Divide the sum of -13/8 and 5/12 by their difference
(-13/8 + 5/12)/(-13/8 - 5/12)
= (-39+10)/(-39-10)
= 29/49
To divide the sum of two fractions by their difference, we need to first find the sum of the fractions and then the difference. Let's calculate step by step.
Step 1: Find the sum of the fractions.
The first fraction is -13/8, and the second fraction is 5/12.
To find their sum, we need a common denominator for both fractions. In this case, we can use the least common multiple (LCM) of 8 and 12, which is 24.
Converting -13/8 to a fraction with a denominator of 24:
-13/8 = (-13/8) * (3/3) = -39/24
Converting 5/12 to a fraction with a denominator of 24:
5/12 = (5/12) * (2/2) = 10/24
Now we can add the two fractions:
-39/24 + 10/24 = -29/24
Step 2: Find the difference of the fractions.
To find the difference, subtract the second fraction from the first fraction:
-13/8 - 5/12
To subtract the fractions, we need a common denominator. Again, using the LCM of 8 and 12 (which is 24), we can convert the fractions:
Converting -13/8 to a fraction with denominator 24:
-13/8 = (-13/8) * (3/3) = -39/24
Converting 5/12 to a fraction with denominator 24:
5/12 = (5/12) * (2/2) = 10/24
Now we can subtract the two fractions:
-39/24 - 10/24 = -49/24
Step 3: Divide the two results.
To divide the sum (-29/24) by the difference (-49/24), we multiply the sum by the reciprocal of the difference:
(-29/24) / (-49/24) = (-29/24) * (24/-49)
Simplifying the fraction:
(-29/24) * (24/-49) = (-29/1) * (1/-49) = 29/49
Therefore, the result of dividing the sum of -13/8 and 5/12 by their difference is 29/49.