Final answer:
The value of 13.75a - 7 1/4a when a=1 1/2 is 9 3/4 after converting mixed numbers into improper fractions, finding the common denominator, and simplifying the expression.
Step-by-step explanation:
To simplify and find the value of 13.75a - 7 \frac{1}{4}a when a=1 \frac{1}{2}, we first convert the mixed numbers into improper fractions. The number a can be written as \( \frac{3}{2} \).
Now we need to express the coefficients of \em{a} in a consistent form: 13.75 can be written as 13 \frac{3}{4}, which is \( \frac{55}{4} \), and 7 \frac{1}{4} is \( \frac{29}{4} \). Thus, our equation becomes \( \frac{55}{4} \times \frac{3}{2} - \frac{29}{4} \times \frac{3}{2} \).
After simplifying, we find the common denominator and subtract the fractions: \( \frac{165}{8} - \frac{87}{8} = \frac{78}{8} \), which can be simplified to \( \frac{39}{4} \), or 9 \frac{3}{4} when converted back to a mixed number.
So, the simplified expression is 9 \frac{3}{4}.
Always remember to eliminate terms wherever possible to simplify the algebra, and check the answer to see if it is reasonable.