Math Problem Statement

(2/3-1/3*7/2)+1/2(-2/3)+1/3:2/5

Solution

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

(2313×72)+12×(23)+13÷25\left(\frac{2}{3} - \frac{1}{3} \times \frac{7}{2}\right) + \frac{1}{2} \times \left(-\frac{2}{3}\right) + \frac{1}{3} \div \frac{2}{5}

Step 1: Simplify 2313×72\frac{2}{3} - \frac{1}{3} \times \frac{7}{2}

First, calculate the multiplication:

13×72=76\frac{1}{3} \times \frac{7}{2} = \frac{7}{6}

Now subtract:

2376=4676=36=12\frac{2}{3} - \frac{7}{6} = \frac{4}{6} - \frac{7}{6} = \frac{-3}{6} = -\frac{1}{2}

Step 2: Simplify 12×(23)\frac{1}{2} \times \left(-\frac{2}{3}\right)

12×(23)=13\frac{1}{2} \times \left(-\frac{2}{3}\right) = -\frac{1}{3}

Step 3: Simplify 13÷25\frac{1}{3} \div \frac{2}{5}

Dividing by a fraction is the same as multiplying by its reciprocal:

13÷25=13×52=56\frac{1}{3} \div \frac{2}{5} = \frac{1}{3} \times \frac{5}{2} = \frac{5}{6}

Step 4: Combine all parts

Now we add up the simplified results from each step:

12+(13)+56-\frac{1}{2} + \left(-\frac{1}{3}\right) + \frac{5}{6}

To add these fractions, convert them to have a common denominator (6):

12=36,13=26,56=56-\frac{1}{2} = -\frac{3}{6}, \quad -\frac{1}{3} = -\frac{2}{6}, \quad \frac{5}{6} = \frac{5}{6}

Now add:

36+(26)+56=32+56=06=0-\frac{3}{6} + \left(-\frac{2}{6}\right) + \frac{5}{6} = \frac{-3 - 2 + 5}{6} = \frac{0}{6} = 0

Final Answer:

The value of the expression is 00.

Would you like more details on any step?

Here are 5 questions to explore further:

  1. What is the general process for simplifying expressions with fractions?
  2. How do you handle multiplication and division of fractions?
  3. Why is it important to find a common denominator when adding or subtracting fractions?
  4. How do you convert a division of fractions into a multiplication?
  5. How can mixed numbers be simplified in more complex expressions?

Tip: When working with multiple fractions in an expression, always perform the operations in the correct order (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

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Math Problem Analysis

Mathematical Concepts

Fractions
Order of Operations
Addition and Subtraction of Fractions
Multiplication and Division of Fractions

Formulas

Multiplication of fractions: (a/b) * (c/d) = (a*c)/(b*d)
Division of fractions: (a/b) ÷ (c/d) = (a/b) * (d/c)
Addition and subtraction of fractions: Convert to a common denominator and then add/subtract numerators

Theorems

PEMDAS (Order of Operations)

Suitable Grade Level

Grades 6-8