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Evaluate the following expression:

[tex]\[ \left[\frac{(3.2-1.7)+0.003}{\left(\frac{29}{35}-\frac{3}{7}\right) \times 4+0.2}-\frac{\left(\frac{33}{20}-1.5\right) \times 1.5}{\left(2.44+\frac{39}{25}\right) \times \frac{1}{8}}\right]+62 \frac{1}{20}+1.364+0.124 \][/tex]

Sagot :

GinnyAnswer
Sure, I will walk you through the solution step-by-step:

### Step 1: Simplify the first part of the numerator
The numerator of the first fraction is:
[tex]\[ (3.2 - 1.7) + 0.003 \][/tex]

Calculations:
[tex]\[ 3.2 - 1.7 = 1.5 \][/tex]
[tex]\[ 1.5 + 0.003 = 1.503 \][/tex]

So, the numerator is:
[tex]\[ 1.503 \][/tex]

### Step 2: Simplify the first part of the denominator
The denominator of the first fraction is:
[tex]\[ \left(\frac{29}{35} - \frac{3}{7}\right) \times 4 + 0.2 \][/tex]

First, convert the fractions to a common base:
[tex]\[ \frac{3}{7} = \frac{15}{35} \][/tex]

Now compute the difference:
[tex]\[ \frac{29}{35} - \frac{15}{35} = \frac{14}{35} = \frac{2}{5} \][/tex]

Multiply by 4:
[tex]\[ \frac{2}{5} \times 4 = \frac{8}{5} = 1.6 \][/tex]

Add 0.2:
[tex]\[ 1.6 + 0.2 = 1.8 \][/tex]

So, the denominator is:
[tex]\[ 1.8 \][/tex]

### Step 3: Compute the first fraction
Now, compute the value of the first fraction:
[tex]\[ \frac{(3.2 - 1.7) + 0.003}{\left(\frac{29}{35} - \frac{3}{7}\right) \times 4 + 0.2} = \frac{1.503}{1.8} = 0.835 \][/tex]

### Step 4: Simplify the second part of the numerator
The numerator of the second fraction is:
[tex]\[ \left(\frac{33}{20} - 1.5\right) \times 1.5 \][/tex]

Convert 1.5 to a fraction with a common base:
[tex]\[ 1.5 = \frac{30}{20} \][/tex]

Compute the difference:
[tex]\[ \frac{33}{20} - \frac{30}{20} = \frac{3}{20} \][/tex]

Multiply by 1.5:
[tex]\[ \frac{3}{20} \times 1.5 = \frac{3}{20} \times \frac{3}{2} = \frac{9}{40} = 0.225 \][/tex]

So, the numerator is:
[tex]\[ 0.225 \][/tex]

### Step 5: Simplify the second part of the denominator
The denominator of the second fraction is:
[tex]\[ \left(2.44 + \frac{39}{25}\right) \times \frac{1}{8} \][/tex]

Convert 2.44 to a fraction with a common base:
[tex]\[ 2.44 = \frac{244}{100} = 2.44 \][/tex]

Convert 39/25:
[tex]\[ \frac{39}{25} = 1.56 \][/tex]

Add the numbers:
[tex]\[ 2.44 + 1.56 = 4 \][/tex]

Multiply by [tex]\(\frac{1}{8}\)[/tex]:
[tex]\[ 4 \times \frac{1}{8} = 0.5 \][/tex]

So, the denominator is:
[tex]\[ 0.5 \][/tex]

### Step 6: Compute the second fraction
Now, compute the value of the second fraction:
[tex]\[ \frac{\left(\frac{33}{20} - 1.5\right) \times 1.5}{\left(2.44 + \frac{39}{25}\right) \times \frac{1}{8}} = \frac{0.225}{0.5} = 0.45 \][/tex]

### Step 7: Subtract the two fractions
Now, subtract the second fraction from the first fraction:
[tex]\[ 0.835 - 0.45 = 0.385 \][/tex]

### Step 8: Add the constant values
Add the constants to the result:
[tex]\[ 62 + \frac{1}{20} + 1.364 + 0.124 \][/tex]

Convert the fraction:
[tex]\[ \frac{1}{20} = 0.05 \][/tex]

Sum the constants:
[tex]\[ 62 + 0.05 + 1.364 + 0.124 = 63.538 \][/tex]

### Step 9: Compute the final result
Add the result from Step 7 to the computed constants:
[tex]\[ 0.385 + 63.538 = 63.923 \][/tex]

Therefore, the final result is:
[tex]\[ 63.923 \][/tex]
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