Final answer:
To simplify and write the given expressions as proper or mixed fractions, convert the mixed numbers to improper fractions, perform the operations between the fractions and mixed numbers, and simplify the final answer.
Step-by-step explanation:
In order to simplify and write the expression as a proper or mixed fraction, we need to perform the operations between the fractions and mixed numbers.
For each given expression (A, B, C, and D), I will simplify them step by step:
Expression A:
- Convert the mixed numbers to improper fractions: 6 1/4 = 25/4 and 3 14/8 = 30/8.
- Add the fractions: 25/4 + 1/8 = 50/8 + 1/8 = 51/8.
- Convert the improper fraction to a mixed fraction: 51/8 = 6 3/8.
Therefore, the answer to expression A is 6 3/8.
Expression B:
- Convert the mixed numbers to improper fractions: 16 31/2 = 63/2 and 12/20 = 3/5.
- Add the fractions: 63/2 + 3/5 = 315/10 + 6/10 = 321/10.
- Convert the improper fraction to a mixed fraction: 321/10 = 32 1/10.
Therefore, the answer to expression B is 32 1/10.
Expression C:
The expression C is already in its simplest form, so we don't need to perform any further operations. Therefore, the answer to expression C is 3.
Expression D:
- Convert the mixed number to an improper fraction: 18 1/21 = 379/21.
- Subtract the fractions: 379/21 - 10/100 = 379/21 - 1/10.
- Find a common denominator: 21 and 10 have a common denominator of 210.
- Adjust the fractions to have a common denominator: 379/21 - 21/210 = 379/21 - 1/10.
- Subtract the numerators: 379 - 21 = 358.
- Write the answer as a mixed fraction: 358/210 = 1 148/210 = 1 74/105.
Therefore, the answer to expression D is 1 74/105.