A man purchased four boards that are each 19 feet to make 17five eighths
 foot boards for his gazebo. Upon​ measuring, he finds they are 18StartFraction 15 Over 16 EndFraction
 ​feet, 19one eighth
 ​feet, 19 ​feet, and 18StartFraction 13 Over 16 EndFraction
 feet. How much must be removed from each board to get 17five eighths
​-foot boards.

We need to calculate how much must be removed from each board to make them all 17 \( \frac{5}{8} \)-foot boards.

Let's start by converting all lengths to fractions for easier calculations.

1. **Target board length**:
   \[
   17 \frac{5}{8} = \frac{141}{8} \text{ feet}
   \]

2. **Board lengths**:

   - **First board**: \( 18 \frac{15}{16} = \frac{303}{16} \)
   - **Second board**: \( 19 \frac{1}{8} = \frac{153}{8} \)
   - **Third board**: \( 19 = \frac{152}{8} \)
   - **Fourth board**: \( 18 \frac{13}{16} = \frac{301}{16} \)

Now, let's calculate how much needs to be removed from each board by subtracting the target length \( \frac{141}{8} \) from each board's current length.

### First board:
\[
18 \frac{15}{16} - 17 \frac{5}{8} = \frac{303}{16} - \frac{141}{8} = \frac{303}{16} - \frac{282}{16} = \frac{21}{16} = 1 \frac{5}{16} \text{ feet}
\]

### Second board:
\[
19 \frac{1}{8} - 17 \frac{5}{8} = \frac{153}{8} - \frac{141}{8} = \frac{12}{8} = 1 \frac{4}{8} = 1 \frac{1}{2} \text{ feet}
\]

### Third board:
\[
19 - 17 \frac{5}{8} = \frac{152}{8} - \frac{141}{8} = \frac{11}{8} = 1 \frac{3}{8} \text{ feet}
\]

### Fourth board:
\[
18 \frac{13}{16} - 17 \frac{5}{8} = \frac{301}{16} - \frac{282}{16} = \frac{19}{16} = 1 \frac{3}{16} \text{ feet}
\]

### Summary of amounts to be removed:
1. **First board**: \( 1 \frac{5}{16} \) feet
2. **Second board**: \( 1 \frac{1}{2} \) feet
3. **Third board**: \( 1 \frac{3}{8} \) feet
4. **Fourth board**: \( 1 \frac{3}{16} \) feet

Would you like further details or clarifications?

Here are 5 related questions to think about:
1. How do you subtract mixed fractions?
2. Can you explain why converting to improper fractions helps in calculations?
3. How would rounding affect the measurements?
4. What is the importance of precise measurements in construction?
5. How would you convert between feet and inches for these measurements?

**Tip**: When dealing with fractional measurements, always convert to improper fractions for easier arithmetic operations!

A man purchased four boards that are each 19 feet to make 17 5/8 foot boards for his gazebo. Upon measuring, he finds they are 18 15/16 feet, 19 1/8 feet, 19 feet, and 18 13/16 feet. How much must be removed from each board to get 17 5/8 foot boards?

Find out how much needs to be removed from boards of different lengths to achieve 17 5/8-foot boards. This problem involves subtracting mixed numbers, converting to improper fractions, and performing precise measurements. Suitable for students in Grades 6-8.

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