Answer :
Sure, let's find the total thickness of the two pieces of wood.
First, we need to add the two mixed numbers: [tex]\( 9 \frac{3}{16} \)[/tex] and [tex]\( 13 \frac{5}{8} \)[/tex].
1. Convert the mixed numbers to improper fractions:
For [tex]\( 9 \frac{3}{16} \)[/tex]:
[tex]\[
9 \frac{3}{16} = 9 + \frac{3}{16} = \frac{9 \times 16}{16} + \frac{3}{16} = \frac{144}{16} + \frac{3}{16} = \frac{147}{16}
\][/tex]
For [tex]\( 13 \frac{5}{8} \)[/tex]:
[tex]\[
13 \frac{5}{8} = 13 + \frac{5}{8} = \frac{13 \times 8}{8} + \frac{5}{8} = \frac{104}{8} + \frac{5}{8} = \frac{109}{8}
\][/tex]
2. Convert the fractions to have the same denominator:
The denominators are 16 and 8. To add them, we need a common denominator. Since 16 is a multiple of 8, we convert [tex]\( \frac{109}{8} \)[/tex] to have a denominator of 16:
[tex]\[
\frac{109}{8} = \frac{109 \times 2}{8 \times 2} = \frac{218}{16}
\][/tex]
3. Add the fractions:
Now we add [tex]\( \frac{147}{16} \)[/tex] and [tex]\( \frac{218}{16} \)[/tex]:
[tex]\[
\frac{147}{16} + \frac{218}{16} = \frac{147 + 218}{16} = \frac{365}{16}
\][/tex]
4. Convert the improper fraction back to a mixed number:
To convert [tex]\( \frac{365}{16} \)[/tex] to a mixed number, divide 365 by 16:
[tex]\[
365 \div 16 = 22 \text{ R } 13
\][/tex]
This means [tex]\( 365 = 16 \times 22 + 13 \)[/tex], so:
[tex]\[
\frac{365}{16} = 22 \frac{13}{16}
\][/tex]
Therefore, the total thickness of the two pieces of wood is:
[tex]\[
\boxed{22 \frac{13}{16} \text{ inches}}
\][/tex]
So, the correct answer is option A.
First, we need to add the two mixed numbers: [tex]\( 9 \frac{3}{16} \)[/tex] and [tex]\( 13 \frac{5}{8} \)[/tex].
1. Convert the mixed numbers to improper fractions:
For [tex]\( 9 \frac{3}{16} \)[/tex]:
[tex]\[
9 \frac{3}{16} = 9 + \frac{3}{16} = \frac{9 \times 16}{16} + \frac{3}{16} = \frac{144}{16} + \frac{3}{16} = \frac{147}{16}
\][/tex]
For [tex]\( 13 \frac{5}{8} \)[/tex]:
[tex]\[
13 \frac{5}{8} = 13 + \frac{5}{8} = \frac{13 \times 8}{8} + \frac{5}{8} = \frac{104}{8} + \frac{5}{8} = \frac{109}{8}
\][/tex]
2. Convert the fractions to have the same denominator:
The denominators are 16 and 8. To add them, we need a common denominator. Since 16 is a multiple of 8, we convert [tex]\( \frac{109}{8} \)[/tex] to have a denominator of 16:
[tex]\[
\frac{109}{8} = \frac{109 \times 2}{8 \times 2} = \frac{218}{16}
\][/tex]
3. Add the fractions:
Now we add [tex]\( \frac{147}{16} \)[/tex] and [tex]\( \frac{218}{16} \)[/tex]:
[tex]\[
\frac{147}{16} + \frac{218}{16} = \frac{147 + 218}{16} = \frac{365}{16}
\][/tex]
4. Convert the improper fraction back to a mixed number:
To convert [tex]\( \frac{365}{16} \)[/tex] to a mixed number, divide 365 by 16:
[tex]\[
365 \div 16 = 22 \text{ R } 13
\][/tex]
This means [tex]\( 365 = 16 \times 22 + 13 \)[/tex], so:
[tex]\[
\frac{365}{16} = 22 \frac{13}{16}
\][/tex]
Therefore, the total thickness of the two pieces of wood is:
[tex]\[
\boxed{22 \frac{13}{16} \text{ inches}}
\][/tex]
So, the correct answer is option A.
