Divide the sum of 78/12 and 8/3 by their difference
(78/12 + 8/3)
------------------- = 55/23
(78/12 - 8/3)
78/12+8/3=110/12
78/12-8/3=46/12
110/12=46/12
110/12÷46/12
110/12×12/46
55/23 answer
to go into detail:
78/12 + 32/12 = 110/12
78/12 - 32/12 = 46/12
so what we really have is
110/46 = 55/23
What don't you understand about Steve's answer?
To divide the sum of two fractions by their difference, we first need to find the sum and difference of the fractions.
Let's start by finding the sum of the fractions:
78/12 + 8/3
To add fractions, we need to have the same denominator. Since 12 and 3 do not have a common denominator, let's find the least common multiple (LCM) of 12 and 3, which is 12.
So, we need to convert both fractions to have a denominator of 12:
78/12 + 8/3 = (78/12) * (1/1) + (8/3) * (4/4)
= 78/12 + 32/12
= (78 + 32)/12
= 110/12
Now, let's find the difference of the fractions:
78/12 - 8/3
To subtract fractions, we also need a common denominator. Since 12 and 3 do not have a common denominator, let's use the same LCM, which is 12.
Converting both fractions to have a denominator of 12, we get:
78/12 - 8/3 = (78/12) * (1/1) - (8/3) * (4/4)
= 78/12 - 32/12
= (78 - 32)/12
= 46/12
Now that we have the sum and difference of the fractions, we can divide them:
(110/12) / (46/12)
To divide fractions, we invert the divisor and multiply:
(110/12) / (46/12) = (110/12) * (12/46)
= (110 * 12) / (12 * 46)
= 1320/552
The fraction 1320/552 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 8:
1320/552 = (1320/8) / (552/8)
= 165/69
So, the result of dividing the sum of 78/12 and 8/3 by their difference is 165/69.