Question

what is the value of this expression when d = 4 7/8 and f = 3 1/2
6 ( d - f) +f

Answer 1

To evaluate the expression \( 6(d - f) + f \) when \( d = 4 \frac{7}{8} \) and \( f = 3 \frac{1}{2} \), we first need to express \( d \) and \( f \) as improper fractions.

1. Convert \( d = 4 \frac{7}{8} \):
\[
d = 4 + \frac{7}{8} = \frac{32}{8} + \frac{7}{8} = \frac{39}{8}
\]

2. Convert \( f = 3 \frac{1}{2} \):
\[
f = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2}
\]

Next, we need to substitute \( d \) and \( f \) into the expression \( 6(d - f) + f \).

3. Calculate \( d - f \):
\[
d - f = \frac{39}{8} - \frac{7}{2}
\]
To subtract these fractions, we need a common denominator:
\[
\frac{7}{2} = \frac{7 \times 4}{2 \times 4} = \frac{28}{8}
\]
Now we can subtract:
\[
d - f = \frac{39}{8} - \frac{28}{8} = \frac{39 - 28}{8} = \frac{11}{8}
\]

4. Now calculate \( 6(d - f) \):
\[
6(d - f) = 6 \times \frac{11}{8} = \frac{66}{8} = \frac{33}{4}
\]

5. Now add \( f \) to this result:
\[
f = \frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4}
\]
Now add \( \frac{33}{4} \) and \( \frac{14}{4} \):
\[
6(d - f) + f = \frac{33}{4} + \frac{14}{4} = \frac{33 + 14}{4} = \frac{47}{4}
\]

Finally, we can convert \( \frac{47}{4} \) back to a mixed number:
\[
\frac{47}{4} = 11 \frac{3}{4}
\]

Thus, the value of the expression \( 6(d - f) + f \) when \( d = 4 \frac{7}{8} \) and \( f = 3 \frac{1}{2} \) is \( \boxed{11 \frac{3}{4}} \).