Name the property used in each of the following: a) 3/8 + 5/12 = 5/12 + 3/8 b) -5/8 + 0 = -5/8 c) -3/11 + 3/11 = 0 d) -5/4 * 4/-5 = 1

Potatoes: $2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{5}{2}$ kg
Onions: $3 \frac{1}{4} = \frac{(3 \times 4) + 1}{4} = \frac{13}{4}$ kg

Total vegetables = $\frac{5}{2} + \frac{13}{4}$
Find a common denominator, which is 4.
$\frac{5}{2} = \frac{5 \times 2}{2 \times 2} = \frac{10}{4}$
Total vegetables = $\frac{10}{4} + \frac{13}{4} = \frac{10+13}{4} = \frac{23}{4}$ kg

$\frac{23}{4} = 5 \frac{3}{4}$ kg

Manish bought \boxed{\text{5 \frac{3}{4} kg}} of vegetables.

8. The sides of a triangular field are $4 \frac{1}{2}$ cm, $4 \frac{3}{4}$ cm and $5 \frac{1}{8}$ cm. Find its perimeter.

Side 1: $4 \frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{9}{2}$ cm
Side 2: $4 \frac{3}{4} = \frac{(4 \times 4) + 3}{4} = \frac{19}{4}$ cm
Side 3: $5 \frac{1}{8} = \frac{(5 \times 8) + 1}{8} = \frac{41}{8}$ cm

Perimeter = $\frac{9}{2} + \frac{19}{4} + \frac{41}{8}$
Find a common denominator, which is the LCM of 2, 4, and 8, which is 8.
$\frac{9}{2} = \frac{9 \times 4}{2 \times 4} = \frac{36}{8}$
$\frac{19}{4} = \frac{19 \times 2}{4 \times 2} = \frac{38}{8}$
Perimeter = $\frac{36}{8} + \frac{38}{8} + \frac{41}{8} = \frac{36+38+41}{8} = \frac{115}{8}$ cm

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