A gardener already has four and one over 2 ft of fencing in his garage. He wants to fence in a square garden for his flowers. The length of one side of the garden will be two and three over four ft. How much more fencing will the gardener need to purchase?

one and one over two ft
two and three over four ft
six and one over two ft
sixteen and one over two ft

If one side measures [tex]2\frac{3}{4}[/tex] ft, and the square garden has 4 sides of equal length, because it's a square, then we must multiply the measure of one side by 4 to find the total length of fence needed:

[tex]4*(2\frac{3}{4})=\\ \\4*(2+\frac{3}{4})=\\ \\(4*2)+(4*\frac{3}{4})=\\ \\8+(\frac{12}{4} )=\\ \\8+3=\\ \\11[/tex]

2. How much more does he need?

The gardener already has [tex]4\frac{1}{2}[/tex] , which equals [tex]4 + \frac{1}{2}[/tex]. Hence, the difference between the amount needed and the amount that the gardeneralready has will give us the remaining amount required. Let's do that:

[tex]11-(4+\frac{1}{2} )=\\ \\11-(\frac{8}{2} +\frac{1}{2} )=\\ \\11-\frac{9}{2}= \\ \\\frac{22}{2} -\frac{9}{2}=\\\\ \frac{13}{2}[/tex]

3. Express your result.

[tex]\frac{13}{2} =\\ \\\frac{2}{2} +\frac{2}{2} +\frac{2}{2} +\frac{2}{2} +\frac{2}{2} +\frac{2}{2} +\frac{1}{2}= \\ \\6+\frac{1}{2}=\\ \\6\frac{1}{2}[/tex]