Math Problem Statement

5/39.(39/5.5/3+25/3.39/5)+(-30/7.7/11+7/11.16/3).5-17/3-(268/15-24/7)-(42/15-4)-(145/69.36/29):5/23+25.0,375.(-10).1

Solution

Let's break down and solve the expression step by step:

Given expression: 539(39553+253395)+(307711+711163)5173(26815247)(42154)(145693629)÷523+250.375(10)1\frac{5}{39} \cdot \left(\frac{39}{5} \cdot \frac{5}{3} + \frac{25}{3} \cdot \frac{39}{5}\right) + \left(-\frac{30}{7} \cdot \frac{7}{11} + \frac{7}{11} \cdot \frac{16}{3}\right) \cdot 5 - \frac{17}{3} - \left(\frac{268}{15} - \frac{24}{7}\right) - \left(\frac{42}{15} - 4\right) - \left(\frac{145}{69} \cdot \frac{36}{29}\right) \div \frac{5}{23} + 25 \cdot 0.375 \cdot (-10) \cdot 1

Now, let's simplify the expression in parts:

  1. First part: 539(39553+253395)\frac{5}{39} \cdot \left(\frac{39}{5} \cdot \frac{5}{3} + \frac{25}{3} \cdot \frac{39}{5}\right)

First, simplify inside the brackets: 39553=19515=13\frac{39}{5} \cdot \frac{5}{3} = \frac{195}{15} = 13 253395=97515=65\frac{25}{3} \cdot \frac{39}{5} = \frac{975}{15} = 65 Adding them: 13+65=7813 + 65 = 78 Now, multiply by 539\frac{5}{39}: 53978=39039=10\frac{5}{39} \cdot 78 = \frac{390}{39} = 10

  1. Second part: (307711+711163)5\left(-\frac{30}{7} \cdot \frac{7}{11} + \frac{7}{11} \cdot \frac{16}{3}\right) \cdot 5

First, simplify inside the brackets: 307711=21077=3011-\frac{30}{7} \cdot \frac{7}{11} = -\frac{210}{77} = -\frac{30}{11} 711163=11233\frac{7}{11} \cdot \frac{16}{3} = \frac{112}{33} Adding them: 3011+11233=9033+11233=2233=23-\frac{30}{11} + \frac{112}{33} = -\frac{90}{33} + \frac{112}{33} = \frac{22}{33} = \frac{2}{3} Now, multiply by 5: 235=103\frac{2}{3} \cdot 5 = \frac{10}{3}

  1. Third part: 173\frac{17}{3}

  2. Fourth part: (26815247)\left(\frac{268}{15} - \frac{24}{7}\right)

First, find a common denominator and subtract: 26872415105=1876360105=1516105\frac{268 \cdot 7 - 24 \cdot 15}{105} = \frac{1876 - 360}{105} = \frac{1516}{105}

  1. Fifth part: (42154)\left(\frac{42}{15} - 4\right)

Simplify by finding a common denominator: 426015=1815=65\frac{42 - 60}{15} = -\frac{18}{15} = -\frac{6}{5}

  1. Sixth part: (145693629)÷523\left(\frac{145}{69} \cdot \frac{36}{29}\right) \div \frac{5}{23}

First, multiply the fractions: 145366929=52202001\frac{145 \cdot 36}{69 \cdot 29} = \frac{5220}{2001} Then, divide: 52202001÷523=52202320015=12006010005=12\frac{5220}{2001} \div \frac{5}{23} = \frac{5220 \cdot 23}{2001 \cdot 5} = \frac{120060}{10005} = 12

  1. Seventh part: 250.375(10)1=25(3.75)=93.7525 \cdot 0.375 \cdot (-10) \cdot 1 = 25 \cdot (-3.75) = -93.75

Finally, combine all the parts: 10+1031731516105651293.7510 + \frac{10}{3} - \frac{17}{3} - \frac{1516}{105} - \frac{6}{5} - 12 - 93.75

Let's compute the final result.The final result of the given expression is approximately 113.72-113.72.

Would you like further details or have any other questions?

Here are some related questions you might find interesting:

  1. How do you simplify complex fractions?
  2. What is the importance of order of operations in evaluating expressions?
  3. How do you convert fractions to decimals?
  4. Can you explain how to find a common denominator?
  5. What are the steps for multiplying and dividing fractions?
  6. How does distribution work with fractions and mixed numbers?
  7. What is the difference between proper fractions, improper fractions, and mixed numbers?
  8. How can negative numbers impact the result in complex expressions?

Tip: Always carefully manage the sign of numbers, especially in complex expressions, to avoid calculation errors.

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Math Problem Analysis

Mathematical Concepts

Fractions
Arithmetic Operations

Formulas

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Theorems

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Suitable Grade Level

Advanced Mathematics