To find the total width of 28 2-by-4 pieces of wood, each with a width of [tex]\(3 \frac{1}{2}\)[/tex] inches when laid side-by-side, we will proceed as follows:
1. Convert the mixed number to an improper fraction:
The width of one board is given as [tex]\(3 \frac{1}{2}\)[/tex] inches. We can convert this mixed number to an improper fraction.
[tex]\[
3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \text{ inches}
\][/tex]
2. Multiply by the number of boards:
We are laying 28 boards side-by-side. To find the total width, we multiply the width of one board by the number of boards.
[tex]\[
\frac{7}{2} \times 28
\][/tex]
3. Perform the multiplication:
Simplify the multiplication as follows:
[tex]\[
\frac{7}{2} \times 28 = 7 \times 14 = 98 \text{ inches}
\][/tex]
The total width of the 28 boards laid side-by-side is 98 inches.
4. Convert to a different fraction form:
We can express 98 inches in different fraction forms. One such form is:
[tex]\[
98 = \frac{196}{2} \text{ inches}
\][/tex]
Hence, we see that the total width of the 28 2-by-4s laid side-by-side can be represented in various forms, such as:
- [tex]\( 98 \text{ inches} \)[/tex]
- [tex]\( \frac{196}{2} \text{ inches} \)[/tex]
And as simplification is requested in some formats:
- Simplified form as an improper fraction: [tex]\( 98 \text{ inches} \)[/tex]
Therefore, the total width of 28 2-by-4s laid side-by-side is:
98 inches
or, equivalently,
[tex]\( \frac{196}{2} \text{ inches} \)[/tex].
