Tamara J. answered • 12/05/12

Math Tutoring - Algebra and Calculus (all levels)

When simplifying fractions, you want to find the greatest common factor (gcf) between the numerator and the denominator, then divide both the numerator and the denominator of the fraction in question by this gcf.

Simplify 60/56 :

Factors of 60 ==> 1, 2, 3, **4**, 5, 6, 10, 12, 15, 20, 30 60

Factors of 56 ==> 1, 2, **4**, 7, 8, 14, 28, 56

We find that the greatest common factor between 60 and 56 is 4. Now we divide both numerator (60) and the denominator (56) by their gcf (4), to simplify the fraction:

60 / 56 = (60/4) / (56/4) = 15 / 14

Thus, the simplification of 60/56 yields the fraction 15/14.

When adding/subtracting fractions with different denominators, you need to change the fractions in a way such that all the fractions share a common denominator. To do this, we first need to find the least common denominator (or, the least common multiple) between the denominators:

(5/8)x - (7/12) ==> the denominators are 8 and 12

Multiples of 8: 8, 16, **24**, 32, 40, 48, 56, 64, ......

Multiples of 12: 12, **24**, 36, 48, 60, 72, 84, 96, ......

We find that the least common multiple of 8 and 12 is 24. So we change each fraction in the problem by multiplying the denominator by a number that will yield a denominator of 24, then multiplying the numerator by that same number so as to not change the value of the fraction. After we have fractions with common denominators, we can add their numerators:

(5/8)x - (7/12) ==> (5x/8) - (7/12)

= (3/3)*(5x/8) - (7/12)*(2/2)

= (3*5x / 3*8) - (7*2 / 12*2)

= (15x/24) - (14/24)

= (15x - 14)/24