Answer :

GinnyAnswer
Sure, let's solve the given expression step-by-step.

The given expression is:

[tex]\[ 1\frac{1}{2} \div \left( 3\frac{1}{3} + 4\frac{1}{5} - 6\frac{1}{2} \right) \][/tex]

First, convert all the mixed fractions to improper fractions.

1. Convert \(1\frac{1}{2}\):
[tex]\[ 1 \frac{1}{2} = \frac{3}{2} = 1.5 \][/tex]

2. Convert \(3\frac{1}{3}\):
[tex]\[ 3 \frac{1}{3} = \frac{10}{3} \approx 3.3333333333333335 \][/tex]

3. Convert \(4\frac{1}{5}\):
[tex]\[ 4 \frac{1}{5} = \frac{21}{5} = 4.2 \][/tex]

4. Convert \(6\frac{1}{2}\):
[tex]\[ 6 \frac{1}{2} = \frac{13}{2} = 6.5 \][/tex]

Now, substitute these values into the expression inside the parentheses:

[tex]\[ 3\frac{1}{3} + 4\frac{1}{5} - 6\frac{1}{2} \approx 3.3333333333333335 + 4.2 - 6.5 \][/tex]

Calculate the sum and the difference inside the parentheses:

[tex]\[ 3.3333333333333335 + 4.2 - 6.5 \approx 1.0333333333333332\ ] Now the expression becomes: \[ 1\frac{1}{2} \div 1.0333333333333332 \][/tex]

Finally, perform the division:

[tex]\[ 1.5 \div 1.0333333333333332 \approx 1.4516129032258067 \][/tex]

So, the value of the given expression is:

[tex]\[ \boxed{1.4516129032258067} \][/tex]

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