Answer :
To determine the total thickness of the two pieces of wood, we need to add their individual thicknesses together.
Here are the steps to solve this problem:
1. Identify the given thicknesses of the two pieces of wood:
- The thickness of the first piece of wood is [tex]\( \frac{5}{16} \)[/tex] inches.
- The thickness of the second piece of wood is [tex]\( \frac{7}{8} \)[/tex] inches.
2. Convert the fractions to a common denominator if necessary:
- To add these fractions together, we need a common denominator. The denominators here are 16 and 8. The least common denominator (LCD) is 16.
3. Convert the fractions:
- The first piece [tex]\( \frac{5}{16} \)[/tex] is already expressed with the denominator of 16.
- Convert the second piece [tex]\( \frac{7}{8} \)[/tex] to have the same denominator:
[tex]\[ \frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16} \][/tex]
4. Add the fractions:
- Now, add [tex]\( \frac{5}{16} \)[/tex] and [tex]\( \frac{14}{16} \)[/tex]:
[tex]\[ \frac{5}{16} + \frac{14}{16} = \frac{5 + 14}{16} = \frac{19}{16} \][/tex]
5. Express the fraction as a mixed number (if needed):
- Divide the numerator by the denominator to get the mixed number:
[tex]\[ \frac{19}{16} = 1 + \frac{3}{16} = 1\frac{3}{16} \][/tex]
6. Convert the mixed number to a decimal form (optional):
- [tex]\( 1\frac{3}{16} \)[/tex] can be written in decimal form as 1.1875 inches.
7. Compare this result to the given options to find the correct answer.
- A: [tex]\( \frac{11}{4} = 2.75 \)[/tex] inches
- B: [tex]\( \frac{13}{16} = 0.8125 \)[/tex] inches
- C: [tex]\( \frac{11}{8} = 1.375 \)[/tex] inches
- D: [tex]\( \frac{15}{8} = 1.875 \)[/tex] inches
The result we calculated, 1.1875 inches, matches none of the provided options as is, but can be confirmed as an exact fractional answer of [tex]\( \frac{19}{16} \)[/tex]. Notice that none of the answers misuse this form incorrectly either.
Therefore, the total thickness of the two pieces of wood glued together is [tex]\( 1\frac{3}{16} \)[/tex] inches, which simplifies accurately to 1.1875 inches, neither aligning with any of the given operators exactly in practical problem context they simulate theoretical practice.
Here are the steps to solve this problem:
1. Identify the given thicknesses of the two pieces of wood:
- The thickness of the first piece of wood is [tex]\( \frac{5}{16} \)[/tex] inches.
- The thickness of the second piece of wood is [tex]\( \frac{7}{8} \)[/tex] inches.
2. Convert the fractions to a common denominator if necessary:
- To add these fractions together, we need a common denominator. The denominators here are 16 and 8. The least common denominator (LCD) is 16.
3. Convert the fractions:
- The first piece [tex]\( \frac{5}{16} \)[/tex] is already expressed with the denominator of 16.
- Convert the second piece [tex]\( \frac{7}{8} \)[/tex] to have the same denominator:
[tex]\[ \frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16} \][/tex]
4. Add the fractions:
- Now, add [tex]\( \frac{5}{16} \)[/tex] and [tex]\( \frac{14}{16} \)[/tex]:
[tex]\[ \frac{5}{16} + \frac{14}{16} = \frac{5 + 14}{16} = \frac{19}{16} \][/tex]
5. Express the fraction as a mixed number (if needed):
- Divide the numerator by the denominator to get the mixed number:
[tex]\[ \frac{19}{16} = 1 + \frac{3}{16} = 1\frac{3}{16} \][/tex]
6. Convert the mixed number to a decimal form (optional):
- [tex]\( 1\frac{3}{16} \)[/tex] can be written in decimal form as 1.1875 inches.
7. Compare this result to the given options to find the correct answer.
- A: [tex]\( \frac{11}{4} = 2.75 \)[/tex] inches
- B: [tex]\( \frac{13}{16} = 0.8125 \)[/tex] inches
- C: [tex]\( \frac{11}{8} = 1.375 \)[/tex] inches
- D: [tex]\( \frac{15}{8} = 1.875 \)[/tex] inches
The result we calculated, 1.1875 inches, matches none of the provided options as is, but can be confirmed as an exact fractional answer of [tex]\( \frac{19}{16} \)[/tex]. Notice that none of the answers misuse this form incorrectly either.
Therefore, the total thickness of the two pieces of wood glued together is [tex]\( 1\frac{3}{16} \)[/tex] inches, which simplifies accurately to 1.1875 inches, neither aligning with any of the given operators exactly in practical problem context they simulate theoretical practice.
