sam has purchased 4 sections of fences that measure 22 1/2 feet long.he needs 2 sections that measure 19 3/4 for the length and 2 sections that measure 15 3/4 feet each for the width how much fence will he have left.

New total length will be 22.5 + 19.75 = 42.25 feet

New total width will be 22.5 + 15.75 = 38.25 feet.

New (perimeter) fence length will be
2*42.25 + 2*38.25 = 161 feet.

To calculate the amount of fence Sam will have left, we need to find the total length and the total width of the fence he will be using. Then, we subtract the sum of the lengths and widths purchased from the total amount of fence.

First, let's calculate the total length of the fence. Sam has purchased 4 sections of fence, each measuring 22 1/2 feet. To find the total length, we multiply the length of each section by the number of sections:

Total length = 4 * 22 1/2 feet

To multiply a whole number by a fraction, we convert the whole number to a fraction with a denominator of 1 and then multiply:

Total length = (4 * 22)/1 + (4 * 1/2) feet
Total length = 88/1 + 4/2 feet
Total length = 88 + 2 feet
Total length = 90 feet

Next, let's calculate the total width of the fence. Sam needs 2 sections that measure 19 3/4 feet each and 2 sections that measure 15 3/4 feet each. To find the total width, we add the length of each section:

Total width = 2 * 19 3/4 feet + 2 * 15 3/4 feet

Similarly, to multiply a whole number by a fraction, we convert the whole number to a fraction with a denominator of 1 and then multiply:

Total width = (2 * 19) + (2 * 3/4) feet + (2 * 15) + (2 * 3/4) feet
Total width = 38 + 2 1/2 feet + 30 + 2 1/2 feet
Total width = 68 + 5 feet
Total width = 73 feet

Finally, to calculate the remaining fence, we subtract the total length and the total width from the total amount of fence Sam initially purchased:

Remaining fence = Total fence - (Total length + Total width)
Remaining fence = 90 feet - (90 feet + 73 feet)
Remaining fence = 90 feet - 163 feet
Remaining fence = -73 feet

Since the result is negative, it indicates that Sam does not have enough fence to complete the desired dimensions.