Question

Simplify 5 1/4a+−2/5c+1/8b−2/5c+3/8b+7 1/4a .(1 point)

Answer 1

To simplify the given expression, we'll combine like terms.

The given expression is:

5 1/4a + (−2/5)c + 1/8b − (2/5)c + 3/8b + 7 1/4a

First, let's convert the mixed numbers to improper fractions in terms of 'a':

5 1/4a can be written as (21/4)a because 5 * 4 + 1 = 21 and similarly, 7 1/4a can be written as (29/4)a.

Now, the expression becomes:

(21/4)a + (−2/5)c + 1/8b − (2/5)c + 3/8b + (29/4)a

Combine like terms (terms with 'a', 'b', and 'c'):

For 'a' terms: (21/4)a + (29/4)a = (21 + 29)/4 * a = 50/4 * a = (25/2)a (since 50/4 simplifies to 25/2)

For 'c' terms: (−2/5)c − (2/5)c = −(2/5 + 2/5)c = −(4/5)c

For 'b' terms: 1/8b + 3/8b = (1 + 3)/8 * b = 4/8 * b = (1/2)b (since 4/8 simplifies to 1/2)

Putting it all together, the simplified expression is:

(25/2)a − (4/5)c + (1/2)b

And that is the simplest form combining like terms.