Question

combine: 2/5-1/4

Answer 1

You need to find a common denominator and rewrite the fractions with it before subtracting. The common denominator can be found by computing the least common multiple of all of the denominators. Or you can find a common multiple that may not be the least common multiple in many cases, but doesn't require computing the least common multiple: just multiply all of the denominators together. Once you know what the common denominator will be, multiply each fraction by 1 expressed as n/n where n is the value that multiplied by the denominator will give the common denominator.

An example:

\[\frac{1}{3} + \frac{2}{7}\]Multiply 3 and 7 to get 21, our common denominator. Next, multiply each fraction by n/n where n is 21/denominator.
\[\frac{1}{3}*\frac{7}{7} + \frac{2}{7}*\frac{3}{3} = \frac{7}{21} + \frac{6}{21} = \frac{6+7}{21} = \frac{13}{21}\]

If you want to find the least common multiple, factor all of the denominators to their prime factors. The least common multiple will be the product of the highest powers of each different factor.

An example:
Find the LCM of 5, 25, 40
Factor 5: 5
Factor 25: 5*5 = 5^2
Factor 40: 2*2*2*5 = 2^3*5

LCM = 2^3*5^2 = 8*25 = 200.

Check by listing multiples:

5: 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200
25: 25 50 75 100 125 150 175 200
40: 40 80 120 160 200
200 is the first number that appears in all 3 lists