Evaluate 1?(15×23)+(5+23)

Question 1 Report

Evaluate $1 - (\frac{1}{5} \times \frac{2}{3}) + (5 + \frac{2}{3})$

2 \frac{2}{3}

3 \frac{2}{3}

Answer Details

To evaluate the given expression step-by-step, let's break it down:

$1 - \left( \frac{1}{5} \times \frac{2}{3} \right) + \left( \frac{5 + \frac{2}{3}}{4} \right)^3$

Step 1: Evaluate $\frac{1}{5} \times \frac{2}{3}$

$\frac{1}{5} \times \frac{2}{3} = \frac{1 \times 2}{5 \times 3} = \frac{2}{15}$

Step 2: Subtract $\frac{2}{15}$ from 1

$1 - \frac{2}{15} = \frac{15}{15} - \frac{2}{15} = \frac{13}{15}$

Step 3: Simplify

$\frac{5 + \frac{2}{3}}{4}$

First, convert $5$ to a fraction with a denominator of 3:

$5 = \frac{15}{3}$

So,

$5 + \frac{2}{3} = \frac{15}{3} + \frac{2}{3} = \frac{17}{3}$

Then divide by 4:

$\frac{17}{3} \div 4 = \frac{17}{3} \times \frac{1}{4} = \frac{17}{12}$

Step 4: Cube $\frac{17}{12}$

$\left( \frac{17}{12} \right)^3 = \frac{17^3}{12^3} = \frac{4913}{1728}$

Step 5: Combine the results

$\frac{13}{15} + \frac{4913}{1728}$

To combine these fractions, find a common denominator. The least common multiple of 15 and 1728 is 1728 (since 15 is a factor of 1728):

Convert $\frac{13}{15}$ to a fraction with a denominator of 1728:

$\frac{13}{15} = \frac{13 \times 115.2}{15 \times 115.2} = \frac{1497.6}{1728}$

Now add the fractions:

$\frac{1497.6}{1728} + \frac{4913}{1728} = \frac{1497.6 + 4913}{1728} = \frac{6410.6}{1728}$

Simplifying the fraction is a bit complex and since none of the provided options directly match our detailed calculation, it looks like we might need to revisit some steps or compare our answer directly to the provided options to see if any approximation matches closely.

Given the complexity, let's directly compare the options:

Considering the given options, the closest approximate value

we calculated is around $\frac{6410.6}{1728}$ which seems close to $3.7$ .