Question

15 POINTS!

The length of Rosie's garden is 21 1/4 feet. fencing comes in pieces 2 1/8 long.


Part A: How many pieces of fencing will Rosie need along the length of her garden?


Part B: For each piece of fencing, 4 stakes are used to secure it in place. The stakes are equally spaced along the fencing piece, with one stake at each end. How far apart are the stakes on one piece of fencing.?

Answer 1

Part A. 10; Part B. 17/24 ft or 8½ in

Explanation:

Part A: Pieces of fencing

Pieces of fencing = length of fence/length of each piece = 21¼/2⅛

Convert each mixed number to an improper fraction

21¼/2⅛ = (85/4)/(17/8)

Invert the denominator and change division to multiplication

(85/4)/(17/8) = (85/4) × (8/17)

Cancel the 4s

(85/4) × (8/17) = 85 × (2/17)

Cancel the 17s

85 × (2/17) = 5 × 2 = 10

Rosie will need 10 pieces of fencing.

Part 2. Distance between stakes

If each piece of fencing has a stake at each end and two in between, it is divided into thirds.

Distance between stakes = 2⅛ ft/3

Convert the mixed number to an improper fraction

2⅛/3 = (17/8)/(3/1)

Invert the denominator and convert division to multiplication

(17/8)/(3/1) = (17/8) × ⅓

Multiply numerators and denominators

(17/8) × ⅓ = 17/24

The stakes are 17/24 ft apart.

Convert feet to inches

17/24 ft × 12 in/1 ft = 17/2 in = 8½ in

The stakes are 8½ in apart.