Simplify the following
i)
40
2700 30
ii)
5
6
5
2 3
2
2
4 4
iii)
3
2 3
( 5)
4 ( 10)
iv)
2 2 1/ 2 1/ 2 3
To simplify the given expressions, we need to perform the necessary arithmetic operations and simplify any fractions. Let's simplify each expression one by one:
i)
To simplify 40 / (2700 / 30):
Step 1: Divide 2700 by 30: 2700 / 30 = 90
Step 2: Divide 40 by 90: 40 / 90 = 4/9
Therefore, the simplified expression is 4/9.
ii)
To simplify 5 / (6 / 5) * (2 / 3) * (2 / 2) * (4 / 4):
Step 1: Divide 6 by 5: 6 / 5 = 6/5
Step 2: Multiply 5 by 6/5: 5 * 6/5 = 6
Step 3: Multiply 6 by 2/3: 6 * 2/3 = 4
Step 4: Multiply 4 by 2/2: 4 * 2/2 = 4
Step 5: Multiply 4 by 4/4: 4 * 4/4 = 4
Therefore, the simplified expression is 4.
iii)
To simplify 3 * (2 / 3) + (5 / 4) * (10 / 4):
Step 1: Multiply 2 by 3/2: 2 * 3/2 = 3
Step 2: Multiply 5 by 10/4: 5 * 10/4 = 12.5 (or 25/2)
Step 3: Add 3 and 12.5: 3 + 12.5 = 15.5 (or 31/2)
Therefore, the simplified expression is 15.5 (or 31/2).
iv)
To simplify 2 + 2 + 1/2 + 1/2 + 3:
Step 1: Add 2 and 2: 2 + 2 = 4
Step 2: Add 1/2 and 1/2: 1/2 + 1/2 = 1
Step 3: Add 4, 1, and 3: 4 + 1 + 3 = 8
Therefore, the simplified expression is 8.
These are the simplified forms for the provided expressions.