Express the difference of these two fractions as one fraction in simplest form:
a/15 - b/5
can it be changed to a/15 - 3b/15 ?
To find the difference of two fractions, you need to have a common denominator. In this case, the common denominator is 15.
Now, let's convert the fractions a/15 and b/5 to have a common denominator of 15.
To convert a/15 to have a denominator of 15, we multiply the numerator and denominator by 3:
(a/15) * (3/3) = (3a/45)
To convert b/5 to have a denominator of 15, we multiply the numerator and denominator by 3:
(b/5) * (3/3) = (3b/15)
Now, we can subtract these two fractions:
(3a/45) - (3b/15)
Since the denominators are now the same, we can subtract the numerators directly and keep the denominator the same:
(3a - 3b)/15
Finally, we simplify the fraction by factoring out the common factor of 3 in the numerator:
3(a - b)/15
So, the difference of the fractions a/15 and b/5 expressed as one fraction in simplest form is 3(a - b)/15.
To express the difference of two fractions as one fraction in simplest form, we need to have a common denominator for the fractions.
In this case, the denominators of the given fractions are 15 and 5. Since 15 is a multiple of 5, it is the least common multiple (LCM) of the two denominators.
To rewrite the fractions with a common denominator, we multiply the numerator and denominator of the first fraction (a/15) by 5, and the numerator and denominator of the second fraction (b/5) by 3:
(a/15) * (5/5) - (b/5) * (3/3)
This gives us:
(5a/75) - (3b/15)
Now that the fractions have the same denominator of 15, we can subtract the numerators and keep the denominator:
(5a - 3b)/15
Therefore, the difference of the two fractions (a/15 - b/5) expressed as one fraction in simplest form is (5a - 3b)/15.