Answer:
18/35 inches of pipe must be removed
Explanation:
Since the 4/5 inch pipe is shortened to 2/7 inches, we can use the following steps determine how many inches of pipe (x):
Step 1: Write the equation and find the least common denominator (LCD) OF 4/5 and 2/7:
4/5 - x = 2/7
- Having two fractions with the same denominator allows us to add or subtract straight across and the LCD allows us to obtain the same denominator.
We find the LCD by multiplying the two denominators:
LCD = 5 * 7
LCD = 35
Step 1: Make 4/5 and 2/7 fractions whose denominators are 35:
- Turning 4/5 into a fraction whose denominator is 35:
5 * 7 = 35, so we multiply both the numerator and denominator by 7:
(4 * 7) / (5 * 7) = 28/35
- Turning 2/7 into a fraction whose denominator is 35:
7 * 5 = 35, so we multiply both the numerator and denominator by 5:
(2 * 5)/ (7 * 5) = 10/35
Thus, our equation with our new fractions is given by:
28/35 - x = 10/35
Step 2: Subtract 28/35 from both sides:
(28/35 - x = 10/35) - 28/35
-x = -18/35
Step 3: Divide both sides by -1 to solve for x:
(-x = -18/35) / -1
x = 18/35
Therefore, in order for the 4/5 inch pipe to be shortened to 2/7 inches, 18/35 inches of pipe must be removed.