Answer :
To determine the total thickness of the two pieces of wood, we'll follow these steps:
1. Convert fractions to a common denominator: This will make it easier to add the fractions together.
2. Add the fractions: Once the fractions have a common denominator, we can add them directly.
3. Simplify the resulting fraction (if necessary): This is to express the answer in its simplest form.
4. Compare against the provided options: We will ensure that our final answer matches one of the given multiple-choice options.
### Step 1: Find a common denominator
The pieces of wood have thicknesses of [tex]\( \frac{6}{16} \)[/tex] inches and [tex]\( \frac{7}{8} \)[/tex] inches. The denominators are 16 and 8, respectively. The least common denominator (LCD) of 16 and 8 is 16.
### Step 2: Convert the fractions to a common denominator
- The first piece is already in terms of the denominator 16:
[tex]\[ \frac{6}{16} \][/tex]
- The second piece needs to be converted to have the denominator of 16:
[tex]\[ \frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16} \][/tex]
### Step 3: Add the fractions
Now, add the two fractions with the common denominator:
[tex]\[ \frac{6}{16} + \frac{14}{16} = \frac{6 + 14}{16} = \frac{20}{16} \][/tex]
### Step 4: Simplify the fraction
We can simplify [tex]\( \frac{20}{16} \)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
[tex]\[ \frac{20 \div 4}{16 \div 4} = \frac{5}{4} \][/tex]
### Step 5: Convert to a mixed number (if necessary)
Since [tex]\( \frac{5}{4} \)[/tex] is an improper fraction, we can convert it to a mixed number:
[tex]\[ \frac{5}{4} = 1 \frac{1}{4} \][/tex]
Now we compare this result with the provided options:
- Option 2-A: 1 [tex]\( \frac{1}{4} \)[/tex] inches (this matches our result).
Therefore, the total thickness of the two pieces of wood glued together is:
[tex]\[ \boxed{1 \frac{1}{4} \text{ inches}} \][/tex]
So, the correct answer is:
2-A 1 [tex]\( \frac{1}{4} \)[/tex] Inches
1. Convert fractions to a common denominator: This will make it easier to add the fractions together.
2. Add the fractions: Once the fractions have a common denominator, we can add them directly.
3. Simplify the resulting fraction (if necessary): This is to express the answer in its simplest form.
4. Compare against the provided options: We will ensure that our final answer matches one of the given multiple-choice options.
### Step 1: Find a common denominator
The pieces of wood have thicknesses of [tex]\( \frac{6}{16} \)[/tex] inches and [tex]\( \frac{7}{8} \)[/tex] inches. The denominators are 16 and 8, respectively. The least common denominator (LCD) of 16 and 8 is 16.
### Step 2: Convert the fractions to a common denominator
- The first piece is already in terms of the denominator 16:
[tex]\[ \frac{6}{16} \][/tex]
- The second piece needs to be converted to have the denominator of 16:
[tex]\[ \frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16} \][/tex]
### Step 3: Add the fractions
Now, add the two fractions with the common denominator:
[tex]\[ \frac{6}{16} + \frac{14}{16} = \frac{6 + 14}{16} = \frac{20}{16} \][/tex]
### Step 4: Simplify the fraction
We can simplify [tex]\( \frac{20}{16} \)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
[tex]\[ \frac{20 \div 4}{16 \div 4} = \frac{5}{4} \][/tex]
### Step 5: Convert to a mixed number (if necessary)
Since [tex]\( \frac{5}{4} \)[/tex] is an improper fraction, we can convert it to a mixed number:
[tex]\[ \frac{5}{4} = 1 \frac{1}{4} \][/tex]
Now we compare this result with the provided options:
- Option 2-A: 1 [tex]\( \frac{1}{4} \)[/tex] inches (this matches our result).
Therefore, the total thickness of the two pieces of wood glued together is:
[tex]\[ \boxed{1 \frac{1}{4} \text{ inches}} \][/tex]
So, the correct answer is:
2-A 1 [tex]\( \frac{1}{4} \)[/tex] Inches
