521−243+462=
To solve this problem, we will perform the following steps:
- Convert each mixed fraction into an improper fraction.
- Find a common denominator for these fractions.
- Perform the subtraction and addition operations.
- Convert the result back into a mixed number.
- Simplify the final answer if necessary.
Let’s proceed with these steps.
Step 1: Convert to improper fractions
For 521:
521=25×2+1=211
For 243:
243=42×4+3=411
For 462 (simplified as 431):
462=431=34×3+1=313
Step 2: Find a common denominator
The denominators are 2, 4, and 3. The least common multiple of these is 12.
Convert each fraction:
211=2×611×6=1266
411=4×311×3=1233
313=3×413×4=1252
Step 3: Perform the operations
First, perform the subtraction:
1266−1233=1233
Now, add 1233 and 1252:
1233+1252=1285
Step 4: Convert back to a mixed number
1285 as a mixed number is 7121 because:
1285=7 remainder 1, thus 7121.
Step 5: Simplify
The fraction 121 is already in its simplest form.
Therefore, the correct answer is 7121.