 5, while the prime factors of 35 are 5 and 7. The greatest common factor of 25 and 35 is 5. We can then divide both the numerator and denominator by 5 to simplify the fraction:
25/35 = (25 ÷ 5) / (35 ÷ 5) = 5/7
So 25/35 is equivalent to 5/7.
In summary, to express a fraction in its simplest form, we need to find the greatest common factor of the numerator and denominator, and then divide both by that factor. This process allows us to write the fraction with the fewest number of terms and makes it easier to compare and perform operations with other fractions.