To simplify the expression (3/5 + 1 1/2) ÷ 1/4 × 3 1/3, we need to follow the order of operations which is parentheses, then multiplication/division (from left to right), and finally addition/subtraction (from left to right).
First, let's simplify the expression inside the parentheses:
3/5 + 1 1/2
To add these fractions, we need a common denominator.
The denominators are 5 and 2, and the least common multiple is 10.
Therefore, we rewrite the fractions with the denominator of 10:
3/5 + 1 1/2 = 6/10 + 5/10
Now, we can add the fractions:
6/10 + 5/10 = 11/10
So, the expression inside the parentheses simplifies to 11/10.
Now, let's simplify the expression after the parentheses:
11/10 ÷ 1/4 × 3 1/3
To divide fractions, we multiply by the reciprocal of the divisor:
11/10 ÷ 1/4 = 11/10 × 4/1 = 44/10 = 22/5
Now we multiply by the mixed number 3 1/3:
22/5 × 3 1/3
To multiply a mixed number, we first convert it to an improper fraction:
3 1/3 = (3 × 3 + 1)/3 = 10/3
Now, we can multiply the fractions:
22/5 × 10/3 = (22 × 10)/(5 × 3) = 220/15
Finally, we can simplify the fraction:
220/15 = 44/3
Therefore, the simplified expression is 44/3.
(3/5 + 1 1/2)÷ 1/4 × 3 1/3)
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