what must be added to 6 3/5 to produce 3 5/6?
6 3 / 5 = 6 * 30 / 30 + 3 * 6 / 30 =
180 / 30 + 18 / 30 = 198 / 30
3 5 / 6 = 3 * 30 / 30 + 5 * 5 / 30 =
90 /30 + 25 / 30 = 115 / 30
6 3 / 5 + x = 3 5 / 6
198 / 30 + x = 115 / 30
x = 115 / 30 - 198 / 30
x = -83 / 30
33/5 + x = 23/6
times 30
198 + 30x = 115
30x = -83
x = -83/30
To find out what must be added to 6 3/5 to produce 3 5/6, we need to subtract 6 3/5 from 3 5/6. Let's break down the process step-by-step:
Step 1: Convert both mixed numbers to improper fractions:
6 3/5 = (6 * 5 + 3) / 5 = 33/5
3 5/6 = (3 * 6 + 5) / 6 = 23/6
Step 2: Subtract 33/5 from 23/6:
23/6 - 33/5
To subtract fractions with different denominators, we need to find a common denominator. The common multiple of 6 and 5 is 30, so we'll use that as the common denominator.
Step 3: Convert the fractions to have a common denominator:
23/6 * 5/5 = 115/30
33/5 * 6/6 = 198/30
Step 4: Subtract the fractions:
115/30 - 198/30 = -83/30
The result is -83/30. Therefore, to produce 3 5/6 from 6 3/5, we need to add -83/30.