In a motor alignment, the following pieces of steel are used under the base

In a motor alignment, the following pieces of steel are used under the base: one piece 5/16 inch thick, one piece 5/8 inch thick, one piece 5/32 inch thick, and one piece 5/64 inch thick, and one piece 564 inch thick. What is the total thickness of all these pieces?​

The Correct Answer and Explanation is:

To find the total thickness of all the pieces of steel used in the motor alignment, we need to add up the thickness of each individual piece. Let’s first list the thicknesses of the steel pieces:

• One piece is 5/16 inch thick
• One piece is 5/8 inch thick
• One piece is 5/32 inch thick
• One piece is 5/64 inch thick
• One piece is 564 inch thick

Step 1: Convert the fractions to a common denominator

To add these fractions, it is helpful to convert them into fractions with a common denominator. The least common denominator (LCD) of the fractions 16, 8, 32, 64, and 564 is 64. We can now rewrite each fraction with a denominator of 64.

1. 5/16: To convert 5/16 to a denominator of 64, multiply both the numerator and the denominator by 4:
   [
   \frac{5}{16} = \frac{5 \times 4}{16 \times 4} = \frac{20}{64}
   ]
2. 5/8: To convert 5/8 to a denominator of 64, multiply both the numerator and the denominator by 8:
   [
   \frac{5}{8} = \frac{5 \times 8}{8 \times 8} = \frac{40}{64}
   ]
3. 5/32: To convert 5/32 to a denominator of 64, multiply both the numerator and the denominator by 2:
   [
   \frac{5}{32} = \frac{5 \times 2}{32 \times 2} = \frac{10}{64}
   ]
4. 5/64: This fraction is already in terms of 64, so it remains the same:
   [
   \frac{5}{64}
   ]
5. 564 inch: This is a whole number, which can be written as 564/1. To express it as a fraction with a denominator of 64, multiply both the numerator and the denominator by 64:
   [
   \frac{564}{1} = \frac{564 \times 64}{1 \times 64} = \frac{36096}{64}
   ]

Step 2: Add the fractions

Now, we can add all the fractions with a denominator of 64. First, add up the numerators:
[
20 + 40 + 10 + 5 + 36096 = 36171
]

So the total thickness of all the pieces is:
[
\frac{36171}{64} = 565.484375
]

Thus, the total thickness is approximately 565.48 inches.

Explanation:

To calculate the total thickness of the steel pieces, we converted the fractions to have a common denominator (64) and then added them together. By finding a common denominator, we could add the fractions directly, which allows for an accurate total thickness calculation. After adding the fractions, we were able to express the result in decimal form to give a precise answer.